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.
Graduating math majors 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 which use mathematics, including some in the social and biological sciences as well as in engineering and the physical sciences, are interested in attracting math majors into their graduate programs. Math Ph.D.'s obtain academic positions at the college and university level and nonacademic positions entailing consulting and research. The math major requirements are flexible enough to allow preparation for various goals, interests, and careers.
Students interested in mathematics might also consider the related degree program in applied mathematics, engineering and physics.
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. Advising information can be found in the Advising and Careers link.
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. Consult your advisor for assistance, as needed. For additional information, see the university Undergraduate General Education Requirements section of the Guide.
General Education 
* The mortarboard symbol appears before the title of any course that fulfills one of the Communication Part A or Part B, Ethnic Studies, or Quantitative Reasoning Part A or Part B requirements. 
College of Letters & Science Degree Requirements: Bachelor of Arts (B.A.)
Students pursuing a bachelor of arts 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 a bachelor of arts or a bachelor of science curriculum.
Bachelor of Arts degree requirements
Mathematics  Complete the University General Education Requirements for Quantitative Reasoning A (QRA) and Quantitative Reasoning B (QRB) coursework. 
Foreign Language 

L&S Breadth 

Liberal Arts and Science Coursework  Complete at least 108 credits. 
Depth of Intermediate/Advanced work  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. 
UWMadison 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 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 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, MATH 331, or MATH/STAT 431).
Mathematics Major requirements
At least seven MATH courses for at least 21 credits are required for the major as follows^{1}:
Code  Title  Credits 

Linear Algebra (complete one): ^{2}  3  
Linear Algebra  
or MATH 320  Linear Algebra and Differential Equations  
or MATH 340  Elementary Matrix and Linear Algebra  
or MATH 375  Topics in MultiVariable Calculus and Linear Algebra  
Analysis, Topology, Algebra (complete two):  6  
Analysis I  
Modern Algebra  
Elementary Topology  
Advanced MATH Elective (complete one):  3  
Numerical Linear Algebra  
Numerical Analysis  
Ordinary Differential Equations  
Analysis I  
Analysis II  
Linear Optimization  
Probability Theory  
Mathematical Methods in Data Science  
Linear Algebra II  
Modern Algebra  
Modern Algebra  
Elementary Topology  
Elementary Geometric and Algebraic Topology  
Differential Geometry  
Modern Number Theory  
Fundamentals of Set Theory  
Mathematical Logic  
Stochastic Methods for Biology  
Topics in Mathematics Study Abroad  
MATH 608  
Mathematical Methods for Systems Biology  
Analysis of Partial Differential Equations  
Introduction to Manifolds  
Complex Analysis  
Introduction to Fourier Analysis  
Introduction to Measure and Integration  
Introduction to Stochastic Processes  
An Introduction to Brownian Motion and Stochastic Calculus  
Introduction to ErrorCorrecting Codes  
Senior Honors Thesis  
Senior Honors Thesis  
Undergraduate Thesis  
Undergraduate Thesis  
Directed Study  
Directed Study  
Additional MATH Elective to achieve 7 courses and 21 credits in the major  9  
Introduction to Probability and Mathematical Statistics I ^{3}  
or MATH 331  An Introduction to Probability and Markov Chain Models  
Introduction to the Theory of Probability  
Introduction to Probability and Mathematical Statistics II  
Techniques in Ordinary Differential Equations ^{4}  
or MATH 376  Topics in MultiVariable Calculus and Differential Equations  
Applied Mathematical Analysis  
Applied Mathematical Analysis  
Topics in Mathematics Study Abroad  
Applied Dynamical Systems, Chaos and Modeling  
The Theory of Single Variable Calculus  
Introduction to Combinatorial Optimization  
Introduction to Cryptography  
Introduction to Modern Algebra  
Applied Linear Algebra  
College Geometry I  
Introduction to Number Theory  
History of Mathematics  
Introduction to Combinatorics  
Undergraduate Seminar  
Topics in Undergraduate Mathematics  
Numerical Linear Algebra  
Numerical Analysis  
Ordinary Differential Equations  
Analysis I  
Analysis II  
Linear Optimization  
Probability Theory  
Mathematical Methods in Data Science  
Linear Algebra II  
Modern Algebra  
Modern Algebra  
Elementary Topology  
Elementary Geometric and Algebraic Topology  
Differential Geometry  
Modern Number Theory  
Fundamentals of Set Theory  
Mathematical Logic  
Stochastic Methods for Biology  
Topics in Mathematics Study Abroad  
MATH 608  
Mathematical Methods for Systems Biology  
Analysis of Partial Differential Equations  
Introduction to Manifolds  
Complex Analysis  
Introduction to Fourier Analysis  
Introduction to Measure and Integration  
Introduction to Stochastic Processes  
An Introduction to Brownian Motion and Stochastic Calculus  
Introduction to ErrorCorrecting Codes  
Senior Honors Thesis  
Senior Honors Thesis  
Undergraduate Thesis  
Undergraduate Thesis  
Directed Study  
Directed Study  
Total Credits  21 
Residence and Quality of Work
 2.000 GPA in all MATH and major courses.
 2.000 GPA on 15 upperlevel major credits, taken in residence.^{5}
 15 credits in MATH, taken on the UW–Madison campus.
Named Options
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 I and Analysis II (Taken for Honors) ^{6}  
Modern Algebra and Modern Algebra (Taken for Honors) ^{6}  
Select at least two more courses from MATH 500 through MATH/E C E 641. These course must be taken for honors. The following will usually be one of the courses: ^{7}  
Elementary Topology  
Select one of these Capstone projects:  
Senior Honors Thesis and Senior Honors Thesis (For a total of 6 credits)  
or  
A sequence of two upperlevel mathematics courses deemed acceptable by the Mathematics Honors advisor ^{7} 
Footnotes
 ^{ 1 }
A course may only apply once toward the courses/credits required for the major. Thus, a course used to meet the Analysis, Topology and Algebra requirement may not also be used to meet the requirement for MATH 500699 requirement and a course used to meet the MATH 500699 requirement may not also be used in the Additional Math requirement.
 ^{ 2 }
Only one of these courses will be used to fulfill minimum course/credit requirements for the major: MATH 320, MATH 340, MATH 341, MATH 375
 ^{ 3 }
At most one course in Introductory Probability may be used to fulfill the course/credit requirements for the major: MATH/STAT 309 and MATH/STAT 431.
 ^{ 4 }
At most one course in Elementary Differential Equations may be used to fulfill the course/credit requirements for the major: MATH 319, MATH 320, MATH 376.
 ^{ 5 }
MATH courses numbered 307–699 are considered upper level in the major.
 ^{ 6 }
At least one of the two sequences (MATH 521–MATH 522 or MATH 541–MATH 542) must be completed prior to enrolling in the Capstone project.
 ^{ 7 }
Chosen in consultation with the Mathematics Honors advisor.
University Degree Requirements
Total Degree  To receive a bachelor's degree from UW–Madison, students must earn a minimum of 120 degree credits. The requirements for some programs may exceed 120 degree credits. Students should consult with their college or department advisor for information on specific credit requirements. 
Residency  Degree candidates are required to earn a minimum of 30 credits in residence at UW–Madison. "In residence" means on the UW–Madison campus with an undergraduate degree classification. “In residence” credit also includes UW–Madison courses offered in distance or online formats and credits earned in UW–Madison Study Abroad/Study Away programs. 
Quality of Work  Undergraduate students must maintain the minimum grade point average specified by the school, college, or academic program to remain in good academic standing. Students whose academic performance drops below these minimum thresholds will be placed on academic probation. 
 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 nonexperts.
Sample FourYear Plan
This Sample FourYear 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 fouryear plan based on their placement scores, credit for transferred courses and approved examinations, and individual interests. As students become involved in athletics, honors, research, student organizations, study abroad, volunteer experiences, and/or work, they might adjust the order of their courses to accommodate these experiences. Students will likely revise their own fouryear plan several times during college.
Mathematics Major  Bachelor of Arts/Science Degree
Freshman  

Fall  Credits  Spring  Credits 
MATH 221^{1,2}  5  MATH 222^{2}  4 
Communication A  3  Ethnic Studies  3 
Foreign Language (if needed)  4  Foreign Language (if needed)  4 
Literature Breadth  3  Literature Breadth  3 
15  14  
Sophomore  
Fall  Credits  Spring  Credits 
MATH 234  4  MATH 341  3 
Communication B  3  Intermediate MATH^{3}  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 
Intermediate MATH^{3}  3  Intermediate MATH^{3}  3 
Advanced MATH^{4}  3  Advanced MATH^{4}  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 
Advanced MATH^{4}  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 
 ^{ 1 }
Math majors will naturally complete Quantitative Reasoning requirements with the introductory calculus courses required to declare the major.
 ^{ 2 }
Declaration of the Mathematics major requires a 2.500 cumulative GPA across the introductory calculus sequence. Students that are unable to establish a GPA for any courses in the introductory calculus sequence are encouraged to speak with a math major advisor as soon as possible.
 ^{ 3 }
An intermediate level math course is any numbered above 306 excluding MATH 320, MATH 340, or MATH 341, or MATH/CURRIC 471.
 ^{ 4 }
An advanced level MATH course is any numbered above 500.
Sample ThreeYear Plan
This Sample ThreeYear 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 threeyear plan based on their placement scores, credit for transferred courses and approved examinations, and individual interests.
Threeyear 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, postgraduation plans (careers, graduate school, etc.), and opportunities they might forgo in pursuit of a threeyear graduation plan.
Departmental Expectations
Historically, students who have successfully complete 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:
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. In this case, students should adjust their plan by reorganizing the remaining degree requirements using the following priorities: 1) Ethnic Studies and Communication Part B (obligatory in the first year); 2) Physical, Biological, and Social Science Breadth (which may be prerequisites for more advanced electives); 3) Humanities and Literature. Remaining schedule space should be considered electives.
 At least 26 of the nonMATH 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  Credits  Spring  Credits 
MATH 234  4  MATH Linear Algebra  3 
Ethnic Studies  3  Intermediate MATH  3 
Communication B  3  Physical Science Breadth  3 
Biological Science Breadth  3  Biological Science Breadth  3 
Physical Science Breadth  3  Foreign Language (if needed for the B.A.) or Elective  3 
16  15  
Second Year  
Fall  Credits  Spring  Credits 
Intermediate MATH  3  Advanced MATH  3 
Advanced MATH  3  Intermediate MATH  3 
Literature Breadth  3  Literature Breadth  3 
Social Science Breadth  3  Social Science Breadth  3 
Elective (Intermediate or Advanced level)  3  Elective (Intermediate or Advanced level)  3 
15  15  
Third Year  
Fall  Credits  Spring  Credits 
Advanced MATH  3  Humanities Breadth (Intermediate or Advanced level)  3 
Social Science Breadth  3  Social Science Breadth (Intermediate or Advanced level)  3 
Humanities Breadth  3  Elective (Intermediate or Advanced level)  9 
Elective (Intermediate or Advanced level)  6  
15  15  
Total Credits 91 
Advising
Students who are interested in the math major should visit a faculty advisor. During the fall and spring semesters faculty advisors have regular office hours. Students are encouraged to make appointments, but drop in advising is also welcome. During the winter break and the summer semester there are no fixed advising hours. Students should contact one of the advisors directly to set up an appointment. The current list of advisors, their schedule of office hours, and available appointments can be found at the Math advising page.
For advice on college algebra, precalculus, and calculus, see the placement advising pages of the department.
Transition courses
All majors are required to complete at least one of the following. It is suggested that majors (and those interested in the major) complete such a course as soon in their academic career as possible.
Code  Title  Credits 

Linear Algebra  
Applied Mathematical Analysis and Applied Mathematical Analysis  
Topics in MultiVariable Calculus and Linear Algebra  
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 MultiVariable Calculus and Linear Algebra  
MATH 521  Analysis I  3 
MATH 522  Analysis II  3 
MATH 541  Modern Algebra  3 
MATH 542  Modern Algebra  3 
MATH 551  Elementary 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 Ph.D. program should acquire a reading knowledge of at least one foreign language as early as possible. For mathematics study, the most useful languages are French, German, and Russian.
Careers
In recent years graduating math majors 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 which use mathematics, including the social and biological sciences as well as in engineering and the physical sciences, are interested in attracting math majors into their graduate programs. Math Ph.D.'s obtain academic positions at the college and university level and nonacademic positions entailing consulting and research. The math major requirements are flexible enough to allow preparation for various goals.
L&S career resources
Every L&S major opens a world of possibilities. SuccessWorks at the College of Letters & Science helps students turn the academic skills learned in their major, certificates, and other coursework into fulfilling lives after graduation, whether that means jobs, public service, graduate school or other career pursuits.
In addition to providing basic support like resume reviews and interview practice, SuccessWorks offers ways to explore interests and build career skills from their very first semester/term at UW all the way through graduation and beyond.
Students can explore careers in oneonone advising, try out different career paths, complete internships, prepare for the job search and/or graduate school applications, and connect with supportive alumni and even employers in the fields that inspire them.
 SuccessWorks
 Set up a career advising appointment
 Enroll in a Career Course  a great idea for first and secondyear students:
 INTERLS 210 L&S Career Development: Taking Initiative (1 credit)
 INTERLS 215 Communicating About Careers (3 credits, fulfills Comm B General Education Requirement)
 Learn about internships and internship funding
 Activate your Handshake account to apply for jobs and internships from 200,000+ employers recruiting UWMadison students
 Learn about the impact SuccessWorks has on students' lives
Professors:
Anderson, David F Andrews, Uri Angenent, Sigurd B. Arinkin, Dima Caldararu, Andrei Craciun, Gheorghe Denisov, Sergey Ellenberg, Jordan Erman, Daniel M Feldman, Mikhail Gong, Xianghong Gurevich, Shamgar Kent, Autumn Exum (Graduate Director) Lempp, Steffen MariBeffa, Gloria Maxim, Laurentiu Miller, Joseph S Paul, Sean T Poltoratski, Alexei Roch, Sebastien Rycroft, Christopher Seeger, Andreas Seppalainen, Timo (Chair) Smith, Leslie M. Soskova, Mariya Spagnolie, Saverio Stechmann, Sam Stovall, Betsy Street, Brian Thomas (Associate Chair) Terwilliger, Paul M. Thiffeault, JeanLuc Valko, Benedek (Undergraduate Director) Waleffe, Fabian Yang, Tonghai
Associate Professors:
Dymarz, Tullia Maria Guo, Shaoming Ifrim, Mihaela Kim, Chanwoo Li, Qin Marshall, Simon Lindsay Tran, Hung Vinh Wang, Botong
Assistant Professors:
Apisa, Paul Chen, Nan Cochran, Amy Fabien, Maurice Kemeny, Michael L J Lawrence, Brian Loving, Marissa Lyu, Hanbaek Rodriguez, Jose Israel Shankar, Ananth Shcherbyna, Tetyana Shen, Hao Uyanik, Caglar Waldron, Alex Wu, Chenxi ZepedaNunez, Leonardo Zimmer, Andrew
Academic staff:
Benguria Andrews, Soledad (Calculus Coordinator) Grizzard, Robert (Associate Director for Instructional Programs) Ivanov, Mikhail (Math Learning Center Instructor) Jackson, Billy (Director of the Precalculus Program) Keller, Mitch (Associate Director of Undergraduate Programs) Kwon, Oh Hoon (Associate Director of the Precalculus Program) Lindsey, Melissa (Director of Instructional Support) Phillipson, Kaitlyn (Linear Algebra Coordinator) Rineck, Leah (Math Learning Center Director) Williams, Cassie (Associate Director of Instructional and Professional Development) Work, Grace (Associate Director of Undergraduate Research)
Enrollment Coordinator:
Kyle Martinez