1. Requirements Change Summary

Combined B.A./B.S. Requirements:

• For B.S. degree with either major, add HWRS 350 to list of lab science options. For B.S. degree with Math major: add ISTA 320, CHEE 270, HWRS 350 to list of Application course options.

Math Major Course Requirements and Emphases:

• No updates

Statistics & Data Science Major Course Requirements:

• Add DATA 201 and DATA 474 to list of required courses in the major. 

 

2. B.A./B.S. in Mathematics or Statistics & Data Science

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

Upon declaring a major in mathematics or statistics & data science, students must select a degree in which the major will appear.  We offer your choice of a Bachelor of Arts (B.A.) or Bachelor of Science (B.S.).  

These degrees have many common requirements, including minimum units, English composition, and many of the general education courses.  There are some differences, however.

Below, you can find the requirements specific to the two degrees. For requirements specific to each major, regardless of degree, see:

• Mathematics Major Requirements
• Statistics & Data Science Major Requirements

Our major checklists also provide a good overview of the requirements for the degree/major of your choice.

Comparing the B.A. and the B.S.

As far as the mathematics or statistics coursework is concerned, the B.A. and B.S. are identical. 

The requirements for the two degrees differ only in the following ways:

• Second language requirement (details below).
• Science/application course requirements (details below).

The B.A. in Mathematics or SDS

**Note: These requirements changed significantly in Spring 2022 to coincide with a new General Education program. If you entered the university in 2021 or earlier, see here for your B.A. degree requirements.**

• Language Requirement: Students must demonstrate fourth semester proficiency in a second language.
• The degree is not science-intensive. Students need to complete only the Exploring Perspectives: Natural Scientist course, as specified in the University General Education requirements.

The B.S. in Mathematics or SDS

**Note: These requirements changed significantly in Spring 2022 to coincide with a new General Education program. If you entered the university in 2021 or earlier, see here for your B.S. degree requirements.**

• Language Requirement: Students must demonstrate second semester proficiency in a second language.
• Laboratory Science Courses Requirement: The degree is science-intensive and requires two of the following laboratory science courses:
  • First-semester courses (no prerequisites other than mathematics): PHYS 141 , PHYS 161H, CHEM 151, CHEM 141 & (CHEM 143 or CHEM 145)^(*), CHEM 161 & CHEM 163^(*), CHEM 181, MCB 181R & MCB 181L^(*), PSIO 201, GEOS 251, HWRS 350
  • Courses that require one or more science prerequisites: PHYS 142, PHYS 241, PHYS 162H, PHYS 261H, CHEM 152, CHEM 142 & (CHEM 144 or CHEM 146)^(*), CHEM 162 & CHEM 164^(*), CHEM 182,ECOL 182R & ECOL 182L^(*), PSIO 202, GEOS 255, GEOS 302, GEOS 304, GEOS 308, GEOS 322

^(*) Lecture and lab must both be taken to constitute one lab science course.

• Application Courses Requirement: (This requirement applies only to the Math major, except the Mathematics Education emphasis. For SDS majors, this requirement has been replaced with an SQL/Data Management course.)  Students must complete at least three units of coursework that applies advanced mathematics to other academic fields. These courses must have a pre- or co-requisite of at least Calculus I (MATH 122B or higher). Up to 3 units of MATH 493 internship credit may apply to application course requirements. 

Note: B.S. students may satisfy both the Application Course Requirement and one of the Laboratory Science Courses by completing one of the Physics courses. 

Choose from the following:

Agric & Biosystems Eng	BE 201, BE 284, BE 428, BE 481A;
Agric & Resource Economics	AREC 304,   AREC 464,    AREC 479;
Astronomy	ASTR 250;
Atmospheric Sciences	ATMO 430, ATMO 436A, ATMO 469A, ATMO 469B;
Biochemistry	BIOC 462A, BIOC 462B,  BIOC 466
Biomedical Engineering	BME 214, BME 481B;
Civil Engineering	CE 214;
Chemical & Environmental Engr	CHEE 201,  CHEE 202,    CHEE 270, CHEE 297, CHEE 481A, CHEE 481B;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 404A, CHEM 480A, CHEM 480B, CHEM 481;
Computer Science	CSC 345, CSC 355, CSC 422, CSC 433, CSC 436, CSC 437,    CSC 444, CSC 445, CSC 453, CSC 460, CSC 477, CSC 483;
Computer Science UA South	CSCV 345;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447, ECOL 496N (ECOL 496N not offered recently);
Economics	ECON 332,ECON 361;
Engineering	ENGR 211C, ENGR 211E, ENGR 211P;
Environmental Science	ENVS 420, ENVS 470, ENVS 479;
Geography & Development	GEOG 463;
Geosciences	GEOS 322, GEOS 356, GEOS 419, GEOS 432, GEOS 434A, GEOS 440, GEOS 469, GEOS 479;
Hydrology and Water Resources	HWRS 349A,    HWRS 350, HWRS 421(HWRS 421 not offered recently), HWRS 431, HWRS 460A;
Information Sci, Tech & Arts	ISTA 320, ISTA 421, ISTA 450;
Molecular & Cellular Biology	MCB 480;
Materials Science & Engr	MSE 222, MSE 345, MSE 404, MSE 415;
Mathematics	MATH 493;
Optical Sciences	OPTI 201R, OPTI 303, OPTI 495B;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143*, PHYS 161H, PHYS 162H, PHYS 240, PHYS 241,PHYS 261H; *Note: PHYS 143 is only 2 units; 6 units are required.
Physiology	PSIO 303, PSIO 305, PSIO 472;
Planetary Sciences	PTYS 407;
Retailing & Consumer Science	RCSC 216;
Systems & Industrial Engr	SIE 250, SIE 265;
Wildlife & Fisheries Science	WFSC 444, WFSC 445;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

 
Double Degrees

Students pursuing a second major that has a degree title different from that of the first major are technically double degree students. Additional requirements may apply to double degree students that do not pertain to double major students (students with two majors that have exactly the same degree title). See an advisor for details. 

Mid-Career Writing Assessment (MCWA)

Every undergraduate degree program at the University of Arizona requires satisfaction of the MCWA. a grade of A or B in ENGL 102, ENGL 108 (for ESL students), or ENGL 109H (for qualified students) will satisfy the requirement. If you earn less than a B in your second-semester composition course, you have several options for completing the MCWA. You may:

• repeat your second-semester English course (with GRO, if eligible) and earn at least a B, or
• complete ENGL 307, 308, or 313 with a grade of at least D.

3. Math Major Course Requirements and Emphases

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Mathematics require a core of basic courses followed by additional courses specific to one of seven possible emphases:

• Applied Mathematics emphasis: This emphasis is for students who intend to enter the job market upon graduation, but may also be appropriate for students who plan to go on to graduate school in a field of science or engineering.
• Comprehensive emphasis: This emphasis prepares students for graduate study in mathematics, applied mathematics, or most other scientific fields.
• Probability and Statistics emphasis: This emphasis is for students considering a career as an actuary or statistician, as well as for students wanting to attend graduate school in statistics.
• Mathematics Education emphasis: This emphasis prepares students for teaching mathematics at the secondary school level with professional licensure from the Arizona Department of Education. The emphasis has three main components: a set of courses in mathematics, a set of courses in teaching and learning mathematics in secondary schools, and a set of courses in education from the College of Education
• Computer Science emphasis: This emphasis is for students interested in applications of computers to mathematical problems, including math majors who plan to attend graduate school in computer science.
• Economics or Business emphasis: This emphasis is for students with a particular interest in business applications of mathematics, especially those preparing for graduate school in economics or finance.
• Life Sciences emphasis: This emphasis is for students considering a career in medicine, as well as for students wanting to attend graduate school in the biological sciences.

Each emphasis requires at least 15 units of 400-level mathematics course work, and each emphasis, except Mathematics Education, requires the student to complete a minor outside the math department. Courses in minors must be distinct from those in the major.

The complete official requirements for each emphasis are given in the University Catalog in the form of an Academic Advisement Report (ADVIP). Below we cover the portion of the requirements specific to the mathematics major. It is important for students to consult with their academic advisor about their choice and order of courses, as well as which additional courses would strengthen their degree program.

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

Supporting Computer Science Requirement

All math and SDS majors are required to complete a computer programming course, regardless of the degree and emphasis selected. One of the following courses is recommended for most students: CSC 110, ISTA 130, ECE 175, or CHEE 205; other options may require additional prerequisites and/or a major or minor declared in another subject.

• CSC 110 — Introduction to Computer Programming I
• ISTA 130 — Computational Thinking and Doing
• ECE 175 — Computer Programming for Engineering Applications
• CHEE 205 — Introduction to MatLab and Python
• BME 225 — Introduction to Computer Programming for Biomedical Engineering
• CSC 120 — Introduction to Computer Programming II
• CSC 250 — Essential Computing for the Sciences
• GEOS 280 — Programming and Data Analysis in the Earth Sciences
• MIS 301 — Data Structures and Algorithms
• NSCS 311 — Scientific Programming using MatLab
• PHYS 305 — Computational Physics

Core Courses

All seven emphases for the B.A./B.S. require the following core courses, which should ideally be completed by the end of the sophomore year.

• MATH 122A AND MATH 122B ⁽¹⁾ or MATH 125 — Calculus I
• MATH 129 — Calculus II
• MATH 223 — Vector Calculus
• MATH 313 — Introduction to Linear Algebra ⁽²⁾ 
• MATH 323 — Formal Mathematical Reasoning and Writing ⁽³⁾
• MATH 355 — Analysis of Ordinary Differential Equations ⁽⁴⁾

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. 

⁽²⁾ MATH 313 replaces MATH 215, which is no longer offered.  Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾MATH 323 is a writing-emphasis course that is the foundation for many of the advanced courses taken by math majors. It is prerequisite for more theoretical 400-level courses in the major. Students who do not do well in MATH 323 should speak to an advisor about their choice of major/emphasis.  MATH 396L, the Wildcat Proofs Workshop, is a 1 unit supplemental instruction course intended to give students additional practice and guidance in learning proof writing techniques. The 396L course is required for students who earned a C or lower in MATH 313, the prerequisite to 323. Students who earn a D in 313 are required to either repeat 313 for a higher grade or take another course (MATH 243, 315, or CSC 245) before moving on to 323 + 396L. 

⁽⁴⁾MATH 355 is the differential equations course that all mathematics majors are expected to take. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticated approach to differential equations. MATH 254 is a differential equations course that is aimed at engineering and science majors. Students with an additional major in engineering or science may ask their math faculty advisors for permission to substitute MATH 254 course for MATH 355 if a scheduling issue arises. Keep in mind that MATH 254 is lower-division - students who take it may need extra upper-division units.

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Applied Mathematics emphasis

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following three sequences:
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. One course from the list: {MATH 413, MATH 424, MATH 443, MATH 445, MATH 447, MATH 454, MATH 456, MATH 464, MATH 475B, MATH 481, MATH 485} ^(*)
• One modeling course; choose either:
  • MATH 481 — Mathematical Modeling of Fluid Flow through and around Organs and Organisms   OR
  • MATH 485 — Mathematical Modeling ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list: MATH 412, MATH 413, MATH 424, MATH 454, MATH 456, MATH 464, MATH 468, MATH 475A, MATH 481, MATH 485, MATH 488.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^(*) The Math Department has discontinued MATH 475B. We will still offer MATH 475A going forward, and have approved the listed alternatives to MATH 475B. These options will not appear in older advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above if your advisement report does not include these options; we will make the adjustment for you.

^(**) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters). In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course.  

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Comprehensive emphasis

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

This emphasis covers the minimum requirements for admission to most graduate programs in mathematics or applied mathematics. We have separate information on selecting the appropriate emphasis and courses to prepare for various types of graduate programs.  Students selecting the comprehensive emphasis should consult with a Mathematics Department faculty advisor in choosing additional course work to ensure that they are prepared for the graduate school of their choice. A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 413— Linear Algebra
• MATH 424— Theory of Complex Variables
• MATH 425A— Real Analysis of One Variable
• MATH 425B— Real Analysis of Several Variables
• One of the following two pairs:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations

Students completing this emphasis are expected to be proficient in proof writing before beginning most of the 400-level courses above. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in proof-intensive 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Probability and Statistics emphasis

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis. The math major with probability and statistics emphasis differs from the Statistics and Data Science (SDS) major in that it gives more theoretical background. Students who wish to attend graduate school in statistics, economics, or another related field are advised to choose this option instead of (or in addition to) the SDS major. In association with the Graduate Interdisciplinary Program in Statistics & Data Science, we offer an Accelerated Master's Program in Statistics & Data Science. 

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• MATH 466— Theory of Statistics
• One of the following two courses:
  • MATH 468— Applied Stochastic Processes
  • MATH 413— Linear Algebra
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list: MATH 412, MATH 413, MATH 422, MATH 425B, MATH 454, MATH 456, MATH 462, MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Mathematics Education emphasis

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

This emphasis is for students preparing to teach mathematics at the secondary school level. The Education emphasis has two main components, a set of courses in mathematics, and a set of pedagogy courses. This emphasis does not require a minor. See the Secondary Math Education Program (SMEP) website for additional information.

Major requirements:

• Core Courses (see above)
• Courses in Mathematics:
  • MATH 315— Introduction to Number Theory and Modern Algebra
  • MATH 330— Topics in Geometry
  • MATH 361— Elements of Statistics Using Calculus
  • MATH 404— History of Mathematics
  • MATH 407— Synthesis of Mathematical Concepts
• Courses in Teaching and Learning Mathematics (Pedagogy):
  • MATH 205— Teaching Secondary Mathematics
  • EDP 301— Educational Psychology and Child and Adolescent Development 
  • SERP 400— Survey of Exceptional Students
  • TLS 416— An Introduction to Structured English Immersion^(*)
  • TLS 435— Content Area Literacy in a Multicultural School
  • MATH 406A— Curriculum and Assessment in Secondary School Mathematics
  • MATH 406B— Methods of Teaching Mathematics in Secondary Schools
  • MATH 494C— Student Teaching
• Constitution Requirement for Arizona State certification.
  • This requirement is fulfilled by completing one of the following: POL 210 or equivalent; a passing score on the Arizona and US Constitution exams. 
• GPA requirements:
  • GPA ≥ 2.5 in MATH 122A&B/125, 129, 223
  • Pedagogy GPA ≥ 2.5
  • Major GPA ≥ 2.0
  • Cumulative UA GPA ≥ 2.0

^(*) LCEV 408—  Methods of Teaching English to English Language Learners also fulfills this requirement but is not currently available to SMEP students through the College of Education.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

Computer Science emphasis

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

A minor in computer science is required with this emphasis.

Major requirements:

• Core Courses (see above)
• One of the following three sequences:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. One course from the list: {MATH 422, MATH 424, MATH 454, MATH 456, MATH 464, MATH 485, MATH 475B}^(*)
• Two of the following six courses:
  • MATH 413— Linear Algebra
  • MATH 443— Theory of Graphs and Networks
  • MATH 445— Introduction to Cryptography
  • MATH 446— Theory of Numbers
  • MATH 447— Combinatorial Mathematics
  • CSC 473— Automata, Grammars and Languages ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 401A, MATH 401B, MATH 402, MATH 412, MATH 413, MATH 415A, MATH 443, MATH 445, MATH 446, MATH 447, MATH 464, MATH 468, MATH 475A, MATH 485, or  CSC 473.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^{(*) The Math Department has discontinued MATH 475B. We will still offer MATH 475A going forward, and have approved the listed alternatives to MATH 475B. These options will not appear in older advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above if your advisement report does not include these options; we will make the adjustment for you.} 

^(**) Students minoring in Computer Science may not double-dip courses with their math major. Students with a double major in Computer Science and Mathematics may be able to double-dip additional courses between the two majors, within reasonable limits. It is important to consult with advisors from both majors when planning your coursework to avoid graduation delays.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Economics or Business emphasis

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

This emphasis requires either

• an Economics Minor, or
• a Business Administration Minor, or
• an Entrepreneurship Minor, or
• a Finance Minor, or
• a Marketing Minor, or
• a Sports Management Minor, or
• a Personal & Family Financial Planning Minor, or
• a Thematic Minor emphasizing courses from two or more disciplines/subject areas such as Economics, Business, and Finance, or
• a second major in the same degree in one of the above fields of study.

The minor should be chosen in consultation with an advisor.

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• Two of the following four courses:
  
  • MATH 413— Linear Algebra
  • MATH 425B— Real Analysis of Several Variables
  • MATH 462— Financial Math
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list: MATH 412, MATH 413, MATH 422,MATH 425B, MATH 432, MATH 454, MATH 456, MATH 462, MATH 466,  MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Life Sciences emphasis

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

A minor or major in the biological sciences is required for this emphasis. Possibilities include Astrobiology, Biochemistry, Bioinformatics (major only), Biology, Biosystems Engineering, Ecology & Evolutionary Biology, Environmental Science, Medicine Thematic, Molecular & Cellular Biology, Pharmaceutical Sciences, Physiology, Physiological and Medical Sciences, and Pre-Health Professions, or a thematic minor with a life sciences emphasis.  A second major in a life science area may also be used to fulfill the minor requirement.  Courses which may be of interest for your minor include: ECOL 320, ECOL 340, ECOL 426, ECOL 453, ECOL 480, ECOL 496J; 

MCB 315, MCB 410, MCB 411, MCB 422.

 

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• MATH 464— Theory of Probability
• One of the following two courses:
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• One of the following two courses:
  • MATH 454— Ordinary Differential Equations and Stability Theory
  • MATH 456— Applied Partial Differential Equations
• One modeling course; choose either:
  • MATH 481 — Mathematical Modeling of Fluid Flow through and around Organs and Organisms   OR
  • MATH 485 — Mathematical Modeling ^(*)

^(*) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters). In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course.  

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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4. Statistics & Data Science Major Course Requirements

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Statistics & Data Science require the same set of supporting and core coursework. A minor in any subject outside the math department is required with this major.

The information and requirements given here apply to the 2024–2025 catalog. For other catalog years, please consult the archive.

The Academic Advising Report (ADVIP) gives complete degree requirements:

• B.A. Statistics & Data Science
• B.S. Statistics & Data Science

Note: this program was brand new for Fall 2018. All SDS majors are expected to meet with an advisor in the Math Center at least once a semester.

Supporting Python Programming Course Requirement

All SDS majors are required to complete a computer programming course in Python, regardless of the degree selected. Enrollment in DATA 363 requires successful completion of a Python programming course, so students have programming background to help them pick up R and to ensure they are getting Python experience along the way. Choose one course:^(*)

• CSC 110— Introduction to Computer Programming I
• ISTA 130— Computational Thinking and Doing

^(*)Either CSC 110 or ISTA 130 is recommended for most students; CSC 120 or CSC 250 will also satisfy the requirement if available. As an alternative, qualified students may complete both ECE 175 AND BE 205 or both ECE 175 AND CHEE 205. Contact the Math Center if you need any of these alternative courses pulled into your advisement report.

Supporting Data Management/SQL Requirement

SDS graduates applying for jobs will find that SQL and Data Management skills are important. Enrollment in DATA 363 requires completion of or concurrent enrollment in a course that teaches SQL and Data Management. These skills will be helpful as students work on their projects in DATA 363. Take one course:

• ISTA 322— Data Engineering

Core Courses

• MATH 122A AND MATH 122B  ⁽¹⁾ or  MATH 125— Calculus I

• MATH 129— Calculus II

• DATA 201 — Foundations of Data Science^(*)

• MATH 223— Vector Calculus

• MATH 313— Introduction to Linear Algebra ⁽²⁾ 

• DATA 363— Introduction to Statistical Methods ⁽³⁾

• DATA 375— Introduction to Statistical Computing

• MATH 464— Theory of Probability 

• MATH 466— Theory of Statistics

• DATA 467 — Applied Linear Models ⁽⁴⁾

• DATA 474— Introduction to Statistical Machine Learning

• DATA 498A — Capstone for Statistics and Data Science ⁽⁵⁾

• One upper-division statistics major elective.

^(*)DATA 201 is not yet in the course catalog (as of spring 2024), but has been approved as a Building Connections General Education course.

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. 

⁽²⁾ Either MATH 313 or MATH 310 may be used to fulfill this requirement in the SDS major. However, please note that 310 is no longer offered at UArizona. Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾ As of Fall 2024, the enrollment requirements for DATA 363 have changed. Students must complete MATH 129 and a Python course (CSC 110 or ISTA 130) prior to 363. In addition, MATH 313 and an SQL course (ISTA 322) must either be complete or in-progress in the same term as 363.

⁽⁴⁾ DATA 467 is offered in-person in fall semesters. Provided we have sufficient enrollment, we plan to offer it online each spring.

 ⁽⁵⁾ DATA 498A is currently primarily a spring course; as of 2024, we are attempting to offer it in fall semesters as well.

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Statistics & Data Science Major Elective Courses

The SDS major requires one upper-division elective course. The current courses that will be accepted toward this requirement are listed below. More course options may be added as the program grows; see your academic advisor for details.

Course options:

• DATA 367— Statistical Methods in Sports Analytics
• DATA 396T— Topics in Undergraduate Statistics & Data Science^(*)
• DATA 412 — Linear Algebra for Data Science
• DATA 462— Financial Math
• DATA 468— Applied Stochastic Processes
• DATA 496T— Advanced Topics in Undergraduate Statistics & Data Science^(*)
• DATA 498H— Honors Thesis^(**)
• SIE 440— Survey of Optimization Methods

 

 

1. Requirements Change Summary

Combined B.A./B.S. Requirements:

• For B.S. degree with SDS major only, the Application course requirement has been removed (it is replaced with a new SQL/Data Management requirement - see SDS Major for details). For B.S. degree with math major, CSC 355 has been added as an Application course. For B.S. degree with either major, lab science CHEM options have been updated to reflect current offerings.

Math Major Course Requirements and Emphases:

• BME 225 and GEOS 280 added to the list of acceptable alternative programming courses. Applied emphasis: added MATH 481 and 485 to list of 475B alternatives. Applied, Computer Science, Economics/Business, and Probability/Statistics emphases: added MATH 412 to pre-approved list for the 5th course. Life Science emphasis: medicine thematic minor (or 2nd major in medicine) added to list of minor options.

Statistics & Data Science Major Course Requirements:

• Data Management/SQL requirement added for all SDS majors. DATA 412 added to the list of DATA elective options.

2. B.A./B.S. in Mathematics or Statistics & Data Science

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

Upon declaring a major in mathematics or statistics & data science, students must select a degree in which the major will appear.  We offer your choice of a Bachelor of Arts (B.A.) or Bachelor of Science (B.S.).  

These degrees have many common requirements, including minimum units, English composition, and many of the general education courses.  There are some differences, however.

Below, you can find the requirements specific to the two degrees. For requirements specific to each major, regardless of degree, see:

• Mathematics Major Requirements
• Statistics & Data Science Major Requirements

Our major checklists also provide a good overview of the requirements for the degree/major of your choice.

Comparing the B.A. and the B.S.

As far as the mathematics or statistics coursework is concerned, the B.A. and B.S. are identical. 

The requirements for the two degrees differ only in the following ways:

• Second language requirement (details below).
• Science/application course requirements (details below).

The B.A. in Mathematics or SDS

**Note: These requirements changed significantly in Spring 2022 to coincide with a new General Education program. If you entered the university in 2021 or earlier, see here for your B.A. degree requirements.**

• Language Requirement: Students must demonstrate fourth semester proficiency in a second language.
• The degree is not science-intensive. Students need to complete only the Exploring Perspectives: Natural Scientist course, as specified in the University General Education requirements.

The B.S. in Mathematics or SDS

**Note: These requirements changed significantly in Spring 2022 to coincide with a new General Education program. If you entered the university in 2021 or earlier, see here for your B.S. degree requirements.**

• Language Requirement: Students must demonstrate second semester proficiency in a second language.
• Laboratory Science Courses Requirement: The degree is science-intensive and requires two of the following laboratory science courses:
  • First-semester courses (no prerequisites other than mathematics): PHYS 141 , PHYS 161H, CHEM 151, CHEM 141 & (CHEM 143 or CHEM 145)^(*), CHEM 161 & CHEM 163^(*), CHEM 181, MCB 181R & MCB 181L^(*), PSIO 201, GEOS 251
  • Courses that require one or more science prerequisites: PHYS 142, PHYS 241, PHYS 162H, PHYS 261H, CHEM 152, CHEM 142 & (CHEM 144 or CHEM 146)^(*), CHEM 162 & CHEM 164^(*), CHEM 182 (not in catalog yet),ECOL 182R & ECOL 182L^(*), PSIO 202, GEOS 255, GEOS 302, GEOS 304, GEOS 308, GEOS 322

^(*) Lecture and lab must both be taken to constitute one lab science course.

• Application Courses Requirement: (This requirement applies only to the Math major, except the Mathematics Education emphasis. For SDS majors, this requirement has been replaced with an SQL/Data Management course.)  Students must complete at least three units of coursework that applies advanced mathematics to other academic fields. These courses must have a pre- or co-requisite of at least Calculus I (MATH 122B or higher). Up to 3 units of MATH 493 internship credit may apply to application course requirements. 

Note: B.S. students may satisfy both the Application Course Requirement and one of the Laboratory Science Courses by completing one of the Physics courses. 

Choose from the following:

Agric & Biosystems Eng	BE 201, BE 284, BE 428, BE 481A;
Agric & Resource Economics	AREC 304,   AREC 464,    AREC 479;
Astronomy	ASTR 250;
Atmospheric Sciences	ATMO 430, ATMO 436A, ATMO 469A, ATMO 469B;
Biochemistry	BIOC 462A, BIOC 462B,  BIOC 466
Biomedical Engineering	BME 214, BME 481B;
Civil Engineering	CE 214;
Chemical & Environmental Engr	CHEE 201,  CHEE 202, CHEE 297, CHEE 481A, CHEE 481B;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 404A, CHEM 480A, CHEM 480B, CHEM 481;
Computer Science	CSC 345, CSC 355, CSC 422, CSC 433, CSC 436, CSC 437,    CSC 444, CSC 445, CSC 453, CSC 460, CSC 477, CSC 483;
Computer Science UA South	CSCV 345;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447, ECOL 496N (ECOL 496N not offered recently);
Economics	ECON 332,ECON 361;
Engineering	ENGR 211C, ENGR 211E, ENGR 211P;
Environmental Science	ENVS 420, ENVS 470, ENVS 479;
Geography & Development	GEOG 463;
Geosciences	GEOS 322, GEOS 356, GEOS 419, GEOS 432, GEOS 434A, GEOS 440, GEOS 469, GEOS 479;
Hydrology and Water Resources	HWRS 349A, HWRS 421(HWRS 421 not offered recently), HWRS 431, HWRS 460A;
Information Sci, Tech & Arts	ISTA 421, ISTA 450;
Molecular & Cellular Biology	MCB 480;
Materials Science & Engr	MSE 222, MSE 345, MSE 404, MSE 415;
Mathematics	MATH 493;
Optical Sciences	OPTI 201R, OPTI 303, OPTI 495B;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143*, PHYS 161H, PHYS 162H, PHYS 240, PHYS 241,PHYS 261H; *Note: PHYS 143 is only 2 units; 6 units are required.
Physiology	PSIO 303, PSIO 305, PSIO 472;
Planetary Sciences	PTYS 407;
Retailing & Consumer Science	RCSC 216;
Systems & Industrial Engr	SIE 250, SIE 265;
Wildlife & Fisheries Science	WFSC 444, WFSC 445;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

 
Double Degrees

Students pursuing a second major that has a degree title different from that of the first major are technically double degree students. Additional requirements may apply to double degree students that do not pertain to double major students (students with two majors that have exactly the same degree title). See an advisor for details. 

Mid-Career Writing Assessment (MCWA)

Every undergraduate degree program at the University of Arizona requires satisfaction of the MCWA. a grade of A or B in ENGL 102, ENGL 108 (for ESL students), or ENGL 109H (for qualified students) will satisfy the requirement. If you earn less than a B in your second-semester composition course, you have several options for completing the MCWA. You may:

• repeat your second-semester English course (with GRO, if eligible) and earn at least a B, or
• complete ENGL 307, 308, or 313 with a grade of at least D.

3. Math Major Course Requirements and Emphases

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Mathematics require a core of basic courses followed by additional courses specific to one of seven possible emphases:

• Applied Mathematics emphasis: This emphasis is for students who intend to enter the job market upon graduation, but may also be appropriate for students who plan to go on to graduate school in a field of science or engineering.
• Comprehensive emphasis: This emphasis prepares students for graduate study in mathematics, applied mathematics, or most other scientific fields.
• Probability and Statistics emphasis: This emphasis is for students considering a career as an actuary or statistician, as well as for students wanting to attend graduate school in statistics.
• Mathematics Education emphasis: This emphasis prepares students for teaching mathematics at the secondary school level. The emphasis has two main components: a set of courses in mathematics, and a set of courses in teaching and learning mathematics in secondary schools.
• Computer Science emphasis: This emphasis is for students interested in applications of computers to mathematical problems, including math majors who plan to attend graduate school in computer science.
• Economics or Business emphasis: This emphasis is for students with a particular interest in business applications of mathematics, especially those preparing for graduate school in economics or finance.
• Life Sciences emphasis: This emphasis is for students considering a career in medicine, as well as for students wanting to attend graduate school in the biological sciences.

Each emphasis requires at least 15 units of 400-level mathematics course work, and each emphasis, except Mathematics Education, requires the student to complete a minor outside the math department. Courses in minors must be distinct from those in the major.

The complete official requirements for each emphasis are given in the University Catalog in the form of an Academic Advisement Report (ADVIP). Below we cover the portion of the requirements specific to the mathematics major. It is important for students to consult with their academic advisor about their choice and order of courses, as well as which additional courses would strengthen their degree program.

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

Supporting Computer Science Requirement

All math and SDS majors are required to complete a computer programming course, regardless of the degree and emphasis selected. One of the following courses is recommended for most students: CSC 110, ISTA 130, ECE 175, or CHEE 205; other options may require additional prerequisites and/or a major or minor declared in another subject.

• CSC 110 — Introduction to Computer Programming I
• ISTA 130 — Computational Thinking and Doing
• ECE 175 — Computer Programming for Engineering Applications
• CHEE 205 — Introduction to MatLab and Python
• BME 225 — Introduction to Computer Programming for Biomedical Engineering
• CSC 120 — Introduction to Computer Programming II
• CSC 250 — Essential Computing for the Sciences
• GEOS 280 — Programming and Data Analysis in the Earth Sciences
• MIS 301 — Data Structures and Algorithms
• NSCS 311 — Scientific Programming using MatLab
• PHYS 305 — Computational Physics

Core Courses

All seven emphases for the B.A./B.S. require the following core courses, which should ideally be completed by the end of the sophomore year.

• MATH 122A AND MATH 122B ⁽¹⁾ or MATH 125 — Calculus I
• MATH 129 — Calculus II
• MATH 223 — Vector Calculus
• MATH 313 — Introduction to Linear Algebra ⁽²⁾ 
• MATH 323 — Formal Mathematical Reasoning and Writing ⁽³⁾
• MATH 355 — Analysis of Ordinary Differential Equations ⁽⁴⁾

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. 

⁽²⁾ MATH 313 replaces MATH 215, which is no longer offered.  Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾MATH 323 is a writing-emphasis course that is the foundation for many of the advanced courses taken by math majors. It is prerequisite for more theoretical 400-level courses in the major. Students who do not do well in MATH 323 should speak to an advisor about their choice of major/emphasis.  MATH 396L, the Wildcat Proofs Workshop, is a 1 unit supplemental instruction course intended to give students additional practice and guidance in learning proof writing techniques. The 396L course is required for students who earned a C or lower in MATH 313, the prerequisite to 323. Students who earn a D in 313 are required to either repeat 313 for a higher grade or take another course (MATH 243, 315, or CSC 245) before moving on to 323 + 396L. 

⁽⁴⁾MATH 355 is the differential equations course that all mathematics majors are expected to take. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticated approach to differential equations. MATH 254 is a differential equations course that is aimed at engineering and science majors. Students with an additional major in engineering or science may ask their math faculty advisors for permission to substitute MATH 254 course for MATH 355 if a scheduling issue arises. Keep in mind that MATH 254 is lower-division - students who take it may need extra upper-division units.

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Applied Mathematics emphasis

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following three sequences:
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. One course from the list: {MATH 413, MATH 424, MATH 443, MATH 445, MATH 447, MATH 454, MATH 456, MATH 464, MATH 475B, MATH 481, MATH 485} ^(*)
• One modeling course; choose either:
  • MATH 481 — Mathematical Modeling of Fluid Flow through and around Organs and Organisms   OR
  • MATH 485 — Mathematical Modeling ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list: MATH 412, MATH 413, MATH 424, MATH 454, MATH 456, MATH 464, MATH 468, MATH 475A, MATH 481, MATH 485, MATH 488.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^(*) The Math Department has discontinued MATH 475B. We will still offer MATH 475A going forward, and have approved the listed alternatives to MATH 475B. These options will not appear in older advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above if your advisement report does not include these options; we will make the adjustment for you.

^(**) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters). In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course.  

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Comprehensive emphasis

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

This emphasis covers the minimum requirements for admission to most graduate programs in mathematics or applied mathematics. We have separate information on selecting the appropriate emphasis and courses to prepare for various types of graduate programs.  Students selecting the comprehensive emphasis should consult with a Mathematics Department faculty advisor in choosing additional course work to ensure that they are prepared for the graduate school of their choice. A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 413— Linear Algebra
• MATH 424— Theory of Complex Variables
• MATH 425A— Real Analysis of One Variable
• MATH 425B— Real Analysis of Several Variables
• One of the following two pairs:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations

Students completing this emphasis are expected to be proficient in proof writing before beginning most of the 400-level courses above. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in proof-intensive 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Probability and Statistics emphasis

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis. The math major with probability and statistics emphasis differs from the Statistics and Data Science (SDS) major in that it gives more theoretical background. Students who wish to attend graduate school in statistics, economics, or another related field are advised to choose this option instead of (or in addition to) the SDS major. In association with the Graduate Interdisciplinary Program in Statistics & Data Science, we offer an Accelerated Master's Program in Statistics & Data Science. 

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• MATH 466— Theory of Statistics
• One of the following two courses:
  • MATH 468— Applied Stochastic Processes
  • MATH 413— Linear Algebra
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list: MATH 412, MATH 413, MATH 422, MATH 425B, MATH 454, MATH 456, MATH 462, MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Mathematics Education emphasis

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

This emphasis is for students preparing to teach mathematics at the secondary school level. The Education emphasis has two main components, a set of courses in mathematics, and a set of pedagogy courses. This emphasis does not require a minor. See the Secondary Math Education Program (SMEP) website for additional information.

Major requirements:

• Core Courses (see above)
• Courses in Mathematics:
  • MATH 315— Introduction to Number Theory and Modern Algebra
  • MATH 330— Topics in Geometry
  • MATH 361— Elements of Statistics Using Calculus
  • MATH 404— History of Mathematics
  • MATH 407— Synthesis of Mathematical Concepts
• Courses in Teaching and Learning Mathematics (Pedagogy):
  • MATH 205— Teaching Secondary Mathematics
  • EDP 301— Educational Psychology and Child and Adolescent Development 
  • SERP 400— Survey of Exceptional Students
  • TLS 416— An Introduction to Structured English Immersion^(*)
  • TLS 435— Content Area Literacy in a Multicultural School
  • MATH 406A— Curriculum and Assessment in Secondary School Mathematics
  • MATH 406B— Methods of Teaching Mathematics in Secondary Schools
  • MATH 494C— Student Teaching
• Constitution Requirement for Arizona State certification.
  • This requirement is fulfilled by completing one of the following: POL 210 or equivalent; a passing score on the Arizona and US Constitution exams. 
• GPA requirements:
  • GPA ≥ 2.5 in MATH 122A&B/125, 129, 223
  • Pedagogy GPA ≥ 2.5
  • Major GPA ≥ 2.0
  • Cumulative UA GPA ≥ 2.0

^(*) LCEV 408—  Methods of Teaching English to English Language Learners also fulfills this requirement but is not currently available to SMEP students through the College of Education.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

Computer Science emphasis

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

A minor in computer science is required with this emphasis.

Major requirements:

• Core Courses (see above)
• One of the following three sequences:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. One course from the list: {MATH 422, MATH 424, MATH 454, MATH 456, MATH 464, MATH 485, MATH 475B}^(*)
• Two of the following six courses:
  • MATH 413— Linear Algebra
  • MATH 443— Theory of Graphs and Networks
  • MATH 445— Introduction to Cryptography
  • MATH 446— Theory of Numbers
  • MATH 447— Combinatorial Mathematics
  • CSC 473— Automata, Grammars and Languages ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 401A, MATH 401B, MATH 402, MATH 412, MATH 413, MATH 415A, MATH 443, MATH 445, MATH 446, MATH 447, MATH 464, MATH 468, MATH 475A, MATH 485, or  CSC 473.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^{(*) The Math Department has discontinued MATH 475B. We will still offer MATH 475A going forward, and have approved the listed alternatives to MATH 475B. These options will not appear in older advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above if your advisement report does not include these options; we will make the adjustment for you.} 

^(**) Students minoring in Computer Science may not double-dip courses with their math major. Students with a double major in Computer Science and Mathematics may be able to double-dip additional courses between the two majors, within reasonable limits. It is important to consult with advisors from both majors when planning your coursework to avoid graduation delays.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Economics or Business emphasis

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

This emphasis requires either

• an Economics Minor, or
• a Business Administration Minor, or
• an Entrepreneurship Minor, or
• a Finance Minor, or
• a Marketing Minor, or
• a Sports Management Minor, or
• a Personal & Family Financial Planning Minor, or
• a Thematic Minor emphasizing courses from two or more disciplines/subject areas such as Economics, Business, and Finance, or
• a second major in the same degree in one of the above fields of study.

The minor should be chosen in consultation with an advisor.

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• Two of the following four courses:
  
  • MATH 413— Linear Algebra
  • MATH 425B— Real Analysis of Several Variables
  • MATH 462— Financial Math
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list: MATH 412, MATH 413, MATH 422,MATH 425B, MATH 432, MATH 454, MATH 456, MATH 462, MATH 466,  MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Life Sciences emphasis

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

A minor or major in the biological sciences is required for this emphasis. Possibilities include Astrobiology, Biochemistry, Bioinformatics (major only), Biology, Biosystems Engineering, Ecology & Evolutionary Biology, Environmental Science, Medicine Thematic, Molecular & Cellular Biology, Pharmaceutical Sciences, Physiology, Physiological and Medical Sciences, and Pre-Health Professions, or a thematic minor with a life sciences emphasis.  A second major in a life science area may also be used to fulfill the minor requirement.  Courses which may be of interest for your minor include: ECOL 320, ECOL 340, ECOL 426, ECOL 453, ECOL 480, ECOL 496J; 

MCB 315, MCB 410, MCB 411, MCB 422.

 

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• MATH 464— Theory of Probability
• One of the following two courses:
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• One of the following two courses:
  • MATH 454— Ordinary Differential Equations and Stability Theory
  • MATH 456— Applied Partial Differential Equations
• One modeling course; choose either:
  • MATH 481 — Mathematical Modeling of Fluid Flow through and around Organs and Organisms   OR
  • MATH 485 — Mathematical Modeling ^(*)

^(*) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters). In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course.  

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

4. Statistics & Data Science Major Course Requirements

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Statistics & Data Science require the same set of supporting and core coursework. A minor in any subject outside the math department is required with this major.

The information and requirements given here apply to the 2023–2024 catalog. For other catalog years, please consult the archive.

The Academic Advising Report (ADVIP) gives complete degree requirements:

• B.A. Statistics & Data Science
• B.S. Statistics & Data Science

Note: this program was brand new for Fall 2018. All SDS majors are expected to meet with an advisor in the Math Center at least once a semester.

Supporting Python Programming Course Requirement

All SDS majors are required to complete a computer programming course in Python, regardless of the degree selected. Beginning in Spring 2023, enrollment in DATA 363 will require completion of a Python programming course, so students have programming background to help them pick up R and to ensure they are getting Python experience along the way. Choose one course:^(*)

• CSC 110— Introduction to Computer Programming I
• ISTA 130— Computational Thinking and Doing

^(*)Either CSC 110 or ISTA 130 is recommended for most students; CSC 120 or CSC 250 will also satisfy the requirement if available. As an alternative, qualified students may complete both ECE 175 AND BE 205.

Supporting Data Management/SQL Requirement

SDS graduates applying for jobs will find that SQL and Data Management skills are important. Beginning in Fall 2023, enrollment in DATA 363 will require completion or concurrent enrollment in a course that teaches SQL and Data Management. These skills will be helpful as students work on their projects in DATA 363. Take one course:

• ISTA 322— Data Engineering

Core Courses

• MATH 122A AND MATH 122B  ⁽¹⁾ or  MATH 125— Calculus I

• MATH 129— Calculus II

• MATH 223— Vector Calculus

• MATH 313— Introduction to Linear Algebra ⁽²⁾ 

• DATA 363— Introduction to Statistical Methods ⁽³⁾

• DATA 375— Introduction to Statistical Computing 

• MATH 464— Theory of Probability 

• MATH 466— Theory of Statistics

• DATA 467 — Applied Linear Models ⁽⁴⁾

• DATA 498A — Capstone for Statistics and Data Science ⁽⁵⁾

• One upper-division statistics major elective.

 

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. 

⁽²⁾ Either MATH 313 or MATH 310 may be used to fulfill this requirement in the SDS major. However, please note that 310 is no longer offered at UArizona. Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾ As of Fall 2024, the enrollment requirements for DATA 363 have changed. Students must complete MATH 129 and a Python course (CSC 110 or ISTA 130) prior to 363. In addition, MATH 313 and an SQL course (ISTA 322) must either be complete or in-progress in the same term as 363.

⁽⁴⁾ DATA 467 is offered in-person in fall semesters. Provided we have sufficient enrollment, we plan to offer it online each spring.

 ⁽⁵⁾ DATA 498A is currently primarily a spring course; as of 2024, we are attempting to offer it in fall semesters as well.

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Statistics & Data Science Major Elective Courses

The SDS major requires one upper-division elective course. The current courses that will be accepted toward this requirement are listed below. More course options may be added as the program grows; see your academic advisor for details.

Course options:

• DATA 367— Statistical Methods in Sports Analytics
• DATA 396T— Topics in Undergraduate Statistics & Data Science^(*)
• DATA 412 — Linear Algebra for Data Science
• DATA 462— Financial Math
• DATA 468— Applied Stochastic Processes
• DATA 496T— Advanced Topics in Undergraduate Statistics & Data Science^(*)
• DATA 498H— Honors Thesis^(**)
• SIE 440— Survey of Optimization Methods

 

 

1. Requirements Change Summary

Combined B.A./B.S. Requirements

A new Gen Ed program is in effect for students admitted in Spring 2022 and later. The following changes were made to mitigate impact on these students. For B.S. degree with either major: require two lab science courses, not necessarily sequence; require three units of application courses instead of six.

 

Math Major Course Requirements and Emphases

CHEE 205 added to the list of acceptable alternative programming courses. Applied emphasis: added MATH 481 and 485 to the pre-approved list for the 5th course.

 

Statistics & Data Science Major Course Requirements

Add recommended Data Management/SQL course. 

2. B.A./B.S. in Mathematics or Statistics & Data Science

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

Upon declaring a major in mathematics or statistics & data science, students must select a degree in which the major will appear.  We offer your choice of a Bachelor of Arts (B.A.) or Bachelor of Science (B.S.).  

These degrees have many common requirements, including minimum units, English composition, and many of the general education courses.  There are some differences, however.

Below, you can find the requirements specific to the two degrees. For requirements specific to each major, regardless of degree, see:

• Mathematics Major Requirements
• Statistics & Data Science Major Requirements

Our major checklists also provide a good overview of the requirements for the degree/major of your choice.

Comparing the B.A. and the B.S.

As far as the mathematics or statistics coursework is concerned, the B.A. and B.S. are identical. 

The requirements for the two degrees differ only in the following ways:

• Second language requirement (details below).
• Science/application course requirements (details below).

The B.A. in Mathematics or SDS

**Note: These requirements apply to students who entered the university in Spring 2022 or later! If you entered the university in 2021 or earlier, see here for your B.A. degree requirements.**

• Language Requirement: Students must demonstrate fourth semester proficiency in a second language.
• The degree is not science-intensive. Students need to complete only the Exploring Perspectives: Natural Scientist course, as specified in the University General Education requirements.

The B.S. in Mathematics or SDS

**Note: These requirements apply to students who entered the university in Spring 2022 or later! If you entered the university in 2021 or earlier, see here for your B.S. degree requirements.**

• Language Requirement: Students must demonstrate second semester proficiency in a second language.
• Laboratory Science Courses Requirement: The degree is science-intensive and requires two of the following laboratory science courses:
  • First-semester courses (no prerequisites other than mathematics): PHYS 141 , PHYS 161H, CHEM 151, CHEM 141 & CHEM 143^(*), CHEM 161 & CHEM 163^(*), MCB 181R & MCB 181L^(*), PSIO 201, GEOS 251
  • Courses that require one or more science prerequisites: PHYS 142, PHYS 241, PHYS 162H, PHYS 261H, CHEM 152, CHEM 142 & CHEM 144^(*), CHEM 162 & CHEM 164^(*), ECOL 182R & ECOL 182L^(*), PSIO 202, GEOS 255, GEOS 302, GEOS 304, GEOS 308, GEOS 322

^(*) Lecture and lab must both be taken to constitute one lab science course.

• Application Courses Requirement: (This requirement does not apply to the Mathematics Education emphasis.) Students must complete at least three units of coursework that applies advanced mathematics or statistics to other academic fields. There are separate lists of available courses for mathematics majors and statistics & data science majors. Up to 3 units of 493 internship credit under the appropriate prefix (MATH/DATA) may apply to application course requirements for Mathematics & SDS majors, respectively.

Note: B.S. students in either major may satisfy both the Application Course Requirement and one of the Laboratory Science Courses by completing one of the Physics courses. 

For mathematics majors, these courses must have a pre- or co-requisite of at least Calculus I (MATH 122B or higher). Choose from the following:

Agric & Biosystems Eng	BE 201, BE 284, BE 428, BE 481A;
Agric & Resource Economics	AREC 304,   AREC 464,    AREC 479;
Astronomy	ASTR 250;
Atmospheric Sciences	ATMO 430, ATMO 436A, ATMO 469A, ATMO 469B;
Biochemistry	BIOC 462A, BIOC 462B,  BIOC 466
Biomedical Engineering	BME 214, BME 481B;
Civil Engineering	CE 214;
Chemical & Environmental Engr	CHEE 201,  CHEE 202, CHEE 297, CHEE 481A, CHEE 481B;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 404A, CHEM 480A, CHEM 480B, CHEM 481;
Computer Science	CSC 345, CSC 422, CSC 433, CSC 436, CSC 437,    CSC 444, CSC 445, CSC 453, CSC 460, CSC 477, CSC 483;
Computer Science UA South	CSCV 345;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447, ECOL 496N (ECOL 496N not offered recently);
Economics	ECON 332,ECON 361;
Engineering	ENGR 211C, ENGR 211E, ENGR 211P;
Environmental Science	ENVS 420, ENVS 470, ENVS 479;
Geography & Development	GEOG 463;
Geosciences	GEOS 322, GEOS 356, GEOS 419, GEOS 432, GEOS 434A, GEOS 440, GEOS 469, GEOS 479;
Hydrology and Water Resources	HWRS 349A, HWRS 421(HWRS 421 not offered recently), HWRS 431, HWRS 460A;
Information Sci, Tech & Arts	ISTA 421, ISTA 450;
Molecular & Cellular Biology	MCB 480;
Materials Science & Engr	MSE 222, MSE 345, MSE 404, MSE 415;
Mathematics	MATH 493;
Optical Sciences	OPTI 201R, OPTI 303, OPTI 495B;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143*, PHYS 161H, PHYS 162H, PHYS 240, PHYS 241,PHYS 261H; *Note: PHYS 143 is only 2 units; 6 units are required.
Physiology	PSIO 303, PSIO 305, PSIO 472;
Planetary Sciences	PTYS 407;
Retailing & Consumer Science	RCSC 216;
Systems & Industrial Engr	SIE 250, SIE 265;
Wildlife & Fisheries Science	WFSC 444, WFSC 445;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

Statistics & data science majors may now use ISTA 322 to fulfill this requirement. Please email the Math Center if you have enrolled in ISTA 322 and need us to adjust your record. Historically, these application courses must have a pre- or co-requisite of a statistics course or at least Calculus I (MATH 122B or higher), but we are finding that SQL/Data Management skills are more important for our graduates.

Application courses: 

 

Agric & Biosystems Engineering	BE 201, BE 284, BE 423, BE 428, BE 485;
Animal & Comp Biomed Sciences	ACBS 313;
Aerospace & Mechanical Engr	AME 472
Astronomy	ASTR 250;
Biochemistry	BIOC 462A, BIOC 462B, BIOC 466;
Civil Engineering	CE 214, CE 310, CE 449;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 404A, CHEM 480A, CHEM 480B;
Computer Science	CSC 345, CSC 422, CSC 433, CSC 436, CSC 437, CSC 444, CSC 445, CSC 453, CSC 460, CSC 477, CSC 483, CSCV 345;
Statistics & Data Science	DATA 493;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447;
Economics	ECON 332, ECON 361;
Engineering	ENGR 211C;
Environmental Science	ENVS 420, ENVS 470;
Epidemiology	EPID 452, EPID 479;
Geosciences	GEOS 322, GEOS 356, GEOS 434A, GEOS 469, GEOS 479;
Information Sci, Tech & Arts	ISTA 321, ISTA 350, ISTA 421, ISTA 450;
Molecular & Cellular Biology	MCB 416A, MCB 480;
Materials Science & Engr	MSE 345, MSE 404;
Neuroscience & Cognitive Sci	NSCS 344;
Optical Sciences	OPTI 201R;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143*, PHYS 161H, PHYS 162H, PHYS 240, PHYS 241, PHYS 261H; *Note: PHYS 143 is only 2 units; 6 units are required.
Physiology	PSIO 303, PSIO 472;
Planetary Sciences	PTYS 407;
Range Management	RAM 456;
Renewable Natural Resources	RNR 321, RNR 417, RNR 473;
Systems & Industrial Engr	SIE 250, SIE 265, SIE 422, SIE 496;
Sociology	SOC 476;
Wildlife & Fisheries Science	WFSC 444, WFSC 445;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

Double Degrees

Students pursuing a second major that has a degree title different from that of the first major are technically double degree students. Additional requirements may apply to double degree students that do not pertain to double major students (students with two majors that have exactly the same degree title). See an advisor for details. 

Mid-Career Writing Assessment (MCWA)

Every undergraduate degree program at the University of Arizona requires satisfaction of the MCWA. a grade of A or B in ENGL 102, ENGL 108 (for ESL students), or ENGL 109H (for qualified students) will satisfy the requirement. If you earn less than a B in your second-semester composition course, you have several options for completing the MCWA. You may:

• repeat your second-semester English course (with GRO, if eligible) and earn at least a B, or
• complete ENGL 307, 308, or 313 with a grade of at least D.

3. Math Major Course Requirements and Emphases

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Mathematics require a core of basic courses followed by additional courses specific to one of seven possible emphases:

• Applied Mathematics emphasis: This emphasis is for students who intend to enter the job market upon graduation, but may also be appropriate for students who plan to go on to graduate school in a field of science or engineering.
• Comprehensive emphasis: This emphasis prepares students for graduate study in mathematics, applied mathematics, or most other scientific fields.
• Probability and Statistics emphasis: This emphasis is for students considering a career as an actuary or statistician, as well as for students wanting to attend graduate school in statistics.
• Mathematics Education emphasis: This emphasis prepares students for teaching mathematics at the secondary school level. The emphasis has two main components: a set of courses in mathematics, and a set of courses in teaching and learning mathematics in secondary schools.
• Computer Science emphasis: This emphasis is for students interested in applications of computers to mathematical problems, including math majors who plan to attend graduate school in computer science.
• Economics or Business emphasis: This emphasis is for students with a particular interest in business applications of mathematics, especially those preparing for graduate school in economics or finance.
• Life Sciences emphasis: This emphasis is for students considering a career in medicine, as well as for students wanting to attend graduate school in the biological sciences.

Each emphasis requires at least 15 units of 400-level mathematics course work, and each emphasis, except Mathematics Education, requires the student to complete a minor outside the math department. Courses in minors must be distinct from those in the major.

The complete official requirements for each emphasis are given in the University Catalog in the form of an Academic Advisement Report (ADVIP). Below we cover the portion of the requirements specific to the mathematics major. It is important for students to consult with their academic advisor about their choice and order of courses, as well as which additional courses would strengthen their degree program.

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

Supporting Computer Science Requirement

All math and SDS majors are required to complete a computer programming course, regardless of the degree and emphasis selected. One of the following courses is recommended for most students: CSC 110, ISTA 130, ECE 175, or CHEE 205; other options may require additional prerequisites and/or a major or minor declared in another subject.

• CSC 110 — Introduction to Computer Programming I
• ISTA 130 — Computational Thinking and Doing
• ECE 175 — Computer Programming for Engineering Applications
• CHEE 205 — Introduction to MatLab and Python
• CSC 120 — Introduction to Computer Programming II
• CSC 250 — Essential Computing for the Sciences
• MIS 301 — Data Structures and Algorithms
• NSCS 311 — Scientific Programming using MatLab
• PHYS 305 — Computational Physics

Core Courses

All seven emphases for the B.A./B.S. require the following core courses, which should ideally be completed by the end of the sophomore year.

• MATH 122A AND MATH 122B ⁽¹⁾ or MATH 125 — Calculus I
• MATH 129 — Calculus II
• MATH 223 — Vector Calculus
• MATH 313 — Introduction to Linear Algebra ⁽²⁾ 
• MATH 323 — Formal Mathematical Reasoning and Writing ⁽³⁾
• MATH 355 — Analysis of Ordinary Differential Equations ⁽⁴⁾

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. 

⁽²⁾ MATH 313 replaces MATH 215, which is no longer offered.  Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾MATH 323 is a writing-emphasis course that is the foundation for many of the advanced courses taken by math majors. It is prerequisite for more theoretical 400-level courses in the major. Students who do not do well in MATH 323 should speak to an advisor about their choice of major/emphasis.  MATH 396L, the Wildcat Proofs Workshop, is a 1 unit supplemental instruction course intended to give students additional practice and guidance in learning proof writing techniques. The 396L course is required for students who earned a C or lower in MATH 313, the prerequisite to 323. Students who earn a D in 313 are required to either repeat 313 for a higher grade or take another course (MATH 243, 315, or CSC 245) before moving on to 323 + 396L. 

⁽⁴⁾MATH 355 is the differential equations course that all mathematics majors are expected to take. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticated approach to differential equations. MATH 254 is a differential equations course that is aimed at engineering and science majors. Students with an additional major in engineering or science may ask their math faculty advisors for permission to substitute MATH 254 course for MATH 355 if a scheduling issue arises. Keep in mind that MATH 254 is lower-division - students who take it may need extra upper-division units.

---

Applied Mathematics emphasis

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following three sequences:
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. One course from the list: {MATH 413, MATH 424, MATH 443, MATH 445, MATH 447, MATH 454, MATH 456, MATH 464, MATH 475B} ^(*)
• One modeling course; choose either:
  • MATH 481 — Mathematical Modeling of Fluid Flow through and around Organs and Organisms   OR
  • MATH 485 — Mathematical Modeling ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 424, MATH 454, MATH 456, MATH 464, MATH 468, MATH 475A, MATH 481, MATH 485, MATH 488.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^(*) The Math Department has discontinued MATH 475B. We will still offer MATH 475A going forward, and have approved the listed alternatives to MATH 475B. These options will not appear in older advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above if your advisement report does not include these options; we will make the adjustment for you.

^(**) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters). In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course. MATH 481 (Mathematical Modeling of Fluid Flow through and around Organs and Organisms) may replace MATH 485. If your catalog requirements do not reflect this, please email mathcenter@math.arizona.edu if you enroll so we can adjust your record. The course will begin appearing in advisement reports for Fall 2021. 

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Comprehensive emphasis

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

This emphasis covers the minimum requirements for admission to most graduate programs in mathematics or applied mathematics. We have separate information on selecting the appropriate emphasis and courses to prepare for various types of graduate programs.  Students selecting the comprehensive emphasis should consult with a Mathematics Department faculty advisor in choosing additional course work to ensure that they are prepared for the graduate school of their choice. A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 413— Linear Algebra
• MATH 424— Theory of Complex Variables
• MATH 425A— Real Analysis of One Variable
• MATH 425B— Real Analysis of Several Variables
• One of the following two pairs:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations

Students completing this emphasis are expected to be proficient in proof writing before beginning most of the 400-level courses above. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in proof-intensive 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Probability and Statistics emphasis

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis. The math major with probability and statistics emphasis differs from the Statistics and Data Science (SDS) major in that it gives more theoretical background. Students who wish to attend graduate school in statistics, economics, or another related field are advised to choose this option instead of (or in addition to) the SDS major. In association with the Graduate Interdisciplinary Program in Statistics & Data Science, we offer an Accelerated Master's Program in Statistics & Data Science. 

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• MATH 466— Theory of Statistics
• One of the following two courses:
  • MATH 468— Applied Stochastic Processes
  • MATH 413— Linear Algebra
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 422, MATH 425B, MATH 454, MATH 456, MATH 462, MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Mathematics Education emphasis

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

This emphasis is for students preparing to teach mathematics at the secondary school level. The Education emphasis has two main components, a set of courses in mathematics, and a set of pedagogy courses. This emphasis does not require a minor. See the Secondary Math Education Program (SMEP) website for additional information.

Major requirements:

• Core Courses (see above)
• Courses in Mathematics:
  • MATH 315— Introduction to Number Theory and Modern Algebra
  • MATH 330— Topics in Geometry
  • MATH 361— Elements of Statistics Using Calculus
  • MATH 404— History of Mathematics
  • MATH 407— Synthesis of Mathematical Concepts
• Courses in Teaching and Learning Mathematics (Pedagogy):
  • MATH 205— Teaching Secondary Mathematics
  • EDP 301— Educational Psychology and Child and Adolescent Development 
  • SERP 400— Survey of Exceptional Students
  • TLS 416— An Introduction to Structured English Immersion^(*)
  • TLS 435— Content Area Literacy in a Multicultural School
  • MATH 406A— Curriculum and Assessment in Secondary School Mathematics
  • MATH 406B— Methods of Teaching Mathematics in Secondary Schools
  • MATH 494C— Student Teaching
• Constitution Requirement for Arizona State certification.
  • This requirement is fulfilled by completing one of the following: POL 210 or equivalent; a passing score on the Arizona and US Constitution exams. 
• GPA requirements:
  • GPA ≥ 2.5 in MATH 122A&B/125, 129, 223
  • Pedagogy GPA ≥ 2.5
  • Major GPA ≥ 2.0
  • Cumulative UA GPA ≥ 2.0

^(*) LCEV 408—  Methods of Teaching English to English Language Learners also fulfills this requirement but is not currently available to SMEP students through the College of Education.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

Computer Science emphasis

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

A minor in computer science is required with this emphasis.

Major requirements:

• Core Courses (see above)
• One of the following three sequences:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. One course from the list: {MATH 422, MATH 424, MATH 454, MATH 456, MATH 464, MATH 485, MATH 475B}^(*)
• Two of the following six courses:
  • MATH 413— Linear Algebra
  • MATH 443— Theory of Graphs and Networks
  • MATH 445— Introduction to Cryptography
  • MATH 446— Theory of Numbers
  • MATH 447— Combinatorial Mathematics
  • CSC 473— Automata, Grammars and Languages ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 401A, MATH 401B, MATH 402, MATH 413, MATH 415A, MATH 443, MATH 445, MATH 446, MATH 447, MATH 464, MATH 468, MATH 475A, MATH 485, or  CSC 473.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^{(*) The Math Department has discontinued MATH 475B. We will still offer MATH 475A going forward, and have approved the listed alternatives to MATH 475B. These options will not appear in older advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above if your advisement report does not include these options; we will make the adjustment for you.} 

^(**) Students minoring in Computer Science may not double-dip courses with their math major. Students with a double major in Computer Science and Mathematics may be able to double-dip additional courses between the two majors, within reasonable limits. It is important to consult with advisors from both majors when planning your coursework to avoid graduation delays.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Economics or Business emphasis

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

This emphasis requires either

• an Economics Minor, or
• a Business Administration Minor, or
• an Entrepreneurship Minor, or
• a Finance Minor, or
• a Marketing Minor, or
• a Sports Management Minor, or
• a Personal & Family Financial Planning Minor, or
• a Thematic Minor emphasizing courses from two or more disciplines/subject areas such as Economics, Business, and Finance, or
• a second major in the same degree in one of the above fields of study.

The minor should be chosen in consultation with an advisor.

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• Two of the following four courses:
  
  • MATH 413— Linear Algebra
  • MATH 425B— Real Analysis of Several Variables
  • MATH 462— Financial Math
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 422,MATH 425B, MATH 432, MATH 454, MATH 456, MATH 462, MATH 466,  MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Life Sciences emphasis

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

A minor or major in the biological sciences is required for this emphasis. Possibilities include Astrobiology, Biochemistry, Bioinformatics (major only), Biology, Biosystems Engineering, Ecology & Evolutionary Biology, Environmental Science, Molecular & Cellular Biology, Pharmaceutical Sciences, Physiology, Physiological and Medical Sciences, and Pre-Health Professions, or a thematic minor with a life sciences emphasis.  A second major in a life science area may also be used to fulfill the minor requirement.  Courses which may be of interest for your minor include: ECOL 320, ECOL 340, ECOL 426, ECOL 453, ECOL 480, ECOL 496J; 

MCB 315, MCB 410, MCB 411, MCB 422.

 

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• MATH 464— Theory of Probability
• One of the following two courses:
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• One of the following two courses:
  • MATH 454— Ordinary Differential Equations and Stability Theory
  • MATH 456— Applied Partial Differential Equations
• One modeling course; choose either:
  • MATH 481 — Mathematical Modeling of Fluid Flow through and around Organs and Organisms   OR
  • MATH 485 — Mathematical Modeling ^(*)

^(*) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters). In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course. MATH 481 (Mathematical Modeling of Fluid Flow through and around Organs and Organisms) may replace MATH 485. If your catalog requirements do not reflect this, please email mathcenter@math.arizona.edu if you enroll so we can adjust your record. The course will begin appearing in advisement reports for Fall 2021.  

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

4. Statistics & Data Science Major Course Requirements

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Statistics & Data Science require the same set of supporting and core coursework. A minor in any subject outside the math department is required with this major.

The information and requirements given here apply to the 2022–2023 catalog. For other catalog years, please consult the archive.

The Academic Advising Report (ADVIP) gives complete degree requirements:

• B.A. Statistics & Data Science
• B.S. Statistics & Data Science

Note: this program was brand new for Fall 2018. All SDS majors are expected to meet with an advisor in the Math Center at least once a semester.

Supporting Python Programming Course Requirement

All SDS majors are required to complete a computer programming course in Python, regardless of the degree selected. Beginning in Spring 2023, enrollment in DATA 363 will require completion of a Python programming course, so students have programming background to help them pick up R and to ensure they are getting Python experience along the way. Choose one course:^(*)

• CSC 110— Introduction to Computer Programming I
• ISTA 130— Computational Thinking and Doing

^(*)Either CSC 110 or ISTA 130 is recommended for most students; CSC 120 or CSC 250 will also satisfy the requirement if available. As an alternative, qualified students may complete both ECE 175 AND BE 205.

Supporting Data Management Course

SDS graduates applying for jobs will find that SQL and Data Management skills are important. Beginning in Fall 2023, enrollment in DATA 363 will require completion or concurrent enrollment in a course that teaches SQL and Data Management. These skills will be helpful as students work on their projects in DATA 363. Take one course:

• ISTA 322— Data Engineering

Core Courses

• MATH 122A AND MATH 122B  ⁽¹⁾ or  MATH 125— Calculus I

• MATH 129— Calculus II

• MATH 223— Vector Calculus

• MATH 313— Introduction to Linear Algebra ⁽²⁾ 

• DATA 363— Introduction to Statistical Methods ⁽³⁾

• DATA 375— Introduction to Statistical Computing 

• MATH 464— Theory of Probability 

• MATH 466— Theory of Statistics

• DATA 467 — Applied Linear Models ⁽⁴⁾

• DATA 498A — Capstone for Statistics and Data Science ⁽⁵⁾

• One upper-division statistics major elective.

 

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. 

⁽²⁾ Either MATH 313 or MATH 310 may be used to fulfill this requirement in the SDS major. However, please note that 310 is no longer offered at UArizona. Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾ As of Fall 2024, the enrollment requirements for DATA 363 have changed. Students must complete MATH 129 and a Python course (CSC 110 or ISTA 130) prior to 363. In addition, MATH 313 and an SQL course (ISTA 322) must either be complete or in-progress in the same term as 363.

⁽⁴⁾ DATA 467 is offered in-person in fall semesters. Provided we have sufficient enrollment, we plan to offer it online each spring.

 ⁽⁵⁾ DATA 498A is currently primarily a spring course; as of 2024, we are attempting to offer it in fall semesters as well.

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Statistics & Data Science Major Elective Courses

The SDS major requires one upper-division elective course. The current courses that will be accepted toward this requirement are listed below. More course options may be added as the program grows; see your academic advisor for details.

Course options:

• DATA 367— Statistical Methods in Sports Analytics
• DATA 396T— Topics in Undergraduate Statistics & Data Science^(*)
• DATA 462— Financial Math
• DATA 468— Applied Stochastic Processes
• DATA 496T— Advanced Topics in Undergraduate Statistics & Data Science^(*)
• DATA 498H— Honors Thesis^(**)
• SIE 440— Survey of Optimization Methods

 

 

1. Requirements Change Summary

Combined B.A./B.S. Requirements

For B.S. degree with either major: add GEOS 255 as an option for completing lab science sequence; updates to application courses for each major.

 

Math Major Course Requirements and Emphases

CSC 250 added to the list of acceptable alternative programming courses. Applied emphasis, Computer Science emphasis: alternative courses set to replace the discontinued 475B. Applied emphasis, Life Science emphasis: students may now choose between MATH 481 and 485 for their modeling course.

 

Statistics & Data Science Major Course Requirements

CSC 250 added to the list of acceptable alternative programming courses. DATA 396T, 496T, and 498H added to list of available DATA electives.

 

2. B.A./B.S. in Mathematics or Statistics & Data Science

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

Upon declaring a major in mathematics or statistics & data science, students must select a degree in which the major will appear.  We offer your choice of a Bachelor of Arts (B.A.) or Bachelor of Science (B.S.).  

These degrees have many common requirements, including minimum units, English composition, and many of the general education courses.  There are some differences, however.

Below, you can find the requirements specific to the two degrees. For requirements specific to each major, regardless of degree, see:

• Mathematics Major Requirements
• Statistics & Data Science Major Requirements

Our major checklists also provide a good overview of the requirements for the degree/major of your choice.

Comparing the B.A. and the B.S.

As far as the mathematics or statistics coursework is concerned, the B.A. and B.S. are identical. 

The requirements for the two degrees differ only in the following ways:

• Second language requirement (details below).
• Science/application course requirements (details below).

The B.A. in Mathematics or SDS

• Language Requirement: Students must demonstrate fourth semester proficiency in a second language.
• The degree is not science-intensive. Students need to complete only the two Tier One NATS (170) and one Tier Two Natural Science courses, as specified in the University General Education requirements.

The B.S. in Mathematics or SDS

• Language Requirement: Students must demonstrate second semester proficiency in a second language.
• Laboratory Science Courses Requirement: The degree is science-intensive and requires one of the following sequences of laboratory science courses:
  • PHYS 141 & either PHYS 142 or PHYS 241
  • PHYS 161H & either PHYS 162H or PHYS 261H
  • CHEM 151 & CHEM 152
  • CHEM 141 & CHEM 143 & CHEM 142 & CHEM 144
  • CHEM 161 & CHEM 163 & CHEM 162 & CHEM 164
  • MCB 181R & MCB 181L & ECOL 182R & ECOL 182L^(*)
  • PSIO 201 & PSIO 202
  • GEOS 251 & one of GEOS 255, GEOS 302^(**), GEOS 304^(**), GEOS 308, or GEOS 322
    
    

^(*)CHEM 151 is recommended prior to beginning this sequence.

^(**)Additional prerequisites must be met.

• Application Courses Requirement: (This requirement does not apply to the Mathematics Education emphasis.) Students must complete at least six units of coursework that applies advanced mathematics or statistics to other academic fields. There are separate lists of available courses for mathematics majors and statistics & data science majors. Up to 3 units of 493 internship credit under the appropriate prefix (MATH/DATA) may apply to application course requirements for Mathematics & SDS majors, respectively.

Note: B.S. students in either major may satisfy both the Laboratory Science Courses Requirement and the Application Courses Requirement by completing one of the Physics sequences. 

For mathematics majors, these courses must have a pre- or co-requisite of at least Calculus I (MATH 122B or higher). Choose from the following:

Agric & Biosystems Eng	BE 201, BE 284, BE 428, BE 481A;
Agric & Resource Economics	AREC 304,   AREC 464,    AREC 479;
Astronomy	ASTR 250;
Atmospheric Sciences	ATMO 430, ATMO 436A, ATMO 469A, ATMO 469B;
Biochemistry	BIOC 462A, BIOC 462B,  BIOC 466
Biomedical Engineering	BME 214, BME 481B;
Civil Engineering	CE 214;
Chemical & Environmental Engr	CHEE 201,  CHEE 202, CHEE 297, CHEE 481A, CHEE 481B;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 404A, CHEM 480A, CHEM 480B, CHEM 481;
Computer Science	CSC 345, CSC 422, CSC 433, CSC 436, CSC 437,    CSC 444, CSC 445, CSC 453, CSC 460, CSC 477, CSC 483;
Computer Science UA South	CSCV 345;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447, ECOL 496N (ECOL 496N not offered recently);
Economics	ECON 332,ECON 361;
Engineering	ENGR 211C, ENGR 211E, ENGR 211P;
Environmental Science	ENVS 420, ENVS 470, ENVS 479;
Geography & Development	GEOG 463;
Geosciences	GEOS 322, GEOS 356, GEOS 419, GEOS 432, GEOS 434A, GEOS 440, GEOS 469, GEOS 479;
Hydrology and Water Resources	HWRS 349A, HWRS 421(HWRS 421 not offered recently), HWRS 431, HWRS 460A;
Information Sci, Tech & Arts	ISTA 421, ISTA 450;
Molecular & Cellular Biology	MCB 480;
Materials Science & Engr	MSE 222, MSE 345, MSE 404, MSE 415;
Mathematics	MATH 493;
Optical Sciences	OPTI 201R, OPTI 303, OPTI 495B;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143*, PHYS 161H, PHYS 162H, PHYS 240, PHYS 241,PHYS 261H; *Note: PHYS 143 is only 2 units; 6 units are required.
Physiology	PSIO 303, PSIO 305, PSIO 472;
Planetary Sciences	PTYS 407;
Retailing & Consumer Science	RCSC 216;
Systems & Industrial Engr	SIE 250, SIE 265;
Wildlife & Fisheries Science	WFSC 444, WFSC 445;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

For statistics & data science majors, we now recommend taking ISTA 322 to fulfill 3 units of this requirement. If you have enrolled in ISTA 322 and want it to fulfill an application course, please email the Math Center. The courses listed below must have a pre- or co-requisite of a statistics course or at least Calculus I (MATH 122B or higher). Choose from the following: 

Agric & Biosystems Engineering	BE 201, BE 284, BE 423, BE 428, BE 485;
Animal & Comp Biomed Sciences	ACBS 313;
Aerospace & Mechanical Engr	AME 472
Astronomy	ASTR 250;
Biochemistry	BIOC 462A, BIOC 462B, BIOC 466;
Civil Engineering	CE 214, CE 310, CE 449;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 404A, CHEM 480A, CHEM 480B;
Computer Science	CSC 345, CSC 422, CSC 433, CSC 436, CSC 437, CSC 444, CSC 445, CSC 453, CSC 460, CSC 477, CSC 483, CSCV 345;
Statistics & Data Science	DATA 493;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447;
Economics	ECON 332, ECON 361;
Engineering	ENGR 211C;
Environmental Science	ENVS 420, ENVS 470;
Epidemiology	EPID 452, EPID 479;
Geosciences	GEOS 322, GEOS 356, GEOS 434A, GEOS 469, GEOS 479;
Information Sci, Tech & Arts	ISTA 321, ISTA 350, ISTA 421, ISTA 450;
Molecular & Cellular Biology	MCB 416A, MCB 480;
Materials Science & Engr	MSE 345, MSE 404;
Neuroscience & Cognitive Sci	NSCS 344;
Optical Sciences	OPTI 201R;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143*, PHYS 161H, PHYS 162H, PHYS 240, PHYS 241, PHYS 261H; *Note: PHYS 143 is only 2 units; 6 units are required.
Physiology	PSIO 303, PSIO 472;
Planetary Sciences	PTYS 407;
Range Management	RAM 456;
Renewable Natural Resources	RNR 321, RNR 417, RNR 473;
Systems & Industrial Engr	SIE 250, SIE 265, SIE 422, SIE 496;
Sociology	SOC 476;
Wildlife & Fisheries Science	WFSC 444, WFSC 445;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

Double Degrees

Students pursuing a second major that has a degree title different from that of the first major are technically double degree students. Additional requirements may apply to double degree students that do not pertain to double major students (students with two majors that have exactly the same degree title). See an advisor for details. 

Mid-Career Writing Assessment (MCWA)

Every undergraduate degree program at the University of Arizona requires satisfaction of the MCWA. a grade of A or B in ENGL 102, ENGL 108 (for ESL students), or ENGL 109H (for qualified students) will satisfy the requirement. If you earn less than a B in your second-semester composition course, you have several options for completing the MCWA. You may:

• repeat your second-semester English course (with GRO, if eligible) and earn at least a B, or
• complete ENGL 307, 308, or 313 with a grade of at least D.

3. Math Major Course Requirements and Emphases

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Mathematics require a core of basic courses followed by additional courses specific to one of seven possible emphases:

• Applied Mathematics emphasis: This emphasis is for students who intend to enter the job market upon graduation, but may also be appropriate for students who plan to go on to graduate school in a field of science or engineering.
• Comprehensive emphasis: This emphasis prepares students for graduate study in mathematics, applied mathematics, or most other scientific fields.
• Probability and Statistics emphasis: This emphasis is for students considering a career as an actuary or statistician, as well as for students wanting to attend graduate school in statistics.
• Mathematics Education emphasis: This emphasis prepares students for teaching mathematics at the secondary school level. The emphasis has two main components: a set of courses in mathematics, and a set of courses in teaching and learning mathematics in secondary schools.
• Computer Science emphasis: This emphasis is for students interested in applications of computers to mathematical problems, including math majors who plan to attend graduate school in computer science.
• Economics or Business emphasis: This emphasis is for students with a particular interest in business applications of mathematics, especially those preparing for graduate school in economics or finance.
• Life Sciences emphasis: This emphasis is for students considering a career in medicine, as well as for students wanting to attend graduate school in the biological sciences.

Each emphasis requires at least 15 units of 400-level mathematics course work, and each emphasis, except Mathematics Education, requires the student to complete a minor outside the math department. Courses in minors must be distinct from those in the major.

The complete official requirements for each emphasis are given in the University Catalog in the form of an Academic Advisement Report (ADVIP). Below we cover the portion of the requirements specific to the mathematics major. It is important for students to consult with their academic advisor about their choice and order of courses, as well as which additional courses would strengthen their degree program.

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

Supporting Computer Science Requirement

All math and SDS majors are required to complete a computer programming course, regardless of the degree and emphasis selected. Choose one course:⁽¹⁾

• CSC 110 — Introduction to Computer Programming I
• CSC 250 — Essential Computing for the Sciences
• ISTA 130 — Computational Thinking and Doing

Core Courses

All seven emphases for the B.A./B.S. require the following core courses, which should ideally be completed by the end of the sophomore year.

• MATH 122A AND MATH 122B ⁽²⁾ or MATH 125 — Calculus I
• MATH 129 — Calculus II
• MATH 223 — Vector Calculus
• MATH 313 — Introduction to Linear Algebra ⁽³⁾ 
• MATH 323 — Formal Mathematical Reasoning and Writing ⁽⁴⁾
• MATH 355 — Analysis of Ordinary Differential Equations ⁽⁵⁾

⁽¹⁾CSC 110, CSC 250, or ISTA 130 is recommended for most students. Other courses that can be used to satisfy the programming requirement are: CSC 120, CSC 127A, CSC 227, ECE 175, MIS 301, NSCS 311, and PHYS 305. These latter courses may require prior programming experience, additional prerequisites and/or a major or minor declared in another subject.

⁽²⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. 

⁽³⁾ MATH 313 replaces MATH 215, which is no longer offered.  Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽⁴⁾MATH 323 is a writing-emphasis course that is the foundation for many of the advanced courses taken by math majors. It is prerequisite for more theoretical 400-level courses in the major. Students who do not do well in MATH 323 should speak to an advisor about their choice of major/emphasis.  MATH 396L, the Wildcat Proofs Workshop, is a 1 unit supplemental instruction course intended to give students additional practice and guidance in learning proof writing techniques. The 396L course is required for students who earned a C or lower in MATH 313, the prerequisite to 323. Students who earn a D in 313 are required to either repeat 313 for a higher grade or take another course (MATH 243, 315, or CSC 245) before moving on to 323 + 396L. 

⁽⁵⁾MATH 355 is the differential equations course that all mathematics majors are expected to take. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticated approach to differential equations. MATH 254 is a differential equations course that is aimed at engineering and science majors. Students with an additional major in engineering or science may ask their math faculty advisors for permission to substitute MATH 254 course for MATH 355 if a scheduling issue arises. Keep in mind that MATH 254 is lower-division - students who take it may need extra upper-division units.

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Applied Mathematics emphasis

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following three sequences:
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. One course from the list: {MATH 413, MATH 424, MATH 443, MATH 445, MATH 447, MATH 454, MATH 456, MATH 464, MATH 475B} ^(*)
• One modeling course; choose either:
  • MATH 481 — Mathematical Modeling of Fluid Flow through and around Organs and Organisms   OR
  • MATH 485 — Mathematical Modeling ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 424, MATH 454, MATH 456, MATH 464, MATH 468, MATH 475A, MATH 488.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^(*) The Math Department has discontinued MATH 475B. We will still offer MATH 475A going forward, and have approved the listed alternatives to MATH 475B. These options will not appear in older advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above if your advisement report does not include these options; we will make the adjustment for you.

^(**) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters). In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course. MATH 481 (Mathematical Modeling of Fluid Flow through and around Organs and Organisms) may replace MATH 485. If your catalog requirements do not reflect this, please email mathcenter@math.arizona.edu if you enroll so we can adjust your record. The course will begin appearing in advisement reports for Fall 2021. 

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Comprehensive emphasis

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

This emphasis covers the minimum requirements for admission to most graduate programs in mathematics or applied mathematics. We have separate information on selecting the appropriate emphasis and courses to prepare for various types of graduate programs.  Students selecting the comprehensive emphasis should consult with a Mathematics Department faculty advisor in choosing additional course work to ensure that they are prepared for the graduate school of their choice. A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 413— Linear Algebra
• MATH 424— Theory of Complex Variables
• MATH 425A— Real Analysis of One Variable
• MATH 425B— Real Analysis of Several Variables
• One of the following two pairs:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations

Students completing this emphasis are expected to be proficient in proof writing before beginning most of the 400-level courses above. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in proof-intensive 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Probability and Statistics emphasis

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis. The math major with probability and statistics emphasis differs from the Statistics and Data Science (SDS) major in that it gives more theoretical background. Students who wish to attend graduate school in statistics, economics, or another related field are advised to choose this option instead of (or in addition to) the SDS major. In association with the Graduate Interdisciplinary Program in Statistics & Data Science, we offer an Accelerated Master's Program in Statistics & Data Science. 

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• MATH 466— Theory of Statistics
• One of the following two courses:
  • MATH 468— Applied Stochastic Processes
  • MATH 413— Linear Algebra
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 422, MATH 425B, MATH 454, MATH 456, MATH 462, MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Mathematics Education emphasis

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

This emphasis is for students preparing to teach mathematics at the secondary school level. The Education emphasis has two main components, a set of courses in mathematics, and a set of pedagogy courses. This emphasis does not require a minor. See the Secondary Math Education Program (SMEP) website for additional information.

The Noyce Interns and Noyce Scholars programs offer experience to students interested in learning more about the teaching profession; see the SMEP website for details and to apply.

Major requirements:

• Core Courses (see above)
• Courses in Mathematics:
  • MATH 315— Introduction to Number Theory and Modern Algebra
  • MATH 330— Topics in Geometry
  • MATH 361— Elements of Statistics Using Calculus
  • MATH 404— History of Mathematics
  • MATH 407— Synthesis of Mathematical Concepts
• Courses in Teaching and Learning Mathematics (Pedagogy):
  • MATH 205— Teaching Secondary Mathematics
  • EDP 301— Educational Psychology and Child and Adolescent Development 
  • SERP 400— Survey of Exceptional Students
  • TLS 416— An Introduction to Structured English Immersion^(*)
  • TLS 435— Content Area Literacy in a Multicultural School
  • MATH 406A— Curriculum and Assessment in Secondary School Mathematics
  • MATH 406B— Methods of Teaching Mathematics in Secondary Schools
  • MATH 494C— Student Teaching
• Constitution Requirement for Arizona State certification.
  • This requirement is fulfilled by completing one of the following: POL 210 or equivalent; a passing score on the Arizona and US Constitution exams. 
• GPA requirements:
  • GPA ≥ 2.5 in MATH 122A&B/125, 129, 223
  • Pedagogy GPA ≥ 2.5
  • Major GPA ≥ 2.0
  • Cumulative UA GPA ≥ 2.0

^(*) LCEV 408— Methods of Teaching English to English Language Learners - also fulfills this requirement but is not currently available to SMEP students through the College of Education.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

Computer Science emphasis

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

A minor in computer science is required with this emphasis.

Major requirements:

• Core Courses (see above)
• One of the following three sequences:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. One course from the list: {MATH 422, MATH 424, MATH 454, MATH 456, MATH 464, MATH 485, MATH 475B}^(*)
• Two of the following six courses:
  • MATH 413— Linear Algebra
  • MATH 443— Theory of Graphs and Networks
  • MATH 445— Introduction to Cryptography
  • MATH 446— Theory of Numbers
  • MATH 447— Combinatorial Mathematics
  • CSC 473— Automata, Grammars and Languages ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 401A, MATH 401B, MATH 402, MATH 413, MATH 415A, MATH 443, MATH 445, MATH 446, MATH 447, MATH 464, MATH 468, MATH 475A, MATH 485, or  CSC 473.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^{(*) The Math Department has discontinued MATH 475B. We will still offer MATH 475A going forward, and have approved the listed alternatives to MATH 475B. These options will not appear in older advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above if your advisement report does not include these options; we will make the adjustment for you.} 

^(**) Students minoring in Computer Science may not double-dip courses with their math major. Students with a double major in Computer Science and Mathematics may be able to double-dip additional courses between the two majors, within reasonable limits. It is important to consult with advisors from both majors when planning your coursework to avoid graduation delays.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Economics or Business emphasis

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

This emphasis requires either

• an Economics Minor, or
• a Business Administration Minor, or
• an Entrepreneurship Minor, or
• a Finance Minor, or
• a Marketing Minor, or
• a Sports Management Minor, or
• a Personal & Family Financial Planning Minor, or
• a Thematic Minor emphasizing courses from two or more disciplines/subject areas such as Economics, Business, and Finance, or
• a second major in the same degree in one of the above or in Personal and Family Financial Planning.

The minor should be chosen in consultation with an advisor.

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• Two of the following four courses:
  
  • MATH 413— Linear Algebra
  • MATH 425B— Real Analysis of Several Variables
  • MATH 462— Financial Math
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 422,MATH 425B, MATH 432, MATH 454, MATH 456, MATH 462, MATH 466,  MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

---

Life Sciences emphasis

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

A minor or major in the biological sciences is required for this emphasis. Possibilities include Astrobiology, Biochemistry, Bioinformatics, Biology, Biosystems Engineering, Ecology & Evolutionary Biology, Environmental Sciences, Molecular & Cellular Biology, Pharmaceutical Sciences, Physiology, Physiological Sciences, and Pre-Health Professions, or a thematic minor with a life sciences emphasis.  A second major in a life science area may also be used to fulfill the minor requirement.  Courses which may be of interest for your minor include: ECOL 320, ECOL 340, ECOL 426, ECOL 453, ECOL 480, ECOL 496J; 

MCB 315, MCB 410, MCB 411, MCB 422.

 

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following two courses:
  • MATH 454— Ordinary Differential Equations and Stability Theory
  • MATH 456— Applied Partial Differential Equations
• MATH 464— Theory of Probability
• One of the following two courses:
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• One modeling course; choose either:
  • MATH 481 — Mathematical Modeling of Fluid Flow through and around Organs and Organisms   OR
  • MATH 485 — Mathematical Modeling ^(*)

^(*) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters). In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course. MATH 481 (Mathematical Modeling of Fluid Flow through and around Organs and Organisms) may replace MATH 485. If your catalog requirements do not reflect this, please email mathcenter@math.arizona.edu if you enroll so we can adjust your record. The course will begin appearing in advisement reports for Fall 2021.  

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

4. Statistics & Data Science Major Course Requirements

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Statistics & Data Science require the same set of supporting and core coursework. A minor in any subject outside the math department is required with this major.

The information and requirements given here apply to the 2021–2022 catalog. For other catalog years, please consult the archive.

The Academic Advising Report (ADVIP) gives complete degree requirements:

• B.A. Statistics & Data Science
• B.S. Statistics & Data Science

Note: this program was brand new for Fall 2018. All SDS majors are expected to meet with an advisor in the Math Center at least once a semester.

Supporting Python Programming Requirement

All SDS majors are required to complete a computer programming course in Python, regardless of the degree selected. Choose one course:^(*)

• CSC 110— Introduction to Computer Programming I
• CSC 250— Essential Computing for the Sciences
• ISTA 130— Computational Thinking and Doing

^(*)Either CSC 110, CSC 250, or ISTA 130 is recommended for most students; CSC 120 will also satisfy the requirement. As an alternative, qualified students may complete both ECE 175 AND BE 205.

Supporting Data Management Course

SDS graduates applying for jobs will find that SQL and Data Management skills are important. Beginning in Fall 2023, enrollment in DATA 363 will require completion or concurrent enrollment in a course that teaches SQL and Data Management. These skills will be helpful as students work on their projects in DATA 363. Take one course:

• ISTA 322— Data Engineering

Core Courses

• MATH 122A AND MATH 122B  ⁽¹⁾ or  MATH 125— Calculus I

• MATH 129— Calculus II

• MATH 223— Vector Calculus

• MATH 313— Introduction to Linear Algebra ⁽²⁾ 

• DATA 363— Introduction to Statistical Methods ⁽³⁾

• DATA 375— Introduction to Statistical Computing 

• MATH 464— Theory of Probability

• MATH 466— Theory of Statistics

• DATA 467 — Applied Linear Models ⁽⁴⁾

• DATA 498A — Capstone for Statistics and Data Science ⁽⁶⁾

• One upper-division statistics major elective.

 

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. 

⁽²⁾ Either MATH 313 or MATH 310 may be used to fulfill this requirement in the SDS major. However, please note that 310 is no longer offered at UArizona. Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾ As of Fall 2024, the enrollment requirements for DATA 363 have changed. Students must complete MATH 129 and a Python course (CSC 110 or ISTA 130) prior to 363. In addition, MATH 313 and an SQL course (ISTA 322) must either be complete or in-progress in the same term as 363.

⁽⁴⁾ DATA 467 is offered in-person in fall semesters. Provided we have sufficient enrollment, we plan to offer it online each spring.

 ⁽⁵⁾ DATA 498A is currently primarily a spring course; as of 2024, we are attempting to offer it in fall semesters as well.

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Statistics & Data Science Major Elective Courses

The SDS major requires one upper-division elective course. The current courses that will be accepted toward this requirement are listed below. More course options may be added as the program grows; see your academic advisor for details.

Course options:

• DATA 367— Statistical Methods in Sports Analytics
• DATA 396T— Topics in Undergraduate Statistics & Data Science^(*)
• DATA 462— Financial Math
• DATA 468— Applied Stochastic Processes
• DATA 496T— Advanced Topics in Undergraduate Statistics & Data Science^(*)
• DATA 498H— Honors Thesis^(**)
• SIE 440— Survey of Optimization Methods

1. Requirements Change Summary

Combined B.A./B.S. Requirements

For B.S. degree with either major: up to 3 units of internship credit (MATH 493 for math major and DATA 493 for SDS major) may count toward application course requirements.  

 

Math Major Course Requirements and Emphases

NSCS 311 added to the list of acceptable alternative programming courses. Minors added to Economics/Business emphasis: Personal & Family Financial Planning, Entrepreneurship, Sports Management, and Marketing. Minor added to Life Sciences emphasis: Pharmaceutical Sciences.

 

Statistics & Data Science Major Course Requirements

Update to course number and title for last required course: DATA 498A - Capstone for Statistics and Data Science. Allow alternative pair of courses to fulfill programming requirement: ECE 175 AND BE 205 together can satisfy. 

2. B.A./B.S. in Mathematics or Statistics & Data Science

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

Upon declaring a major in mathematics or statistics & data science, students must select a degree in which the major will appear.  We offer your choice of a Bachelor of Arts (B.A.) or Bachelor of Science (B.S.).  

These degrees have many common requirements, including minimum units, English composition, and many of the general education courses.  There are some differences, however.

Below, you can find the requirements specific to the two degrees. For requirements specific to each major, regardless of degree, see:

• Mathematics Major Requirements
• Statistics & Data Science Major Requirements

Comparing the B.A. and the B.S.

As far as the mathematics or statistics coursework is concerned, the B.A. and B.S. are identical. 

The requirements for the two degrees differ only in the following ways:

• Second language requirement (details below).
• Science/application course requirements (details below).

The B.A. in Mathematics or SDS

• Language Requirement: Students must demonstrate fourth semester proficiency in a second language.
• The degree is not science-intensive. Students need to complete only the two Tier One NATS (170) and one Tier Two Natural Science courses, as specified in the University General Education requirements.

The B.S. in Mathematics or SDS

• Language Requirement: Students must demonstrate second semester proficiency in a second language.
• Laboratory Science Courses Requirement: The degree is science-intensive and requires one of the following sequences of laboratory science courses:
  • PHYS 141 & either PHYS 142 or PHYS 241
  • PHYS 161H & either PHYS 162H or PHYS 261H
  • CHEM 151 & CHEM 152
  • CHEM 141 & CHEM 143 & CHEM 142 & CHEM 144
  • CHEM 161 & CHEM 163 & CHEM 162 & CHEM 164
  • MCB 181R & MCB 181L & ECOL 182R & ECOL 182L^(*)
  • PSIO 201 & PSIO 202
  • GEOS 251 & one of GEOS 302^(**), GEOS 304^(**), GEOS 308, or GEOS 322
    
    

^(*)CHEM 151 is recommended prior to beginning this sequence.

^(**)Additional prerequisites must be met.

• Application Courses Requirement: (This requirement does not apply to the Mathematics Education emphasis.) Students must complete at least six units coursework that applies advanced mathematics or statistics to other academic fields. There are separate lists of available courses for mathematics majors and statistics & data science majors. 

^(*)Up to 3 units of 493 internship credit under the appropriate prefix (MATH/DATA) may apply to application course requirements for Mathematics & SDS majors, respectively.

For mathematics majors, these courses must have a pre- or co-requisite of at least Calculus I (MATH 122B or higher). Choose from the following:

Agric & Biosystems Eng	BE 201, BE 284, BE 428, BE 481A;
Astronomy	ASTR 250;
Atmospheric Sciences	ATMO 421C (ATMO 421C no longer offered), ATMO 436A, ATMO 469A, ATMO 469B;
Biochemistry	BIOC 462A, BIOC 462B, BIOC 463A, BIOC 466
Biomedical Engineering	BME 481B;
Civil Engineering	CE 214;
Chemical & Environmental Engr	CHEE 201, CHEE 201L, CHEE 202, CHEE 301A, CHEE 481A, CHEE 481B;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 326, CHEM 404A, CHEM 480A, CHEM 480B, CHEM 481;
Computer Science	CSC 345, CSC 422, CSC 433, CSC 436, CSC 437 (CSC 437 not offered recently), CSC 445, CSC 453, CSC 460, CSC 477;
Computer Science UA South	CSCV 345;
Electrical & Computer Engr	ECE 381A, ECE 429;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447, ECOL 496N (ECOL 496N not offered recently);
Economics	ECON 332,ECON 361;
Engineering	ENGR 211C, ENGR 211P;
Environmental Science	ENVS 420, ENVS 470;
Geography & Development	GEOG 463;
Geosciences	GEOS 322, GEOS 356, GEOS 419, GEOS 432, GEOS 434A, GEOS 440 (GEOS 440 not offered recently), GEOS 469, GEOS 479;
Hydrology and Water Resources	HWRS 421(HWRS 421 not offered recently), HWRS 431, HWRS 460A;
Information Sci, Tech & Arts	ISTA 352, ISTA 421;
Molecular & Cellular Biology	MCB 315, MCB 480;
Materials Science & Engr	MSE 345, MSE 404, MSE 415;
Mathematics	MATH 493*
Optical Sciences	OPTI 201R, OPTI 303;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143, PHYS 151 (PHYS 151 not offered recently), PHYS 152 (PHYS 152 not offered recently), PHYS 161H, PHYS 162H, PHYS 240, PHYS 241, PHYS 251 (PHYS 251 not offered recently),PHYS 261H;
Physiology	PSIO 303, PSIO 472;
Planetary Sciences	PTYS 407;
Systems & Industrial Engr	SIE 250, SIE 265;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

For statistics & data science majors, these courses must have a pre- or co-requisite of a statistics course or at least Calculus I (MATH 122B or higher). Choose from the following: 

Agric & Biosystems Engineering	BE 201, BE 284, BE 423, BE 428;
Animal & Comp Biomed Sciences	ACBS 313;
Aerospace & Mechanical Engr	AME 472
Astronomy	ASTR 250;
Biochemistry	BIOC 462A, BIOC 462B, BIOC 466;
Biomedical Engineering	BME 481B;
Civil Engineering	CE 214;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 326, CHEM 404A, CHEM 480A, CHEM 480B;
Computer Science	CSC 345, CSC 422, CSC 433, CSC 436, CSC 437, CSC 445, CSC 453, CSC 460, CSC 477, CSCV 345;
Statistics & Data Science	DATA 493*
Electrical & Computer Engr	ECE 381A, ECE 429;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447;
Economics	ECON 332, ECON 361;
Engineering	ENGR 211C;
Environmental Science	ENVS 420, ENVS 470;
Epidemiology	EPID 479;
Geography & Development	GEOG 463;
Geosciences	GEOS 322, GEOS 356, GEOS 419, GEOS 432, GEOS 434A, GEOS 440, GEOS 469, GEOS 479;
Information Sci, Tech & Arts	ISTA 321, ISTA 350, ISTA 421, ISTA 450;
Molecular & Cellular Biology	MCB 315, MCB 416A, MCB 480;
Materials Science & Engr	MSE 345, MSE 404, MSE 415;
Neuroscience & Cognitive Sci	NSCS 344;
Optical Sciences	OPTI 201R;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143, PHYS 161H, PHYS 162H, PHYS 240, PHYS 241, PHYS 261H;
Physiology	PSIO 303, PSIO 472;
Planetary Sciences	PTYS 407;
Range Management	RAM 456;
Renewable Natural Resources	RNR 417, RNR 473;
Systems & Industrial Engr	SIE 250, SIE 265, SIE 422, SIE 496;
Sociology	SOC 476;
Wildlife & Fisheries Science	WFSC 444;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

Note: B.S. students may satisfy both the Laboratory Science Courses Requirement and the Application Courses Requirement by completing one of the Physics sequences. 

Double Degrees

Students pursuing a second major that has a degree title different from that of the first major are technically double degree students. Additional requirements may apply to double degree students that do not pertain to double major students (students with two majors that have exactly the same degree title). See an advisor for details. 

Mid-Career Writing Assessment (MCWA)

Every undergraduate degree program at the University of Arizona requires satisfaction of the MCWA. a grade of A or B in ENGL 102, ENGL 108 (for ESL students), or ENGL 109H (for qualified students) will satisfy the requirement. If you earn less than a B in your second-semester composition course, you have several options for completing the MCWA. You may:

• repeat your second-semester English course (with GRO, if eligible) and earn at least a B, or
• complete ENGL 307, 308, or 313 with a grade of at least D.

3. Math Major Course Requirements and Emphases

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Mathematics require a core of basic courses followed by additional courses specific to one of seven possible emphases:

• Applied Mathematics emphasis: This emphasis is for students who intend to enter the job market upon graduation, but may also be appropriate for students who plan to go on to graduate school in a field of science or engineering.
• Comprehensive emphasis: This emphasis prepares students for graduate study in mathematics, applied mathematics, or most other scientific fields.
• Probability and Statistics emphasis: This emphasis is for students considering a career as an actuary or statistician, as well as for students wanting to attend graduate school in statistics.
• Mathematics Education emphasis: This emphasis prepares students for teaching mathematics at the secondary school level. The emphasis has two main components: a set of courses in mathematics, and a set of courses in teaching and learning mathematics in secondary schools.
• Computer Science emphasis: This emphasis is for students interested in applications of computers to mathematical problems, including math majors who plan to attend graduate school in computer science.
• Economics or Business emphasis: This emphasis is for students with a particular interest in business applications of mathematics, especially those preparing for graduate school in economics or finance.
• Life Sciences emphasis: This emphasis is for students considering a career in medicine, as well as for students wanting to attend graduate school in the biological sciences.

Each emphasis requires at least 15 units of 400-level mathematics course work, and each emphasis, except Mathematics Education, requires the student to complete a minor outside the math department. Courses in minors must be distinct from those in the major.

The complete official requirements for each emphasis are given in the University Catalog in the form of an Academic Advisement Report (ADVIP). Below we cover the portion of the requirements specific to the mathematics major. It is important for students to consult with their academic advisor about their choice and order of courses, as well as which additional courses would strengthen their degree program.

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

Supporting Computer Science Requirement

All math and SDS majors are required to complete a computer programming course, regardless of the degree and emphasis selected. Choose one course:⁽¹⁾

• CSC 110 — Introduction to Computer Programming I
• ISTA 130 — Computational Thinking and Doing

Core Courses

All seven emphases for the B.A./B.S. require the following core courses, which should ideally be completed by the end of the sophomore year.

• MATH 122A AND MATH 122B ⁽²⁾ or MATH 125 — Calculus I
• MATH 129 — Calculus II
• MATH 223 — Vector Calculus
• MATH 313 — Introduction to Linear Algebra ⁽³⁾ 
• MATH 323 — Formal Mathematical Reasoning and Writing ⁽⁴⁾
• MATH 355 — Analysis of Ordinary Differential Equations ⁽⁵⁾

⁽¹⁾Either CSC 110 or ISTA 130 is recommended for most students. Other courses that can be used to satisfy the programming requirement are: CSC 120, CSC 127A, CSC 227, ECE 175, MIS 301, NSCS 311, and PHYS 305. These latter courses may require prior programming experience, additional prerequisites and/or a major or minor declared in another subject.

⁽²⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. They are equivalent to the old MATH 124 course, which is no longer offered.

⁽³⁾ MATH 313 replaces MATH 215, which is no longer offered.  Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽⁴⁾MATH 323 is a writing-emphasis course that is the foundation for many of the advanced courses taken by math majors. It is prerequisite for more theoretical 400-level courses in the major. Students who do not do well in MATH 323 should speak to an advisor about their choice of major/emphasis.  MATH 396L, the Wildcat Proofs Workshop, is a 1 unit supplemental instruction course intended to give students additional practice and guidance in learning proof writing techniques. The 396L course is required for students who earned a C or lower in MATH 313, the prerequisite to 323. Students who earn a D in 313 are required to either repeat 313 for a higher grade or take another course (MATH 243, 315, or CSC 245) before moving on to 323 + 396L. 

⁽⁵⁾MATH 355 is the differential equations course that all mathematics majors are expected to take. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticated approach to differential equations. MATH 254 is a differential equations course that is aimed at engineering and science majors. Students with an additional major in engineering or science may ask their math faculty advisors for permission to substitute MATH 254 course for MATH 355 if a scheduling issue arises. Keep in mind that MATH 254 is lower-division - students who take it may need extra upper-division units.

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Applied Mathematics emphasis

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following three sequences:
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. MATH 475B— Mathematical Principles of Numerical Analysis^(*)
• MATH 485— Mathematical Modeling ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 424, MATH 454, MATH 456, MATH 464, MATH 468, MATH 475A, MATH 488.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^(*) The Math Department has discontinued MATH 475B after spring 2020. We will still offer MATH 475A going forward, and have approved some alternatives to MATH 475B for students who may have planned to complete the MATH 475A/475B sequence, which is part of the Applied emphasis: Students may take MATH 475A + one from {MATH 413, 424, 443, 445, 447, 454, 456, 464}. These options will not appear in current advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above, and we will make the adjustment for you.

^(**) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters).  In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course. Starting in Spring 2021, MATH 481 (Mathematical Modeling of Fluid Flow through and around Organs and Organisms) may replace MATH 485 OR may be used as the 5th course. Email mathcenter@math.arizona.edu if you enroll so we can adjust your record. The course will begin appearing in advisement reports for Fall 2021. 

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Comprehensive emphasis

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

This emphasis covers the minimum requirements for admission to most graduate programs in mathematics or applied mathematics. We have separate information on selecting the appropriate emphasis and courses to prepare for various types of graduate programs.  Students selecting the comprehensive emphasis should consult with a Mathematics Department faculty advisor in choosing additional course work to ensure that they are prepared for the graduate school of their choice. A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 413— Linear Algebra
• MATH 424— Theory of Complex Variables
• MATH 425A— Real Analysis of One Variable
• MATH 425B— Real Analysis of Several Variables
• One of the following two pairs:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations

Students completing this emphasis are expected to be proficient in proof writing before beginning most of the 400-level courses above. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in proof-intensive 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Probability and Statistics emphasis

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis. The math major with probability and statistics emphasis differs from the Statistics and Data Science (SDS) major in that it gives more theoretical background. Students who wish to attend graduate school in statistics, economics, or another related field are advised to choose this option instead of (or in addition to) the SDS major. In association with the Graduate Interdisciplinary Program in Statistics, we offer an Accelerated Master's Program in Statistics. 

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• MATH 466— Theory of Statistics
• One of the following two courses:
  • MATH 468— Applied Stochastic Processes
  • MATH 413— Linear Algebra
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 422, MATH 425B, MATH 454, MATH 456, MATH 462, MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Mathematics Education emphasis

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

This emphasis is for students preparing to teach mathematics at the secondary school level. The Education emphasis has two main components, a set of courses in mathematics, and a set of pedagogy courses. This emphasis does not require a minor. See the Secondary Math Education Program (SMEP) website for additional information.

The Noyce Interns and Noyce Scholars programs offer experience to students interested in learning more about the teaching profession; see the SMEP website for details and to apply.

Major requirements:

• Core Courses (see above)
• Courses in Mathematics:
  • MATH 315— Introduction to Number Theory and Modern Algebra
  • MATH 330— Topics in Geometry
  • MATH 361— Elements of Statistics Using Calculus
  • MATH 404— History of Mathematics
  • MATH 407— Synthesis of Mathematical Concepts
• Courses in Teaching and Learning Mathematics (Pedagogy):
  • MATH 205— Teaching Secondary Mathematics
  • EDP 301— Educational Psychology and Child and Adolescent Development 
  • SERP 400— Survey of Exceptional Students
  • LCEV 408— Methods of Teaching English to English Language Learners^(*)
  • TLS 435— Content Area Literacy in a Multicultural School
  • MATH 406A— Curriculum and Assessment in Secondary School Mathematics
  • MATH 406B— Methods of Teaching Mathematics in Secondary Schools
  • MATH 494C— Student Teaching
• Constitution Requirement for Arizona State certification.
  • This requirement is fulfilled by completing one of the following: POL 210 or equivalent; a passing score on the Arizona and US Constitution exams. 
• GPA requirements:
  • GPA ≥ 2.5 in MATH 122A&B/125, 129, 223
  • Pedagogy GPA ≥ 2.5
  • Major GPA ≥ 2.0
  • Cumulative UA GPA ≥ 2.0

^(*) TLS 416— An Introduction to Structured English Immersion - also fulfills this requirement but is not currently available to SMEP students through the College of Education.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

Computer Science emphasis

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

A minor in computer science is required with this emphasis.

Major requirements:

• Core Courses (see above)
• One of the following three sequences:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. MATH 475B — Mathematical Principles of Numerical Analysis^(*)
• Two of the following six courses:
  • MATH 413— Linear Algebra
  • MATH 443— Theory of Graphs and Networks
  • MATH 445— Introduction to Cryptography
  • MATH 446— Theory of Numbers
  • MATH 447— Combinatorial Mathematics
  • CSC 473— Automata, Grammars and Languages ^(**)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 401A, MATH 401B, MATH 402, MATH 413, MATH 415A, MATH 443, MATH 445, MATH 446, MATH 447, MATH 464, MATH 468, MATH 475A, MATH 485, or  CSC 473.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^{(*) The Math Department has discontinued MATH 475B after spring 2020. We will still offer MATH 475A going forward, and have approved some alternatives to MATH 475B for students who may have planned to complete the MATH 475A/475B sequence, which is part of the Computer Science emphasis: Students may take MATH 475A + one from {MATH 422, 424, 454, 456, 464, 485} . These options will not appear in current advisement reports, so the Math Center will need to make substitutions for students. Please email mathcenter@math.arizona.edu when you enroll in the second course for the "sequence" as listed above, and we will make the adjustment for you.}

^(**) Students minoring in Computer Science may not double-dip courses with their math major. Students with a double major in Computer Science and Mathematics may be able to double-dip additional courses between the two majors, within reasonable limits. It is important to consult with advisors from both majors when planning your coursework to avoid graduation delays.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Economics or Business emphasis

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

This emphasis requires either

• an Economics Minor, or
• a Business Administration Minor, or
• an Entrepreneurship Minor, or
• a Finance Minor, or
• a Marketing Minor, or
• a Sports Management Minor, or
• a Personal & Family Financial Planning Minor, or
• a Thematic Minor emphasizing courses from two or more disciplines/subject areas such as Economics, Business, and Finance, or
• a second major in the same degree in one of the above or in Personal and Family Financial Planning.

The minor should be chosen in consultation with an advisor.

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• Two of the following four courses:
  
  • MATH 413— Linear Algebra
  • MATH 425B— Real Analysis of Several Variables
  • MATH 462— Financial Math
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 422,MATH 425B, MATH 432, MATH 454, MATH 456, MATH 462, MATH 466,  MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Life Sciences emphasis

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

A minor or major in the biological sciences is required for this emphasis. Possibilities include Astrobiology, Biochemistry, Bioinformatics, Biology, Biosystems Engineering, Ecology & Evolutionary Biology, Environmental Sciences, Molecular & Cellular Biology, Pharmaceutical Sciences, Physiology, Physiological Sciences, and Pre-Health Professions, or a thematic minor with a life sciences emphasis.  A second major in a life science area may also be used to fulfill the minor requirement.  Courses which may be of interest for your minor include: ECOL 320, ECOL 340, ECOL 426, ECOL 453, ECOL 480, ECOL 496J; 

MCB 315, MCB 410, MCB 411, MCB 422.

 

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following two courses:
  • MATH 454— Ordinary Differential Equations and Stability Theory
  • MATH 456— Applied Partial Differential Equations
• MATH 464— Theory of Probability
• One of the following two courses:
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• MATH 485— Mathematical Modeling ^(*)

^(*) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters).  In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course. Starting in Spring 2021, MATH 481 (Mathematical Modeling of Fluid Flow through and around Organs and Organisms) may replace MATH 485. Email mathcenter@math.arizona.edu if you enroll so we can adjust your record. The course will begin appearing in advisement reports for Fall 2021.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

4. Statistics & Data Science Major Course Requirements

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Statistics & Data Science require the same set of supporting and core coursework. A minor in any subject outside the math department is required with this major.

The information and requirements given here apply to the 2020–2021 catalog. For other catalog years, please consult the archive.

The Academic Advising Report (ADVIP) gives complete degree requirements:

• B.A. Statistics & Data Science
• B.S. Statistics & Data Science

Note: this program was brand new for Fall 2018. All SDS majors are expected to meet with an advisor in the Math Center at least once a semester.

Supporting Computer Science Requirement

All SDS majors are required to complete a computer programming course, regardless of the degree selected. Choose one course:^(*)

• CSC 110— Introduction to Computer Programming I
• ISTA 130— Computational Thinking and Doing

^(*)Either CSC 110 or ISTA 130 is recommended for most students. As an alternative, more advanced students may use CSC 120 to fill the requirement. Contact the Computer Science department for more information about placement into CSC 120. Students may complete both ECE 175 AND BE 205 to fulfill the requirement.

Core Courses

• MATH 122A AND MATH 122B  ⁽¹⁾ or  MATH 125— Calculus I

• MATH 129— Calculus II

• MATH 223— Vector Calculus

• MATH 313— Introduction to Linear Algebra ⁽²⁾ 

• DATA 363— Introduction to Statistical Methods

• DATA 375— Introduction to Statistical Computing ⁽³⁾

• MATH 464— Theory of Probability ⁽⁴⁾

• MATH 466— Theory of Statistics

• DATA 467 — Applied Linear Models ⁽⁵⁾

• DATA 498A — Capstone for Statistics and Data Science ⁽⁶⁾

• One upper-division statistics major elective.

 

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. They are equivalent to the old MATH 124 course, which is no longer offered.

⁽²⁾ Either MATH 313 or MATH 310 may be used to fulfill this requirement in the SDS major. However, please note that 310 has a prerequisite of MATH 254. Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾ DATA 375 was offered for the first time in Spring 2019; hereafter it will be offered every fall and spring semester. 

⁽⁴⁾ Students who have completed MATH 313 and MATH/DATA 363 AND are declared SDS majors or minors will receive assistance from the Math Center to enroll in MATH 464, bypassing the MATH 323 prerequisite. Once there are enough SDS majors to support independent courses, we plan to open new versions with the appropriate prerequisites.

⁽⁵⁾ DATA 467 was offered for the first time Fall 2019; hereafter it will be offered every fall semester. 

⁽⁶⁾ DATA 498A was offered for the first time in Spring 2020; hereafter it will be offered every spring semester.

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Statistics & Data Science Major Elective Courses

The SDS major requires one upper-division elective course. The current courses that will be accepted toward this requirement are listed below. More course options will be added as the program grows; see your academic advisor for details.

Course options:

• DATA 367— Statistical Methods in Sports Analytics
• DATA 462— Financial Math
• DATA 468— Applied Stochastic Processes
• SIE 440— Survey of Optimization Methods

1. Requirements Change Summary

Combined B.A./B.S. Requirements

For B.S. degree with either major: additional GEOS options added to complete lab science sequence; Mid-Career Writing Assessment (MCWA) now fulfilled by either an A or B in ENGL 102/108/109H OR a passing grade in ENGL 307/308/313 (for students who earn a C or D in ENGL 102/108/109H).

 

Math Major Course Requirements and Emphases

CSC 120 fulfills programming requirement for students who place out of CSC 110; Economics/Business emphasis now includes MATH 462 as a choice for the elective courses, and the Personal & Family Fin Planning major may be used to fulfill the minor requirement for students working on both majors in the same degree; Life Science emphasis now includes the Bioinformatics major as an option to satisfy the minor requirement for students working on both majors in the same degree; Education emphasis allows for either TLS 416 or LCEV 408 to satisfy SEI requirements.

 

Statistics & Data Science Major Course Requirements

CSC 120 fulfills programming requirement for students who place out of CSC 110; capstone course "Intro to Data Science" has been proposed with a different number (DATA 469).

2. B.A./B.S. in Mathematics or Statistics & Data Science

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

Upon declaring a major in mathematics or statistics & data science, students must select a degree in which the major will appear.  We offer your choice of a Bachelor of Arts (B.A.) or Bachelor of Science (B.S.).  

These degrees have many common requirements, including minimum units, English composition, and many of the general education courses.  There are some differences, however.

Below, you can find the requirements specific to the two degrees. For requirements specific to each major, regardless of degree, see:

• Mathematics Major Requirements
• Statistics & Data Science Major Requirements

Comparing the B.A. and the B.S.

As far as the mathematics or statistics coursework is concerned, the B.A. and B.S. are identical. 

The requirements for the two degrees differ only in the following ways:

• Second language requirement (details below).
• Science/application course requirements (details below).

The B.A. in Mathematics or SDS

• Language Requirement: Students must demonstrate fourth semester proficiency in a second language.
• The degree is not science-intensive. Students need to complete only the two Tier One NATS (170) and one Tier Two Natural Science courses, as specified in the University General Education requirements.

The B.S. in Mathematics or SDS

• Language Requirement: Students must demonstrate second semester proficiency in a second language.
• Laboratory Science Courses Requirement: The degree is science-intensive and requires one of the following sequences of laboratory science courses:
  • PHYS 141 & either PHYS 142 or PHYS 241
  • PHYS 161H & either PHYS 162H or PHYS 261H
  • CHEM 151 & CHEM 152
  • CHEM 141 & CHEM 143 & CHEM 142 & CHEM 144
  • CHEM 161 & CHEM 163 & CHEM 162 & CHEM 164
  • MCB 181R & MCB 181L & ECOL 182R & ECOL 182L^(*)
  • PSIO 201 & PSIO 202
  • GEOS 251 & one of GEOS 302^(**), GEOS 304^(**), GEOS 308, or GEOS 322
    
    

^(*)CHEM 151 is recommended prior to beginning this sequence.

^(**)Additional prerequisites must be met.

• Application Courses Requirement: (This requirement does not apply to the Mathematics Education emphasis.) Students must complete at least six units coursework that applies advanced mathematics or statistics to other academic fields. There are separate lists of available courses for mathematics majors and statistics & data science majors.

For mathematics majors, these courses must have a pre- or co-requisite of at least Calculus I (MATH 122B or higher). Choose from the following:

Agric & Biosystems Eng	BE 201, BE 284, BE 428, BE 481A;
Astronomy	ASTR 250;
Atmospheric Sciences	ATMO 421C (ATMO 421C no longer offered), ATMO 436A, ATMO 469A, ATMO 469B;
Biochemistry	BIOC 462A, BIOC 462B, BIOC 463A, BIOC 466
Biomedical Engineering	BME 481B;
Civil Engineering	CE 214;
Chemical & Environmental Engr	CHEE 201, CHEE 201L, CHEE 202, CHEE 301A, CHEE 481A, CHEE 481B;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 326, CHEM 404A, CHEM 480A, CHEM 480B, CHEM 481;
Computer Science	CSC 345, CSC 422, CSC 433, CSC 436, CSC 437 (CSC 437 not offered recently), CSC 445, CSC 453, CSC 460, CSC 477;
Computer Science UA South	CSCV 345;
Electrical & Computer Engr	ECE 381A, ECE 429;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447, ECOL 496N (ECOL 496N not offered recently);
Economics	ECON 332,ECON 361;
Engineering	ENGR 211C, ENGR 211P;
Environmental Science	ENVS 420, ENVS 470;
Geography & Development	GEOG 463;
Geosciences	GEOS 322, GEOS 356, GEOS 419, GEOS 432, GEOS 434A, GEOS 440 (GEOS 440 not offered recently), GEOS 469, GEOS 479;
Hydrology and Water Resources	HWRS 421(HWRS 421 not offered recently), HWRS 431, HWRS 460A;
Information Sci, Tech & Arts	ISTA 352, ISTA 421;
Molecular & Cellular Biology	MCB 315, MCB 480;
Materials Science & Engr	MSE 345, MSE 404, MSE 415;
Optical Sciences	OPTI 201R, OPTI 303;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143, PHYS 151 (PHYS 151 not offered recently), PHYS 152 (PHYS 152 not offered recently), PHYS 161H, PHYS 162H, PHYS 240, PHYS 241, PHYS 251 (PHYS 251 not offered recently),PHYS 261H;
Physiology	PSIO 303, PSIO 472;
Planetary Sciences	PTYS 407;
Systems & Industrial Engr	SIE 250, SIE 265;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

For statistics & data science majors, these courses must have a pre- or co-requisite of a statistics course or at least Calculus I (MATH 122B or higher). Choose from the following: 

Agric & Biosystems Engineering	BE 201, BE 284, BE 423, BE 428;
Animal & Comp Biomed Sciences	ACBS 313;
Aerospace & Mechanical Engr	AME 472
Astronomy	ASTR 250;
Biochemistry	BIOC 462A, BIOC 462B, BIOC 466;
Biomedical Engineering	BME 481B;
Civil Engineering	CE 214;
Chemistry	CHEM 161, CHEM 162, CHEM 325, CHEM 326, CHEM 404A, CHEM 480A, CHEM 480B;
Computer Science	CSC 345, CSC 422, CSC 433, CSC 436, CSC 437, CSC 445, CSC 453, CSC 460, CSC 477, CSCV 345;
Statistics & Data Science	DATA 493
Electrical & Computer Engr	ECE 381A, ECE 429;
Ecology & Evolutionary Biology	ECOL 302, ECOL 447;
Economics	ECON 332, ECON 361;
Engineering	ENGR 211C;
Environmental Science	ENVS 420, ENVS 470;
Epidemiology	EPID 479;
Geography & Development	GEOG 463;
Geosciences	GEOS 322, GEOS 356, GEOS 419, GEOS 432, GEOS 434A, GEOS 440, GEOS 469, GEOS 479;
Information Sci, Tech & Arts	ISTA 321, ISTA 350, ISTA 421, ISTA 450;
Molecular & Cellular Biology	MCB 315, MCB 416A, MCB 480;
Materials Science & Engr	MSE 345, MSE 404, MSE 415;
Neuroscience & Cognitive Sci	NSCS 344;
Optical Sciences	OPTI 201R;
Physics	PHYS 140, PHYS 141, PHYS 142, PHYS 143, PHYS 161H, PHYS 162H, PHYS 240, PHYS 241, PHYS 261H;
Physiology	PSIO 303, PSIO 472;
Planetary Sciences	PTYS 407;
Range Management	RAM 456;
Renewable Natural Resources	RNR 417, RNR 473;
Systems & Industrial Engr	SIE 250, SIE 265, SIE 422, SIE 496;
Sociology	SOC 476;
Wildlife & Fisheries Science	WFSC 444;
Watershed Management	WSM 460A;
or courses approved by your academic advisor.

Note: B.S. students may satisfy both the Laboratory Science Courses Requirement and the Application Courses Requirement by completing one of the Physics sequences. 

Double Degrees

Students pursuing a second major that has a degree title different from that of the first major are technically double degree students. Additional requirements may apply to double degree students that do not pertain to double major students (students with two majors that have exactly the same degree title). See an advisor for details. 

Mid-Career Writing Assessment

Every undergraduate degree program at the University of Arizona requires satisfaction of the MCWA. a grade of A or B in ENGL 102, ENGL 108 (for ESL students), or ENGL 109H (for qualified students) will satisfy the requirement. If you earn less than a B in your second-semester composition course, you have several options for completing the MCWA. You may:

• repeat your second-semester English course (with GRO, if eligible) and earn at least a B, or
• complete ENGL 307, 308, or 313 with a grade of at least D.

3. Math Major Course Requirements and Emphases

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Mathematics require a core of basic courses followed by additional courses specific to one of seven possible emphases:

• Applied Mathematics emphasis: This emphasis is for students who intend to enter the job market upon graduation, but may also be appropriate for students who plan to go on to graduate school in a field of science or engineering.
• Comprehensive emphasis: This emphasis prepares students for graduate study in mathematics, applied mathematics, or most other scientific fields.
• Probability and Statistics emphasis: This emphasis is for students considering a career as an actuary or statistician, as well as for students wanting to attend graduate school in statistics.
• Mathematics Education emphasis: This emphasis prepares students for teaching mathematics at the secondary school level. The emphasis has two main components: a set of courses in mathematics, and a set of courses in teaching and learning mathematics in secondary schools.
• Computer Science emphasis: This emphasis is for students interested in applications of computers to mathematical problems, including math majors who plan to attend graduate school in computer science.
• Economics or Business emphasis: This emphasis is for students with a particular interest in business applications of mathematics, especially those preparing for graduate school in economics or finance.
• Life Sciences emphasis: This emphasis is for students considering a career in medicine, as well as for students wanting to attend graduate school in the biological sciences.

Each emphasis requires at least 15 units of 400-level mathematics course work, and each emphasis, except Mathematics Education, requires the student to complete a minor outside the math department. Courses in minors must be distinct from those in the major.

The complete official requirements for each emphasis are given in the University Catalog in the form of an Academic Advisement Report (ADVIP). Below we cover the portion of the requirements specific to the mathematics major. It is important for students to consult with their academic advisor about their choice and order of courses, as well as which additional courses would strengthen their degree program.

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

Supporting Computer Science Requirement

All math and SDS majors are required to complete a computer programming course, regardless of the degree and emphasis selected. Choose one course:⁽²⁾

• CSC 110 — Introduction to Computer Programming I
• ISTA 130 — Computational Thinking and Doing

Core Courses

All seven emphases for the B.A./B.S. require the following core courses, which should ideally be completed by the end of the sophomore year.

• MATH 122A AND MATH 122B ⁽²⁾ or MATH 125 — Calculus I
• MATH 129 — Calculus II
• MATH 223 — Vector Calculus
• MATH 313 — Introduction to Linear Algebra ⁽³⁾ 
• MATH 323 — Formal Mathematical Reasoning and Writing ⁽⁴⁾
• MATH 355 — Analysis of Ordinary Differential Equations ⁽⁵⁾

⁽¹⁾Either CSC 110 or ISTA 130 is recommended for most students. Other courses that can be used to satisfy the programming requirement are: CSC 120, CSC 127A, CSC 227, ECE 175, MIS 301, and PHYS 305. These latter courses may require prior programming experience, additional prerequisites and/or a major or minor declared in another subject.

⁽²⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. They are equivalent to the old MATH 124 course, which is no longer offered.

⁽³⁾ MATH 313 replaces MATH 215, which is no longer offered.  Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽⁴⁾MATH 323 is a writing-emphasis course that is the foundation for many of the advanced courses taken by math majors. It is prerequisite for more theoretical 400-level courses in the major. Students who do not do well in MATH 323 should speak to an advisor about their choice of major/emphasis.  MATH 396L, the Wildcat Proofs Workshop, is a 1 unit supplemental instruction course intended to give students additional practice and guidance in learning proof writing techniques.  The course is optional, but recommended!

⁽⁵⁾MATH 355 is the differential equations course that all mathematics majors are expected to take. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticated approach to differential equations. MATH 254 is a differential equations course that is aimed at engineering and science majors. Students with an additional major in engineering or science may ask their math faculty advisors for permission to substitute MATH 254 course for MATH 355 if a scheduling issue arises.

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Applied Mathematics emphasis

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following three sequences:
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. MATH 475B— Mathematical Principles of Numerical Analysis
• MATH 485— Mathematical Modeling ^(*)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 424, MATH 454, MATH 456, MATH 464, MATH 468, MATH 475A, MATH 488.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^(*) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters).  In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Comprehensive emphasis

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

This emphasis covers the minimum requirements for admission to most graduate programs in mathematics or applied mathematics. We have separate information on selecting the appropriate emphasis and courses to prepare for various types of graduate programs.  Students selecting the comprehensive emphasis should consult with a Mathematics Department faculty advisor in choosing additional course work to ensure that they are prepared for the graduate school of their choice. A minor in any subject outside the math department is required with this emphasis.

Major requirements:

• Core Courses (see above)
• MATH 413— Linear Algebra
• MATH 424— Theory of Complex Variables
• MATH 425A— Real Analysis of One Variable
• MATH 425B— Real Analysis of Several Variables
• One of the following two pairs:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations

Students completing this emphasis are expected to be proficient in proof writing before beginning most of the 400-level courses above. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in proof-intensive 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Probability and Statistics emphasis

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

A minor in any subject outside the math department is required with this emphasis. The math major with probability and statistics emphasis differs from the Statistics and Data Science (SDS) major in that it gives more theoretical background. Students who wish to attend graduate school in statistics, economics, or another related field are advised to choose this option instead of (or in addition to) the SDS major. In association with the Graduate Interdisciplinary Program in Statistics, we offer an Accelerated Master's Program in Statistics. 

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• MATH 466— Theory of Statistics
• One of the following two courses:
  • MATH 468— Applied Stochastic Processes
  • MATH 413— Linear Algebra
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 422, MATH 425B, MATH 454, MATH 456, MATH 462, MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Mathematics Education emphasis

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

This emphasis is for students preparing to teach mathematics at the secondary school level. The Education emphasis has two main components, a set of courses in mathematics, and a set of pedagogy courses. This emphasis does not require a minor. See the Secondary Math Education Program (SMEP) website for additional information.

The Noyce Interns and Noyce Scholars programs offer experience to students interested in learning more about the teaching profession; see the SMEP website for details and to apply.

Major requirements:

• Core Courses (see above)
• Courses in Mathematics:
  • MATH 315— Introduction to Number Theory and Modern Algebra
  • MATH 330— Topics in Geometry
  • MATH 361— Elements of Statistics Using Calculus
  • MATH 404— History of Mathematics
  • MATH 407— Synthesis of Mathematical Concepts
• Courses in Teaching and Learning Mathematics (Pedagogy):
  • MATH 205— Teaching Secondary Mathematics
  • EDP 301— Educational Psychology and Child and Adolescent Development 
  • SERP 400— Survey of Exceptional Students
  • One SEI course, either 
    
    • LCEV 408— Methods of Teaching English to English Language Learners OR
    • TLS 416— An Introduction to Structured English Immersion
  • TLS 435— Content Area Literacy in a Multicultural School
  • MATH 406A— Curriculum and Assessment in Secondary School Mathematics
  • MATH 406B— Methods of Teaching Mathematics in Secondary Schools
  • MATH 494C— Student Teaching
• Constitution Requirement for Arizona State certification.
  • This requirement is fulfilled by completing one of the following: POL 210 or equivalent; a passing score on the Arizona and US Constitution exams. 
• GPA requirements:
  • GPA ≥ 2.5 in MATH 122A&B/125, 129, 223
  • Pedagogy GPA ≥ 2.5
  • Major GPA ≥ 2.0
  • Cumulative UA GPA ≥ 2.0

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

Computer Science emphasis

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

A minor in computer science is required with this emphasis.

Major requirements:

• Core Courses (see above)
• One of the following three sequences:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. MATH 475B— Mathematical Principles of Numerical Analysis
• Two of the following six courses:
  • MATH 413— Linear Algebra
  • MATH 443— Theory of Graphs and Networks
  • MATH 445— Introduction to Cryptography
  • MATH 446— Theory of Numbers
  • MATH 447— Combinatorial Mathematics
  • CSC 473— Automata, Grammars and Languages ^(*)
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 401A, MATH 401B, MATH 402, MATH 413, MATH 415A, MATH 443, MATH 445, MATH 446, MATH 447, MATH 464, MATH 468, MATH 475A, MATH 485, or  CSC 473.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

^(*) Students minoring in Computer Science may not double-dip courses with their math major. Students with a double major in Computer Science and Mathematics may be able to double-dip additional courses between the two majors, within reasonable limits. It is important to consult with advisors from both majors when planning your coursework to avoid graduation delays.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Economics or Business emphasis

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

This emphasis requires either

• an Economics Minor, or
• a Business Administration Minor, or
• a Finance Minor, or
• a Thematic Minor emphasizing courses from two or more disciplines/subject areas such as Economics, Business, and Finance, or
• a second major in one of the above or in Personal and Family Financial Planning.

The minor should be chosen in consultation with an advisor.

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• Two of the following four courses:
  
  • MATH 413— Linear Algebra
  • MATH 425B— Real Analysis of Several Variables
  • MATH 462— Financial Math
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• A 5^th 400-level MATH course, to be selected with approval from your math faculty advisor.  You may choose from the pre-approved list:  MATH 413, MATH 422,MATH 425B, MATH 432, MATH 454, MATH 456, MATH 462, MATH 466,  MATH 468, MATH 485.  If you prefer to select another course, you may do so ONLY if approved by your math faculty advisor.

Students completing this emphasis are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major emphasis before enrolling in 400-level courses.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

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Life Sciences emphasis

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

A minor or major in the biological sciences is required for this emphasis. Possibilities include Astrobiology, Biochemistry, Bioinformatics, Biology, Biosystems Engineering, Ecology & Evolutionary Biology, Environmental Sciences, Molecular & Cellular Biology, Physiology, Physiological Sciences, and Pre-Health Professions, or a thematic minor with a life sciences emphasis.  A second major in a life science area may also be used to fulfill the minor requirement.  Courses which may be of interest for your minor include: ECOL 320, ECOL 340, ECOL 426, ECOL 453, ECOL 480, ECOL 496J; MCB 315, MCB 410, MCB 411, MCB 422.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• One of the following two courses:
  • MATH 454— Ordinary Differential Equations and Stability Theory
  • MATH 456— Applied Partial Differential Equations
• MATH 464— Theory of Probability
• One of the following two courses:
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• MATH 485— Mathematical Modeling ^(*)

^(*) Students should plan to take MATH 485 in their final spring semester (it is only offered in spring semesters).  In addition to more typical prerequisites, MATH 485 requires completion of at least one 400-level MATH course (422, 454, 456, 464, or 475A).  Prerequisites also include linear algebra (313), differential equations (254 or 355), and a programming course.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.  Students planning to enroll in three MATH courses in a single semester are advised to talk to their math faculty advisor before finalizing their schedule. The Math Department requires that students enrolling in four or more MATH courses for a single term obtain permission from their math faculty advisor.  Note that special courses like Supplemental Instruction, Workshops, Teaching Assistantship enrollment, and Pedagogy courses for the Secondary Math Education Program are not counted toward this limit.

4. Statistics & Data Science Major Course Requirements

Overview

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Statistics & Data Science require the same set of supporting and core coursework. A minor in any subject outside the math department is required with this major.

The information and requirements given here apply to the 2019–2020 catalog. For other catalog years, please consult the archive.

The Academic Advising Report (ADVIP) gives complete degree requirements:

• B.A. Statistics & Data Science
• B.S. Statistics & Data Science

Note:  since this program was brand new for Fall 2018, the Advisement Reports may still have some issues to be worked out.  All SDS majors are expected to meet with an advisor in the Math Center at least once a semester.

Supporting Computer Science Requirement

All SDS majors are required to complete a computer programming course, regardless of the degree selected. Choose one course:^(*)

• CSC 110— Introduction to Computer Programming I
• ISTA 130— Computational Thinking and Doing

^(*)Either CSC 110 or ISTA 130 is recommended for most students. As an alternative, more advanced students may use CSC 120 to fill the requirement. Contact the Computer Science department for more information about placement into CSC 120.

Core Courses

• MATH 122A AND MATH 122B  ⁽¹⁾ or  MATH 125— Calculus I

• MATH 129— Calculus II

• MATH 223— Vector Calculus

• MATH 313— Introduction to Linear Algebra ⁽²⁾ 

• DATA 363— Introduction to Statistical Methods

• DATA 375— Introduction to Statistical Computing ⁽³⁾

• MATH 464— Theory of Probability ⁽⁴⁾

• MATH 466— Theory of Statistics

• DATA 467 — Applied Linear Models ⁽⁵⁾

• DATA 469 — Introduction to Data Science ⁽⁶⁾

• One upper-division statistics major elective.

 

⁽¹⁾MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. They are equivalent to the old MATH 124 course, which is no longer offered.

⁽²⁾ Either MATH 313 or MATH 310 may be used to fulfill this requirement in the SDS major. However, please note that 310 has a prerequisite of MATH 254. Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

⁽³⁾ DATA 375 was offered for the first time in Spring 2019; hereafter it will be offered every fall and spring semester. 

⁽⁴⁾ Students who have completed MATH 313 and MATH/DATA 363 AND are declared SDS majors or minors will receive assistance from the Math Center to enroll in MATH 464 for the 2018-19 and 2019-20 academic years, bypassing the MATH 323 prerequisite. Once there are enough SDS majors to support independent courses, we will open new versions with the appropriate prerequisites.

⁽⁵⁾ DATA 467 will be offered for the first time Fall 2019; hereafter it will be offered every fall semester. 

⁽⁶⁾ DATA 469 will be offered for the first time in Spring 2020; thereafter it will be offered every spring semester.

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Statistics & Data Science Major Elective Courses

The SDS major requires one upper-division elective course. The current courses that will be accepted toward this requirement are listed below. More course options will be added as the program grows; see your academic advisor for details.

Course options:

• DATA 367— Statistical Methods in Sports Analytics
• DATA 462— Financial Math
• DATA 468— Applied Stochastic Processes
• SIE 440— Survey of Optimization Methods