The University of Arizona

3. Math Major Course Requirements and Emphases

Undergraduate Requirements Archive → 2022/2023 Undergraduate Requirements → 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:

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.

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.

flow chart of core prerequisites (click image for downloadable PDF)

(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.

Catalog Requirements
prerequisite flowchart for applied emphasis (click image for downloadable PDF)

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

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

Major requirements:

(*) 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.

Catalog Requirementsprerequisite flowchart for comprehensive emphasis (click image for downloadable PDF)

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

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:

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.

Catalog Requirementsprerequisite flowchart for probability & statistics emphasis (click image for downloadable PDF)

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

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:

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.

Catalog Requirementsprerequisite flowchart for education emphasis (click image for downloadable PDF)

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

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:

(*) 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.

Catalog Requirementsprerequisite flowchart for computer science emphasis (click image for downloadable PDF)

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

A minor in computer science is required with this emphasis.

Major requirements:

(*) 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.

Catalog Requirementsprerequisite flowchart for economics/business emphasis (click image for downloadable PDF)

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

This emphasis requires either

The minor should be chosen in consultation with an advisor.

Major requirements:

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.

Catalog Requirementsprerequisite flowchart for life sciences emphasis (click image for downloadable PDF)

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

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:

(*) 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.

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