Mathematics is about understanding the world through studies of quantity, structure, pattern, and change to create logical solutions that make life more meaningful and more beautiful. Mathematics bridges the humanities and the sciences. Its position among the humanities is based on the study of mathematics as one of the liberal arts for more than two thousand years. The natural sciences have invariably turned to mathematics for techniques needed to explore the consequences of scientific theories. In the last few decades, social scientists have increasingly found higher mathematics of value in their training and research. Still an expanding subject, mathematics is a part of more new and challenging frontiers than at any time in its long history, with many new fields, from data science to quantum computing, requiring new techniques and inspiring ideas for exploration.
The Mathematics major requirements include exposure to at least two areas of advanced mathematics. The program is ideal for any student who has a broad interest in mathematics both pure and applied, and functions well as a standalone or complementary program. The Mathematics major also offers six named options for students interested in pursuing an applied focus area outside of mathematics as part of their major.
Students interested in Mathematics may also wish to consider the Bachelor of Science—Applied Mathematics, Engineering, and Physics (BS AMEP).
How to Get in
| Requirements | Details |
|---|---|
| How to get in | No application required. All students who meet the requirements listed below are eligible to declare. For information on how to declare, see Advising & Careers. |
| Courses required to get in | Students must complete preparatory work in Calculus with either: If Calculus was not taken in-residence at UW–Madison, students must complete a course in Linear Algebra: |
| GPA requirements to get in | Students must earn either:
Only courses completed in-residence at UW–Madison are eligible for computation in the GPA or consideration on a graded basis. |
| Credits required to get in | None. |
| Other | Students may have non-residence credit for the courses required for eligibility. These students should consult with the Mathematics department on an appropriate MATH course to complete in-residence prior to declaring the major. Students must earn a grade of BC or better in that course. |
Students who are declared in the Bachelor of Science-Applied Mathematics, Engineering, and Physics degree may not be declared in the Mathematics for Physical and Biological Sciences named option.
Students declared in the Mathematics certificate may not be declared in the Mathematics major at the same time. Students who wish to declare this major must first cancel their declaration in the Mathematics certificate.
University Requirements
All undergraduate students must complete both the following Core General Education (Core GenEd) and University Degree and Quality of Work requirements. The requirements below apply to students whose first term at UW-Madison or whose earliest post-high school college attendance at any institution is Summer 2026 or later.
Students whose first term at UW-Madison or whose earliest post-high school college attendance at any institution occurred before Summer 2026 should refer to the archived Guide for the requirements that apply to them.
Core General Education (Core GenEd) Requirements
| Civics & Perspectives | 3 credits of Civics & Perspectives coursework. |
| Communication & Literacy | 6 credits of Communication & Literacy coursework. This requirement may be partially satisfied by a qualifying placement test score. More information: https://go.wisc.edu/qualifyingenglishplacement |
| Humanities & Arts | 6 credits of Humanities & Arts coursework. |
| Mathematics & Quantitative Reasoning | 6 credits of Mathematics & Quantitative Reasoning coursework. This requirement may be partially satisfied by a qualifying placement test score. More information: https://go.wisc.edu/qualifyingmathplacement |
| Natural Science & Wellness | Complete both:
|
| Social & Behavioral Science | 3 credits of Social & Behavioral Science coursework. |
| Total Credits | 30 credits. |
For more information see the policy.
University Degree and Quality of Work Requirements
All undergraduate degree recipients must complete the following minimum requirements. Requirements for some programs will exceed these requirements; see program requirements for additional information.
| Total Degree | 120 degree credits. |
| Residency | Complete 30 credits in residence. A course is considered “in residence” if it is taken when in undergraduate degree-seeking status and:
|
| Quality of Work | Achieve at least the minimum grade point average specified by the school, college, and/or academic program. |
| Math | Demonstrate minimal mathematics competence by: |
| English Language | If required to take the UW-Madison English as a Second Language Assessment Test (MSN-ESLAT), demonstrate minimal English language competence by:
|
| Language | Complete one:
|
| Major Declaration | Declare and complete the requirements for at least one major. |
College of Letters & Science Degree Requirements: Bachelor of Arts (BA)
Students pursuing a Bachelor of Arts degree in the College of Letters & Science must complete all of the requirements below. Some courses satisfy more than one L&S degree requirement (visit College of Letters & Science: Requirements for details).
This major can be paired with either the Bachelor of Arts or Bachelor of Science degree requirements.
Bachelor of Arts Degree Requirements
| Communication | Complete both:
|
| Quantitative Reasoning | Complete both:
|
| Ethnic Studies | one 3+ credit course with the Ethnic Studies designation |
| Language | Complete either:
|
| L&S Breadth: Humanities | Complete 12 credits with the Humanities or Literature designation, which must include at least 6 credits with the Literature designation. |
| L&S Breadth: Social Sciences | Complete 12 credits with the Social Science designation. |
| L&S Breadth: Natural Sciences | Complete 12 credits with the Natural Science, Biological Science, or Physical Science designations, which must include both:
|
| Liberal Arts and Science (LAS) Coursework | at least 108 credits |
| Depth of Intermediate/Advanced work | at least 60 credits at the Intermediate or Advanced level |
| Major | Declare and complete at least one major. |
| Total Credits | at least 120 credits |
| UW-Madison Experience |
|
| Quality of Work |
|
Non–L&S students pursuing an L&S major
Non–L&S students who have permission from their School/College to pursue an additional major within L&S only need to fulfill the major requirements. They do not need to complete the L&S Degree Requirements above.
Requirements for the Major
The requirements below are for the standard Mathematics major. The Mathematics major also offers six named options for students interested in pursuing an applied focus area outside of mathematics as part of their major.
At least seven MATH courses for at least 21 credits are required for the major as follows:
Linear Algebra
Complete one course from the list below. Only one of these courses will be used to fulfill minimum course/credit requirements for the major.
| Code | Title | Credits |
|---|---|---|
| MATH 341 | Linear Algebra | 3-5 |
| or MATH 320 | Linear Algebra and Differential Equations | |
| or MATH 340 | Elementary Matrix and Linear Algebra | |
| or MATH 345 | Linear Algebra and Optimization | |
| or MATH 375 | Topics in Multi-Variable Calculus and Linear Algebra | |
Transition to Advanced Mathematics
Complete one course or sequence from the list below. If a student takes MATH 341 or MATH 375 to complete the Linear Algebra requirement, they may also use that course for this requirement. The course and credits will only count once toward the course/credit requirements for the major.
| Code | Title | Credits |
|---|---|---|
| MATH 341 | Linear Algebra | 3-5 |
| or MATH 375 | Topics in Multi-Variable Calculus and Linear Algebra | |
| MATH 421 | The Theory of Single Variable Calculus | 3 |
| MATH 467 | Introduction to Number Theory | 3 |
| MATH 321 & MATH 322 | Applied Mathematical Analysis 1: Vector and Complex Calculus and Applied Mathematical Analysis 2: Partial Differential Equations | 6 |
Analysis, Topology, and Algebra
Complete two courses from:
| Code | Title | Credits |
|---|---|---|
| MATH 521 | Analysis I | 3 |
| MATH 541 | Modern Algebra 1 | 3 |
| MATH 551 | Point-Set Topology | 3 |
MATH Electives
Complete at least seven MATH courses for at least 21 credits to satisfy the overall requirements of the major by choosing additional MATH courses from the lists below. The courses chosen for MATH Electives must be distinct from the courses used for the requirements above.
Complete at least one course for at least three credits from the list of Advanced MATH Electives. The remaining courses required to reach the required minimum courses and credits may be chosen from either the list of Advanced MATH Elective courses or the Additional MATH Electives
Advanced MATH Elective
| Code | Title | Credits |
|---|---|---|
| MATH/COMP SCI 513 | Numerical Linear Algebra | 3 |
| MATH/COMP SCI 514 | Numerical Analysis | 3 |
| MATH 519 | Ordinary Differential Equations | 3 |
| MATH 521 | Analysis I | 3 |
| MATH 522 | Analysis II | 3 |
| MATH/COMP SCI/I SY E/STAT 525 | Linear Optimization | 3 |
| MATH 531 | Probability Theory | 3 |
| MATH 535 | Mathematical Methods in Data Science | 3 |
| MATH 540 | Linear Algebra II | 3 |
| MATH 541 | Modern Algebra 1 | 3 |
| MATH 542 | Modern Algebra 2 | 3 |
| MATH 551 | Point-Set Topology | 3 |
| MATH 552 | Introduction to Algebraic Topology | 3 |
| MATH 561 | Differential Geometry | 3 |
| MATH 567 | Modern Number Theory | 3 |
| MATH 570 | Fundamentals of Set Theory | 3 |
| MATH/PHILOS 571 | Mathematical Logic | 3 |
| MATH 607 | Study Abroad: Proof-based Advanced Mathematics | 1-5 |
| MATH/B M I/BIOCHEM/BMOLCHEM 609 | Mathematical Methods for Systems Biology | 3 |
| MATH 616 | Data-Driven Dynamical Systems, Stochastic Modeling and Prediction | 3 |
| MATH 619 | Analysis of Partial Differential Equations | 3 |
| MATH 621 | Introduction to Manifolds | 3 |
| MATH 623 | Complex Analysis | 3 |
| MATH 627 | Introduction to Fourier Analysis | 3 |
| MATH 629 | Introduction to Measure and Integration | 3 |
| MATH/I SY E/OTM/STAT 632 | Introduction to Stochastic Processes | 3 |
| MATH 635 | An Introduction to Brownian Motion and Stochastic Calculus | 3 |
| MATH 681 | Senior Honors Thesis | 3 |
| MATH 682 | Senior Honors Thesis | 3 |
| MATH 691 | Undergraduate Thesis | 2-4 |
| MATH 692 | Undergraduate Thesis | 2-4 |
| MATH 698 | Directed Study | 1-3 |
| MATH 699 | Directed Study | 1-6 |
Additional MATH Electives
| Code | Title | Credits |
|---|---|---|
| MATH/STAT 431 | Introduction to the Theory of Probability | 3 |
| or MATH/STAT 309 | Introduction to Probability and Mathematical Statistics I | |
At most one course in Introductory Probability (STAT/MATH 309 and MATH/STAT 431) may be used to fulfill the course/credit requirements for the major. | ||
| MATH/STAT 310 | Introduction to Probability and Mathematical Statistics II | 3 |
| MATH 319 | Techniques in Ordinary Differential Equations | 3 |
| or MATH 376 | Topics in Multi-Variable Calculus and Differential Equations | |
| MATH 321 | Applied Mathematical Analysis 1: Vector and Complex Calculus | 3 |
| MATH 322 | Applied Mathematical Analysis 2: Partial Differential Equations | 3 |
| MATH 390 | Undergraduate Research with Madison Experimental Mathematics Lab | 3 |
MATH 390 will only count once toward the major requirements. | ||
| MATH 407 | Study Abroad: Advanced Mathematics | 1-5 |
| MATH 415 | Applied Dynamical Systems, Chaos and Modeling | 3 |
| MATH 421 | The Theory of Single Variable Calculus | 3 |
| MATH/COMP SCI/I SY E 425 | Introduction to Combinatorial Optimization | 3 |
| MATH/COMP SCI/E C E 435 | Introduction to Cryptography | 3 |
| MATH 443 | Applied Linear Algebra | 3 |
| MATH 444 | Graphs and Networks in Data Science | 3 |
| MATH 461 | College Geometry I | 3 |
| MATH 467 | Introduction to Number Theory | 3 |
| MATH/HIST SCI 473 | History of Mathematics | 3 |
| MATH/COMP SCI/STAT 475 | Introduction to Combinatorics | 3 |
| MATH 490 | Undergraduate Seminar | 1-3 |
| MATH 491 | Topics in Undergraduate Mathematics | 3 |
Residence and Quality of Work
- 2.000 GPA in all MATH and major courses.
- 2.000 GPA on 15 upper-level major credits, taken in residence.
- MATH courses numbered 307–699 are considered upper level in the major.
- 15 credits in MATH, taken on the UW–Madison campus.
Named Options
Mathematics: Mathematics for Data Science
Mathematics: Mathematics for Economics and Finance
Mathematics: Mathematics for Programming and Computing
Mathematics: Mathematics for Secondary Education
Mathematics: Mathematics for Statistical Analysis and Risk Assessment
Mathematics: Mathematics for the Physical and Biological Sciences
Honors in the Major
Students may declare Honors in the Major in consultation with the Mathematics Honors advisor; this should be done by the start of the junior year. Honors in the major is not available in any Named Option program.
Honors in the Mathematics Major Requirements
To earn Honors in the Major, students must satisfy both the requirements for the mathematics major (above) and the following additional requirements:
- Earn a 3.300 University GPA
- Earn a 3.300 GPA for all MATH courses, and all courses accepted in the major
- Complete the following courses, with individual grades of B or better:
| Code | Title | Credits |
|---|---|---|
| Analysis and Algebra | ||
| Analysis I and Analysis II (Taken for Honors) | ||
| Modern Algebra 1 and Modern Algebra 2 (Taken for Honors) | ||
| Additional Advanced MATH Courses | ||
Complete at least two additional courses from MATH 500 through MATH 680 selected in consultation with a Mathematics Honors advisor. These courses must be taken for Honors. | ||
The following will usually be one of the courses: | ||
| Point-Set Topology | ||
| Complete one Capstone project: | ||
| Senior Honors Thesis and Senior Honors Thesis (For a total of 6 credits.) | ||
or | ||
A sequence of two upper-level mathematics courses approved by a Mathematics Honors advisor | ||
At least one of the sequences MATH 521-MATH 522 or MATH 541-MATH 542 must be completed prior to enrolling in the Capstone project.
Learning Outcomes
- State, explain, and apply the principal results, definitions, and theorems of a wide collection of mathematical areas including at least one area of advanced undergraduate mathematics.
- Construct and evaluate mathematical proofs and arguments.
- Acquire a diverse set of skills and strategies in mathematical reasoning/problem solving.
- Use mathematics to model and analyze phenomena in other disciplines.
- Write, explain, and present mathematics to both experts and non-experts.
Four-Year Plan
This Four-Year Plan is only one way a student may complete an L&S degree with this major. Many factors can affect student degree planning, including placement scores, credit for transferred courses, credits earned by examination, and individual scholarly interests. In addition, many students have commitments (e.g., athletics, honors, research, student organizations, study abroad, work and volunteer experiences) that necessitate they adjust their plans accordingly. Informed students engage in their own unique Wisconsin Experience by consulting their academic advisors, Guide, DARS, and Course Search & Enroll for assistance making and adjusting their plan.
Mathematics Major - Bachelor of Arts/Science Degree
| Freshman | |||
|---|---|---|---|
| Fall | Credits | Spring | Credits |
| MATH 221 | 5 | MATH 222 | 4 |
| Communication A | 3 | Ethnic Studies | 3 |
| Language (if needed) | 4 | Language (if needed) | 4 |
| Literature Breadth | 3 | Literature Breadth | 3 |
| 15 | 14 | ||
| Sophomore | |||
| Fall | Credits | Spring | Credits |
| MATH 2341 | 4 | MATH 341 | 3 |
| Communication B | 3 | Required Transition to Advanced Math | 3 |
| Humanities Breadth | 3 | Humanities Breadth | 3 |
| Physical Science Breadth | 3 | Physical Sciences Breadth | 3 |
| Elective | 3 | Elective | 3 |
| 16 | 15 | ||
| Junior | |||
| Fall | Credits | Spring | Credits |
| 300/400-level MATH2 | 3 | 300/400-level MATH2 | 3 |
| Analysis, Algebra, or Topology | 3 | Analysis, Algebra, or Topology | 3 |
| Social Sciences Breadth | 3 | Social Sciences Breadth | 3 |
| Biological Sciences Breadth | 3 | Biological Sciences Breadth | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Senior | |||
| Fall | Credits | Spring | Credits |
| 500/600-level MATH elective | 3 | Social Sciences Breadth | 3 |
| Social Science Breadth | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Total Credits 120 | |||
Advising and Careers
Advising
Students who are interested in the Mathematics major should visit a faculty advisor. Information about current advisor availability is on the Math advising page.
For advice on college algebra, pre-calculus, and calculus, see the placement advising pages of the department.
Transition Courses
All majors are required to complete at least one of the following as the prerequisite for one or more proof-based 500-level courses required in the major. It is suggested that Mathematics-declared students (and those interested in the major) complete such a course as soon in their academic career as possible.
| Code | Title | Credits |
|---|---|---|
| Linear Algebra | ||
or MATH 375 | Topics in Multi-Variable Calculus and Linear Algebra | |
| Applied Mathematical Analysis 1: Vector and Complex Calculus and Applied Mathematical Analysis 2: Partial Differential Equations | ||
| The Theory of Single Variable Calculus | ||
| Introduction to Number Theory | ||
Graduate Study
Students preparing for graduate work in mathematics should take the following courses:
| Code | Title | Credits |
|---|---|---|
| MATH 341 | Linear Algebra | 3 |
| or MATH 375 | Topics in Multi-Variable Calculus and Linear Algebra | |
| MATH 521 | Analysis I | 3 |
| MATH 522 | Analysis II | 3 |
| MATH 541 | Modern Algebra 1 | 3 |
| MATH 542 | Modern Algebra 2 | 3 |
| MATH 551 | Point-Set Topology | 3 |
| or MATH 561 | Differential Geometry | |
| Select at least two other courses at the 500 level or higher | ||
Students who plan to enter a mathematics PhD program should acquire a reading knowledge of at least one language other than English as early as possible; the most useful languages are French, German, and Russian.
Careers
In recent years, students graduating with the Mathematics major have obtained employment in a variety of jobs in business, industry, and governmental agencies and also have obtained teaching positions at the secondary school level (such teaching positions normally require teaching certification). Others have continued their education at the graduate level in mathematics and other fields. Departments in a variety of fields that use mathematics, including the social and biological sciences as well as in engineering and the physical sciences, are interested in attracting Mathematics students into their graduate programs. Students with a Mathematics PhD obtain academic positions at the college and university level and nonacademic positions entailing consulting and research. The Mathematics major requirements are flexible enough to allow preparation for various goals.
For information about opportunities related to possible careers with a Mathematics major, refer to our Advising page under “Career Advising.”
Study Abroad
Learning in Letters & Science emphasizes discovery, growth, understanding different perspectives, and challenging yourself, which makes studying abroad an excellent fit for many L&S students: studyabroad.wisc.edu
As a university with global influence, we have more than 300 study abroad programs in over 80 countries. These vary in length, academic focus, teaching format, language requirements, cost, and level of independence. There are many programs to complement every major and any year of college (including the final semester)—and all meet UW–Madison’s high academic standards. Students admitted into Letters & Science can even choose a short program in the summer before they start college or their whole first year: studyabroad.wisc.edu/launch. Talk with your academic advisor about how studying abroad might fit with your academic plan.
SuccessWorks
SuccessWorks at the College of Letters & Science helps you turn the academic skills learned in your classes into a fulfilling life, guiding you every step of the way to securing jobs, internships, or admission to graduate school.
Through one-on-one career advising, events, and resources, you can explore career options, build valuable internship and research experience, and connect with supportive alumni and employers who open doors of opportunity.
- What you can do with your major (Major Skills & Outcomes Sheets)
- Make a career advising appointment
- Learn about internships and internship funding
- Try “Jobs, Internships, & How to Get Them,” an interactive guide in Canvas for enrolled UW–Madison students
Resources and Scholarships
The Department of Mathematics offers scholarships, awards, and prizes to students declared in the Mathematics major. Award applications are open during the spring semester so that award recipients may be selected before the end of spring semester and applied to fall enrollment.
Awards vary in scope and criteria. Some awards are open to students who exhibit financial need, while others are granted to students based on academic merit. Other awards are related to undergraduate research. Awards may be open to specific student populations such as early-career majors or those interested in a career as a teacher.
Students declared in the Mathematics major are encouraged to apply for any scholarships for which they meet the qualifications.