Program Overview
Mathematics, BS
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.
Students interested in Mathematics may also wish to consider the Bachelor of ScienceApplied Mathematics, Engineering, and Physics (BS AMEP).
How to Get in
Declaration
To declare a major in mathematics, a student must have completed the sequence MATH 221, MATH 222, and MATH 234, or the sequence MATH 375 and MATH 376, with a 2.500 GPA or better. Major advisors may waive this requirement for students with alternative coursework and experiences (e.g., transfer students). Students should meet with a math advisor before declaring in order to discuss course selection and major plan.
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 General Education Requirements
All undergraduate students at the University of Wisconsin-Madison are required to fulfill a minimum set of common university general education requirements to ensure that every graduate acquires the essential core of an undergraduate education. This core establishes a foundation for living a productive life, being a citizen of the world, appreciating aesthetic values, and engaging in lifelong learning in a continually changing world. Various schools and colleges will have requirements in addition to the requirements listed below.
- BreadthHumanities/Literature/Arts: 6 credits
- BreadthNatural Science: 4 to 6 credits, consisting of one 4- or 5-credit course with a laboratory component; or two courses providing a total of 6 credits
- BreadthSocial Studies: 3 credits
- Communication Part A & Part B
- Ethnic Studies
- Quantitative Reasoning Part A & Part B
College of Letters & Science Degree Requirements: Bachelor of Science (BS)
Students pursuing a Bachelor of Science degree in the College of Letters & Science must complete all of the requirements below. The College of Letters & Science allows this major to be paired with either the Bachelor of Arts or the Bachelor of Science degree requirements.
Bachelor of Science Degree Requirements
- Mathematics: Complete two courses of 3+ credits at the Intermediate or Advanced level in MATH, COMP SCI, or STAT subjects. A maximum of one course in each of COMP SCI and STAT subjects counts toward this requirement.
- Language: Complete the third unit of a language other than English.
- L&S Breadth: Complete:
- 12 credits of Humanities, which must include at least 6 credits of Literature; and
- 12 credits of Social Science; and
- 12 credits of Natural Science, which must include 6 credits of Biological Science and 6 credits of Physical Science.
- Liberal Arts and Science Coursework: Complete at least 108 credits.
- Depth of Intermediate/Advanced Coursework: Complete at least 60 credits at the Intermediate or Advanced level.
- Major: Declare and complete at least one major.
- Total Credits: Complete at least 120 credits.
- UW-Madison Experience: Complete both:
- 30 credits in residence, overall, and
- 30 credits in residence after the 86th credit.
- Quality of Work:
- 2.000 in all coursework at UWMadison
- 2.000 in Intermediate/Advanced level coursework at UWMadison
NonL&S students pursuing an L&S major
NonL&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 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.
The mathematics major requires 7 distinct courses for at least 21 credits as described below. Note that at most one course from each of the following groupings may be used to fulfill the minimum course and credit requirement (i.e., seven courses and at least 21 credits): Intro Linear Algebra (MATH 320, MATH 340, MATH 341, MATH 375), Intro Differential Equations (MATH 319, MATH 320, or MATH 376), and Intro Probability (MATH/STAT 309 or MATH/STAT 431).
Course Requirements
- Linear Algebra (complete one):
- MATH 341: Linear Algebra
- or MATH 320: Linear Algebra and Differential Equations
- or MATH 340: Elementary Matrix and Linear Algebra
- or MATH 375: Topics in Multi-Variable Calculus and Linear Algebra
- Analysis, Topology, Algebra (complete two):
- MATH 521: Analysis I
- MATH 541: Modern Algebra
- MATH 551: Elementary Topology
- Advanced MATH Elective (complete one):
- Complete at least one for three credits:
- MATH/COMP SCI 513: Numerical Linear Algebra
- MATH/COMP SCI 514: Numerical Analysis
- MATH 519: Ordinary Differential Equations
- MATH 521: Analysis I
- MATH 522: Analysis II
- MATH/COMP SCI/I SY E/STAT 525: Linear Optimization
- MATH 531: Probability Theory
- MATH 535: Mathematical Methods in Data Science
- MATH 540: Linear Algebra II
- MATH 541: Modern Algebra
- MATH 542: Modern Algebra
- MATH 551: Elementary Topology
- MATH 552: Elementary Geometric and Algebraic Topology
- MATH 561: Differential Geometry
- MATH 567: Modern Number Theory
- MATH 570: Fundamentals of Set Theory
- MATH/PHILOS 571: Mathematical Logic
- MATH 607: Topics in Mathematics Study Abroad
- MATH/B M I/BIOCHEM/BMOLCHEM 609: Mathematical Methods for Systems Biology
- MATH 616: Data-Driven Dynamical Systems, Stochastic Modeling and Prediction
- MATH 619: Analysis of Partial Differential Equations
- MATH 621: Introduction to Manifolds
- MATH 623: Complex Analysis
- MATH 627: Introduction to Fourier Analysis
- MATH 629: Introduction to Measure and Integration
- MATH/I SY E/OTM/STAT 632: Introduction to Stochastic Processes
- MATH 635: An Introduction to Brownian Motion and Stochastic Calculus
- MATH 681: Senior Honors Thesis
- MATH 682: Senior Honors Thesis
- MATH 691: Undergraduate Thesis
- MATH 692: Undergraduate Thesis
- MATH 698: Directed Study
- MATH 699: Directed Study
- Complete at least one for three credits:
- Additional MATH Elective to achieve 7 courses and 21 credits in the major:
- Choose from the following:
- MATH/STAT 431: Introduction to the Theory of Probability
- or MATH/STAT 309: Introduction to Probability and Mathematical Statistics I
- MATH/STAT 310: Introduction to Probability and Mathematical Statistics II
- MATH 319: Techniques in Ordinary Differential Equations
- or MATH 376: Topics in Multi-Variable Calculus and Differential Equations
- MATH 321: Applied Mathematical Analysis 1: Vector and Complex Calculus
- MATH 322: Applied Mathematical Analysis 2: Partial Differential Equations
- MATH 390: Undergraduate Research with Madison Experimental Mathematics Lab
- MATH 407: Topics in Mathematics Study Abroad
- MATH 415: Applied Dynamical Systems, Chaos and Modeling
- MATH 421: The Theory of Single Variable Calculus
- MATH/COMP SCI/I SY E 425: Introduction to Combinatorial Optimization
- MATH/COMP SCI/E C E 435: Introduction to Cryptography
- MATH 443: Applied Linear Algebra
- MATH 444: Graphs and Networks in Data Science
- MATH 461: College Geometry I
- MATH 467: Introduction to Number Theory
- MATH/HIST SCI 473: History of Mathematics
- MATH/COMP SCI/STAT 475: Introduction to Combinatorics
- MATH 490: Undergraduate Seminar
- MATH 491: Topics in Undergraduate Mathematics
- MATH/COMP SCI 513: Numerical Linear Algebra
- MATH/COMP SCI 514: Numerical Analysis
- MATH 519: Ordinary Differential Equations
- MATH 521: Analysis I
- MATH 522: Analysis II
- MATH/COMP SCI/I SY E/STAT 525: Linear Optimization
- MATH 531: Probability Theory
- MATH 535: Mathematical Methods in Data Science
- MATH 540: Linear Algebra II
- MATH 541: Modern Algebra
- MATH 542: Modern Algebra
- MATH 551: Elementary Topology
- MATH 552: Elementary Geometric and Algebraic Topology
- MATH 561: Differential Geometry
- MATH 567: Modern Number Theory
- MATH 570: Fundamentals of Set Theory
- MATH/PHILOS 571: Mathematical Logic
- MATH 607: Topics in Mathematics Study Abroad
- MATH/B M I/BIOCHEM/BMOLCHEM 609: Mathematical Methods for Systems Biology
- MATH 616: Data-Driven Dynamical Systems, Stochastic Modeling and Prediction
- MATH 619: Analysis of Partial Differential Equations
- MATH 621: Introduction to Manifolds
- MATH 623: Complex Analysis
- MATH 627: Introduction to Fourier Analysis
- MATH 629: Introduction to Measure and Integration
- MATH/I SY E/OTM/STAT 632: Introduction to Stochastic Processes
- MATH 635: An Introduction to Brownian Motion and Stochastic Calculus
- MATH 681: Senior Honors Thesis
- MATH 682: Senior Honors Thesis
- MATH 691: Undergraduate Thesis
- MATH 692: Undergraduate Thesis
- MATH 698: Directed Study
- MATH 699: Directed Study
- Choose from the following:
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.
- 15 credits in MATH, taken on the UWMadison 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:
- MATH 521 and MATH 522: Analysis I and Analysis II (Taken for Honors)
- MATH 541 and MATH 542: Modern Algebra and Modern Algebra (Taken for Honors)
- Select at least two more courses from MATH 500 through MATH 641. These courses must be taken for honors.
- Select one of these Capstone projects:
- MATH 681 and MATH 682: Senior Honors Thesis and Senior Honors Thesis (For a total of 6 credits)
- or
- A sequence of two upper-level mathematics courses deemed acceptable by the Mathematics Honors advisor
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.
Mathematics Major - Bachelor of Arts/Science Degree
Freshman
- Fall: MATH 221, Communication A, Foreign Language (if needed), Literature Breadth
- Spring: MATH 222, Ethnic Studies, Foreign Language (if needed), Literature Breadth
Sophomore
- Fall: MATH 234, Communication B, Humanities Breadth, Physical Science Breadth, Elective
- Spring: MATH 341, 300/400-level MATH, Humanities Breadth, Physical Sciences Breadth, Elective
Junior
- Fall: 300/400-level MATH, Analysis, Algebra, or Topology, Social Sciences Breadth, Biological Sciences Breadth, Elective
- Spring: 300/400-level MATH, Analysis, Algebra, or Topology, Social Sciences Breadth, Biological Sciences Breadth, Elective
Senior
- Fall: 500/600-level MATH elective, Social Science Breadth, Elective, Elective, Elective
- Spring: Social Sciences Breadth, Elective, Elective, Elective
Total Credits 120
Three-Year Plan
This Sample Three-Year Plan is a tool to assist students and their advisor(s). Students should use it along with their DARS report, the Degree Planner, and Course Search & Enroll tools to make their own three-year plan based on their placement scores, credit for transferred courses and approved examinations, and individual interests.
Three-year plans may vary considerably from student to student, depending on their individual preparation and circumstances. Students interested in graduating in three years should meet with an advisor as early as possible to discuss feasibility, appropriate course sequencing, post-graduation plans (careers, graduate school, etc.), and opportunities they might forgo in pursuit of a three-year graduation plan.
Departmental Expectations
Historically, students who have successfully completed a three-year undergraduate degree with a major in Mathematics have the following qualifications: a minimum of 29 advanced standing credits, which include completion of the following with either course credit or via placement examination:
- MATH 221 and MATH 222
- Communication Part A
- 3-4 units of foreign language
Therefore, the plan below assumes these requirements, but none other. When considering the plan below, students should note the following:
- Advanced standing credits may satisfy Ethnic Studies, Communication Part B, and/or Letters & Science Breadth degree requirements which are listed in the plan.
- At least 26 of the non-MATH credits must be at the Intermediate or Advanced level.
- Consider using the elective space in the plan as follows: additional major or certificate, career readiness, graduate school preparation, and other personal interests.
First Year
- Fall: MATH 234, Ethnic Studies, Communication B, Biological Science Breadth, Biological Science Breadth, Physical Science Breadth
- Spring: MATH Linear Algebra, 300/400-level MATH, Physical Science Breadth, Foreign Language (if needed for the BA) or Elective
Second Year
- Fall: 300/400-level MATH, Analysis, Algebra, or Topology, Literature Breadth, Social Science Breadth, Elective (Intermediate or Advanced level)
- Spring: 300/400-level MATH, Analysis, Algebra, or Topology, Literature Breadth, Social Science Breadth, Elective (Intermediate or Advanced level)
Third Year
- Fall: 500/600-level MATH elective, Social Science Breadth, Humanities Breadth (Intermediate or Advanced level), Elective (Intermediate or Advanced level), Elective (Intermediate or Advanced level)
- Spring: Humanities Breadth (Intermediate or Advanced level), Social Science Breadth (Intermediate or Advanced level), Elective (Intermediate or Advanced level), Elective (Intermediate or Advanced level)
Total Credits 91
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.
- MATH 341: Linear Algebra
- or MATH 375: Topics in Multi-Variable Calculus and Linear Algebra
- MATH 321 and MATH 322: Applied Mathematical Analysis 1: Vector and Complex Calculus and Applied Mathematical Analysis 2: Partial Differential Equations
- MATH 421: The Theory of Single Variable Calculus
- MATH 467: Introduction to Number Theory
Graduate Study
Students preparing for graduate work in mathematics should take the following courses:
- MATH 341: Linear Algebra
- or MATH 375: Topics in Multi-Variable Calculus and Linear Algebra
- MATH 521: Analysis I
- MATH 522: Analysis II
- MATH 541: Modern Algebra
- MATH 542: Modern Algebra
- MATH 551: Elementary Topology
- 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.
For information about opportunities related to possible careers with a Mathematics major, refer to our page under Career Advising.
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.
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.