Mathematics is classified with both 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. Still an expanding subject, mathematics offers more new and challenging frontiers than at any time in its long history—with many new fields, requiring new techniques and ideas for exploration.
The place of mathematics among the sciences is well founded. 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.
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 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.
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 MATH 221, MATH 222, and MATH 234 with a 2.500 GPA or better. Major advisors may waive this requirement for students with alternative coursework and experiences. Students should meet with a math advisor before declaring in order to discuss course selection and major plan. Majors are provided with math advisor information at the math advising page.
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 Breadth and Degree Requirements: Bachelor of Science (B.S.)
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 a bachelor of arts or a bachelor of science curriculum. View a comparison of the degree requirements here.
Bachelor of Science DEGREE REQUIREMENTS
| Mathematics | Two (2) 3+ credits of intermediate/advanced level MATH, COMP SCI, STAT Limit one each: COMP SCI, STAT |
| Foreign Language | Complete the third unit of a foreign language Note: A unit is one year of high school work or one semester/term of college work. |
| L&S Breadth |
|
| Liberal Arts and Science Coursework | 108 credits |
| Depth of Intermediate/Advanced work | 60 intermediate or advanced credits |
| Major | Declare and complete at least one (1) major |
| Total Credits | 120 credits |
| UW-Madison Experience | 30 credits in residence, overall 30 credits in residence after the 90th credit |
| Minimum GPAs | 2.000 in all coursework at UW–Madison 2.000 in intermediate/advanced coursework at UW–Madison |
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 and do not need to complete the L&S breadth and degree requirements above. Please note that the following special degree programs are not considered majors so are not available to non-L&S-degree-seeking candidates:
- Applied Mathematics, Engineering and Physics (Bachelor of Science–Applied Mathematics, Engineering and Physics)
- Journalism (Bachelor of Arts–Journalism; Bachelor of Science–Journalism)
- Music (Bachelor of Music)
- Social Work (Bachelor of Social Work)
TRADITIONAL & FOCUSED math
There are two ways to complete a Mathematics major: the traditional or focused path. The traditional path emphasizes breadth in the field by requiring students to explore at least two areas of advanced mathematics. The focused path allows students to choose one area of mathematics (e.g., probability) or associated application field (e.g., bioinformatics) and choose a course plan which may combine courses offered by mathematics and other department. Both programs are flexible by design and course selection should be done with the guidance of an advisor. In particular, any focused major plan must be approved by an advisor prior to declaration.
REQUIREMENTS FOR THE MAJOR
traditional PATH
The traditional mathematics program requires exposure to at least two areas of mathematics at the advanced undergraduate level. This major is best for students who have a broad interest in many areas of mathematics. Students interested in honors in the major should also choose this option.
Seven MATH courses are required, as follows:
| Code | Title | Credits |
|---|---|---|
| Linear Algebra (complete one): 1 | 3 | |
| Linear Algebra (recommended) | ||
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): | 6 | |
| Analysis I | ||
| Modern Algebra | ||
| Elementary Topology | ||
| Math 500-699 (complete one): 2 | 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 | ||
| Mathematical Methods for Structural Biology | ||
| Topics in Mathematics Study Abroad | ||
| Mathematical Methods for Continuum Modeling in Biology | ||
| Mathematical Methods for Systems Biology | ||
| Analysis of Partial Differential Equations | ||
| Analysis III | ||
| Complex Analysis | ||
| Introduction to Fourier Analysis | ||
| Introduction to Measure and Integration | ||
| Introduction to Stochastic Processes | ||
| Queuing Theory and Stochastic Modeling | ||
| An Introduction to Brownian Motion and Stochastic Calculus | ||
| Introduction to Error-Correcting Codes | ||
| Senior Honors Thesis | ||
| Senior Honors Thesis | ||
| Undergraduate Thesis | ||
| Undergraduate Thesis | ||
| Directed Study | ||
| Directed Study | ||
| Additional Math above 306 to achieve 7 courses in the major 2 | 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 320 | Linear Algebra and Differential Equations | |
or MATH 376 | Topics in Multi-Variable 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 | ||
| Mathematical Methods for Structural Biology | ||
| Topics in Mathematics Study Abroad | ||
| Mathematical Methods for Continuum Modeling in Biology | ||
| Mathematical Methods for Systems Biology | ||
| Analysis of Partial Differential Equations | ||
| Analysis III | ||
| Complex Analysis | ||
| Introduction to Fourier Analysis | ||
| Introduction to Measure and Integration | ||
| Introduction to Stochastic Processes | ||
| Queuing Theory and Stochastic Modeling | ||
| An Introduction to Brownian Motion and Stochastic Calculus | ||
| Introduction to Error-Correcting Codes | ||
| Senior Honors Thesis | ||
| Senior Honors Thesis | ||
| Undergraduate Thesis | ||
| Undergraduate Thesis | ||
| Directed Study | ||
| Directed Study | ||
| Total Credits | 21 | |
| 1 | Only one of these courses will count toward the major: MATH 320 Linear Algebra and Differential Equations, MATH 340 Elementary Matrix and Linear Algebra, MATH 341 Linear Algebra, MATH 375 Topics in Multi-Variable Calculus and Linear Algebra |
| 2 | A course may only apply once toward the seven courses 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 500-699 requirement and a course used to meet the MATH 500-699 requirement may not also be used in the Additional Math requirement. |
| 3 | Only one course in Probability may count in the major from: MATH/STAT 309 Introduction to Probability and Mathematical Statistics I, MATH 331 An Introduction to Probability and Markov Chain Models, MATH/STAT 431 Introduction to the Theory of Probability. |
| 4 | Only one course in Elementary Differential Equations may count in the major, from MATH 319 Techniques in Ordinary Differential Equations, MATH 320 Linear Algebra and Differential Equations, MATH 376 Topics in Multi-Variable Calculus and Differential Equations. |
focused path
This program allows students to focus on mathematics associated to one specific area or application. Students interested in a focused mathematics program (e.g., actuarial mathematics, cryptography, etc.) or a dual major program often choose this path. A mathematics advisor must approve the collection of courses used to complete major requirements prior to major declaration.
Mathematics requirements: Six courses required
| Code | Title | Credits |
|---|---|---|
| Linear Algebra (complete one): 1 | 3 | |
| 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 | |
| Math 500-699 (complete two): 2 | 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 | ||
| Mathematical Methods for Structural Biology | ||
| Topics in Mathematics Study Abroad | ||
| Mathematical Methods for Continuum Modeling in Biology | ||
| Mathematical Methods for Systems Biology | ||
| Analysis of Partial Differential Equations | ||
| Analysis III | ||
| Complex Analysis | ||
| Introduction to Fourier Analysis | ||
| Introduction to Measure and Integration | ||
| Introduction to Stochastic Processes | ||
| Queuing Theory and Stochastic Modeling | ||
| An Introduction to Brownian Motion and Stochastic Calculus | ||
| Introduction to Error-Correcting Codes | ||
| Senior Honors Thesis | ||
| Senior Honors Thesis | ||
| Undergraduate Thesis | ||
| Undergraduate Thesis | ||
| Directed Study | ||
| Directed Study | ||
| Additional Math to achieve six MATH courses 2 | 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 320 | Linear Algebra and Differential Equations | |
or MATH 376 | Topics in Multi-Variable 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 | ||
| Mathematical Methods for Structural Biology | ||
| Topics in Mathematics Study Abroad | ||
| Mathematical Methods for Continuum Modeling in Biology | ||
| Mathematical Methods for Systems Biology | ||
| Analysis of Partial Differential Equations | ||
| Analysis III | ||
| Complex Analysis | ||
| Introduction to Fourier Analysis | ||
| Introduction to Measure and Integration | ||
| Introduction to Stochastic Processes | ||
| Queuing Theory and Stochastic Modeling | ||
| An Introduction to Brownian Motion and Stochastic Calculus | ||
| Introduction to Error-Correcting Codes | ||
| Senior Honors Thesis | ||
| Senior Honors Thesis | ||
| Undergraduate Thesis | ||
| Undergraduate Thesis | ||
| Directed Study | ||
| Directed Study | ||
| Total Credits | 15 | |
Applied Concentration Area
Four additional courses focused in an applied area.
- The following focus areas have been pre-approved and may be useful for planning purposes, though any collection of four courses approved by a mathematics advisor can be used to fulfill the focus area requirement.
- Math courses may fulfill the requirements in the focus, but cannot also count for the six mathematics courses required.
- Course listed here may have prerequisites. Students should plan for appropriate prerequisite coursework for approved courses. Permission to enroll in courses taught outside of MATH is determined by the subject-area department.
Pre-Approved Focus areas:
Actuarial Mathematics
| Code | Title | Credits |
|---|---|---|
| ACT SCI 303 | Theory of Interest | 3 |
| ACT SCI 650 & ACT SCI 652 | Actuarial Mathematics I and Loss Models I | 6 |
| ACT SCI 651 | Actuarial Mathematics II | 3 |
| or ACT SCI 653 | Loss Models II | |
| Total Credits | 12 | |
Astronomy
| Code | Title | Credits |
|---|---|---|
| Select two from the following: | 12 | |
| Stellar Astrophysics | ||
| The Interstellar Medium | ||
| Cosmology | ||
| Any two 3-credit PHYSICS courses numbered 400 and above, excluding labs | ||
| Total Credits | 12 | |
Atmospheric & Oceanic Studies
| Code | Title | Credits |
|---|---|---|
| ATM OCN 310 | Dynamics of the Atmosphere and Ocean I | 3 |
| ATM OCN 311 | Dynamics of the Atmosphere and Ocean II | 3 |
| ATM OCN 330 | Physics of the Atmosphere and Ocean I | 3 |
| PHYSICS 208 | General Physics | 5 |
| or PHYSICS 248 | A Modern Introduction to Physics | |
| Total Credits | 14 | |
Bio-Informatics
| Code | Title | Credits |
|---|---|---|
| B M I/COMP SCI 576 | Introduction to Bioinformatics | 3 |
| COMP SCI 300 | Programming II | 3 |
| COMP SCI 400 | Programming III | 3 |
| GENETICS 466 | Principles of Genetics | 3 |
| Total Credits | 12 | |
Bio-Statistics
| Code | Title | Credits |
|---|---|---|
| STAT 333 | Applied Regression Analysis | 3 |
| STAT/M E 424 | Statistical Experimental Design | 3 |
| STAT 575 | Statistical Methods for Spatial Data | 3 |
| STAT/B M I 641 | Statistical Methods for Clinical Trials | 3 |
| STAT/B M I 642 | Statistical Methods for Epidemiology | 3 |
| Total Credits | 15 | |
Business
| Code | Title | Credits |
|---|---|---|
| MATH/COMP SCI/I SY E/STAT 525 | Linear Optimization | 3 |
| OTM 410 | Operations Research I | 3 |
| And two from the following: | 6 | |
| Business Analytics I | ||
| Business Analytics II | ||
| Service Operations Management | ||
| Operations Research II | ||
| Queuing Theory and Stochastic Modeling | ||
| Production Planning and Control | ||
| Total Credits | 12 | |
Chemical Engineering
| Code | Title | Credits |
|---|---|---|
| CBE/B M E 320 | Introductory Transport Phenomena | 4 |
| CBE 326 | Momentum and Heat Transfer Operations | 3 |
| CBE 426 | Mass Transfer Operations | 3 |
| CBE 470 | Process Dynamics and Control | 3 |
| Total Credits | 13 | |
Chemistry
| Code | Title | Credits |
|---|---|---|
| CHEM 327 | Fundamentals of Analytical Science | 4 |
| or CHEM 329 | Fundamentals of Analytical Science | |
| CHEM 561 | Physical Chemistry | 3 |
| CHEM 562 | Physical Chemistry | 3 |
| PHYSICS 208 | General Physics | 5 |
| or PHYSICS 248 | A Modern Introduction to Physics | |
| Total Credits | 15 | |
Civil and Environmental Engineering
| Code | Title | Credits |
|---|---|---|
| CIV ENGR 310 | Fluid Mechanics | 3 |
| CIV ENGR 311 | Hydroscience | 3 |
| CIV ENGR 340 | Structural Analysis I | 3 |
| And one of the following: | 3 | |
| Structural Analysis II | ||
| Wood Structures I | ||
| Steel Structures I | ||
| Concrete Structures I | ||
| Total Credits | 12 | |
Computational Methods
| Code | Title | Credits |
|---|---|---|
| Complete four courses from: | 12 | |
| Digital System Fundamentals | ||
| Programming III | ||
| Introduction to Numerical Methods | ||
| Introduction to Cryptography | ||
| Introduction to Combinatorics | ||
| Numerical Linear Algebra | ||
| Numerical Analysis | ||
| Linear Optimization | ||
| Image Processing | ||
| Introduction to Artificial Intelligence | ||
| Natural Language and Computing | ||
| Introduction to Computational Geometry | ||
| Computer Graphics | ||
| Total Credits | 12 | |
Cryptography
| Code | Title | Credits |
|---|---|---|
| COMP SCI 300 | Programming II | 3 |
| COMP SCI 400 | Programming III | 3 |
| And two of the following: | 6 | |
| Introduction to Operating Systems | ||
| Introduction to Information Security | ||
| Digital System Fundamentals | ||
| Introduction to Error-Correcting Codes | ||
| Total Credits | 12 | |
Computer Sciences Theory
| Code | Title | Credits |
|---|---|---|
| COMP SCI 520 | Introduction to Theory of Computing | 3 |
| COMP SCI 577 | Introduction to Algorithms | 4 |
| And two of the following: | 6 | |
| Digital System Fundamentals | ||
| Programming III | ||
| Introduction to Numerical Methods | ||
| Introduction to Cryptography | ||
| Introduction to Combinatorics | ||
| Numerical Linear Algebra | ||
| Numerical Analysis | ||
| Linear Optimization | ||
| Image Processing | ||
| Introduction to Artificial Intelligence | ||
| Natural Language and Computing | ||
| Introduction to Computational Geometry | ||
| Computer Graphics | ||
| Total Credits | 13 | |
Ecology
| Code | Title | Credits |
|---|---|---|
| COMP SCI 412 | Introduction to Numerical Methods | 3 |
| ENVIR ST/A A E/F&W ECOL 652 | Decision Methods for Natural Resource Managers | 3-4 |
| ZOOLOGY 504 | Modeling Animal Landscapes | 3-5 |
| ZOOLOGY/BOTANY/F&W ECOL 460 | General Ecology | 4 |
| ZOOLOGY/ENTOM 540 | Theoretical Ecology | 3 |
| Total Credits | 16-19 | |
Ecology, Forestry, Wildlife Ecology
| Code | Title | Credits |
|---|---|---|
| MATH/STAT 310 | Introduction to Probability and Mathematical Statistics II | 3 |
| COMP SCI 412 | Introduction to Numerical Methods | 3 |
| And two of the following: | 6 | |
| General Ecology | ||
| Modeling Animal Landscapes | ||
| Theoretical Ecology | ||
| Forest Biometry | ||
| Principles of Silviculture | ||
| General Ecology | ||
| Natural Resource Economics | ||
| Decision Methods for Natural Resource Managers | ||
| Animal Population Dynamics | ||
| Total Credits | 12 | |
Economics
| Code | Title | Credits |
|---|---|---|
| ECON 301 | Intermediate Microeconomic Theory | 3-4 |
| or ECON 311 | Intermediate Microeconomic Theory - Advanced Treatment | |
| ECON 302 | Intermediate Macroeconomic Theory | 3-4 |
| or ECON 312 | Intermediate Macroeconomic Theory - Advanced Treatment | |
| And two of the following: | 6-8 | |
| Introductory Econometrics | ||
| Economics of Growth | ||
| Markets with Frictions | ||
| Game Theory and Economic Analysis | ||
| Economics of Education: Theory and Measurement | ||
| Issues in International Finance | ||
| Applied Dynamical Systems, Chaos and Modeling | ||
| Introduction to Stochastic Processes | ||
| Introduction to Probability and Mathematical Statistics II | ||
| Total Credits | 12-16 | |
Electrical and Computer Engineering
| Code | Title | Credits |
|---|---|---|
| E C E 220 | Electrodynamics I | 3 |
| E C E 230 | Circuit Analysis | 4 |
| E C E/COMP SCI 352 | Digital System Fundamentals | 3 |
| And one of the following: | 3 | |
| Introduction to Cryptography | ||
| Introduction to Plasmas | ||
| Image Processing | ||
| Total Credits | 13 | |
Engineering Mechanics and Astronautics
| Code | Title | Credits |
|---|---|---|
| E M A 201 | Statics | 3 |
| E M A 202 | Dynamics | 3 |
| E M A 303 | Mechanics of Materials | 3 |
| And one of the following: | 3 | |
| Aerodynamics | ||
| Advanced Dynamics | ||
| Mechanical Vibrations | ||
Finance
| Code | Title | Credits |
|---|---|---|
| ECON 410 | Introductory Econometrics | 4 |
| or MATH/STAT 310 | Introduction to Probability and Mathematical Statistics II | |
| FINANCE/ECON 300 | Introduction to Finance | 3 |
| FINANCE/ECON 320 | Investment Theory | 3 |
| FINANCE 330 | Derivative Securities | 3 |
| Total Credits | 13 | |
Forestry
| Code | Title | Credits |
|---|---|---|
| F&W ECOL 300 | Forest Biometry | 4 |
| F&W ECOL 410 | Principles of Silviculture | 3 |
| F&W ECOL/A A E/ENVIR ST 652 | Decision Methods for Natural Resource Managers | 3-4 |
| F&W ECOL 635 | Forest Stand Dynamics | 1-2 |
| Total Credits | 11-13 | |
Genetics
| Code | Title | Credits |
|---|---|---|
| GENETICS 466 | Principles of Genetics | 3 |
| GENETICS 564 | Genomics and Proteomics | 3 |
| GENETICS/MD GENET 565 | Human Genetics | 3 |
| GENETICS/CHEM 626 | Genomic Science | 2 |
| Total Credits | 11 | |
Industrial Engineering
| Code | Title | Credits |
|---|---|---|
| I SY E 315 | Production Planning and Control | 3 |
| I SY E 320 | Simulation and Probabilistic Modeling | 3 |
| I SY E 323 | Operations Research-Deterministic Modeling | 3 |
| And one of the following: | 3 | |
| Introduction to Combinatorial Optimization | ||
| Introduction to Decision Analysis | ||
| Linear Optimization | ||
| Advanced Linear Programming | ||
| Introduction to Computational Geometry | ||
| Introduction to Quality Engineering | ||
| Production Systems Control | ||
| Simulation Modeling and Analysis | ||
| Stochastic Modeling Techniques | ||
| Tools and Environments for Optimization | ||
| Performance Analysis of Manufacturing Systems | ||
| Total Credits | 12 | |
Mechanical Engineering
| Code | Title | Credits |
|---|---|---|
| M E 340 | Dynamic Systems | 3 |
| M E 361 | Thermodynamics | 3 |
| M E 363 | Fluid Dynamics | 3 |
| M E 364 | Elementary Heat Transfer | 3 |
| Total Credits | 12 | |
Materials Science
| Code | Title | Credits |
|---|---|---|
| M S & E 330 | Thermodynamics of Materials | 4 |
| M S & E 331 | Transport Phenomena in Materials | 3 |
| M S & E 351 | Materials Science-Structure and Property Relations in Solids | 3 |
| And one of the following: | 3 | |
| Introduction to Chemical Process Modeling | ||
| Programming II | ||
| Problem Solving Using Computers | ||
| Circuit Analysis | ||
| Electrical and Electronic Circuits | ||
| Introduction to Real-Time Digital Signal Processing | ||
| Electric Circuits and Electronics | ||
| Statistical Experimental Design | ||
| Total Credits | 13 | |
Nuclear Engineering
| Code | Title | Credits |
|---|---|---|
| N E 305 | Fundamentals of Nuclear Engineering | 3 |
| N E 405 | Nuclear Reactor Theory | 3 |
| N E 408 | Ionizing Radiation | 3 |
| And one of the following: | 3 | |
| Nuclear Reactor Engineering | ||
| Electric Circuits and Electronics | ||
| Electromagnetic Fields | ||
| Electrical and Electronic Circuits | ||
| Radiological Physics and Dosimetry | ||
| Total Credits | 12 | |
Physics
| Code | Title | Credits |
|---|---|---|
| PHYSICS 311 | Mechanics | 3 |
| PHYSICS 322 | Electromagnetic Fields | 3 |
| And two from the following: | 6 | |
| Thermal Physics | ||
| Atomic and Quantum Physics | ||
| Atomic and Quantum Physics | ||
| Introduction to Plasmas | ||
| Introduction to Quantum Mechanics | ||
| Introduction to Particle Physics | ||
| Introduction to Atomic Structure | ||
| Solid State Physics | ||
| Total Credits | 12 | |
Secondary Education
| Code | Title | Credits |
|---|---|---|
| MATH/CURRIC 471 | Mathematics for Secondary School Teachers | 3 |
| MATH/HIST SCI 473 | History of Mathematics | 3 |
| And two from the following: | 6 | |
| Programming II | ||
| The Theory of Single Variable Calculus | ||
| Introduction to Combinatorics | ||
| Differential Geometry | ||
| Modern Number Theory | ||
| General Physics | ||
| Total Credits | 12 | |
Statistics
| Code | Title | Credits |
|---|---|---|
| STAT 333 | Applied Regression Analysis | 3 |
| STAT/M E 424 | Statistical Experimental Design | 3 |
| And two from the following: | 6 | |
| Introduction to Probability and Mathematical Statistics I | ||
| Introduction to Probability and Mathematical Statistics II | ||
| Introduction to Time Series | ||
| Introductory Nonparametric Statistics | ||
| An Introduction to Sample Survey Theory and Methods | ||
| Applied Categorical Data Analysis | ||
| Applied Multivariate Analysis | ||
| Introduction to Computational Statistics | ||
| Introduction to Combinatorics | ||
| Special Topics in Statistics | ||
| Mathematical Statistics I | ||
| Introduction to Statistical Inference | ||
| Introduction to Stochastic Processes | ||
| Total Credits | 12 | |
Structural Biology
| Code | Title | Credits |
|---|---|---|
| MATH/B M I/BIOCHEM/BMOLCHEM 606 | Mathematical Methods for Structural Biology | 3 |
| CHEM 327 | Fundamentals of Analytical Science | 4 |
| or CHEM 329 | Fundamentals of Analytical Science | |
| CHEM 561 | Physical Chemistry | 3 |
| CHEM 562 | Physical Chemistry | 3 |
| Total Credits | 13 | |
Systems Biology
| Code | Title | Credits |
|---|---|---|
| BIOCHEM 501 | Introduction to Biochemistry | 3 |
| CHEM 341 | Elementary Organic Chemistry | 3 |
| or CHEM 343 | Introductory Organic Chemistry | |
| MATH/B M I/BIOCHEM/BMOLCHEM 609 | Mathematical Methods for Systems Biology | 3 |
| Any one BIOCHEM course numbered 600 and higher | 3 | |
| Total Credits | 12 | |
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 1
15 credits in MATH, taken on the UW–Madison campus
| 1 | MATH courses numbered 307–699 are considered upper level in the major. |
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 Mathematics Major Requirements
To earn Honors in the Major, students must satisfy both the requirements for the 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) 1 | ||
| Modern Algebra and Modern Algebra (Taken for Honors) 1 | ||
| Select at least two more courses from MATH 500 through MATH/E C E 641, the following will usually be one of the courses: 2 | ||
| Elementary Topology | ||
| Select one of these Capstone projects: 2 | ||
| Senior Honors Thesis and Senior Honors Thesis (For a total of 6 credits) | ||
| A sequence of two upper-level mathematics courses deemed acceptable by the Mathematics Honors advisor 2 | ||
| 1 | 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. |
| 2 | 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 non-experts.
The Sample Four-Year Plan is a tool to assist you and your advisor(s). Use it along with your DARS report and the Course Guide. You will make your own Four-Year Plan based on your placement scores, incoming credits, and individual interests. As you become involved in athletics, research, student organizations, study abroad, volunteer experiences, and/or work, you might adjust the order of your courses to make room for these experiences. You will likely revise your 4-year plan several times during college.
Traditional Mathematics Major - Bachelor of Arts/Science Degree
| Freshman | |||
|---|---|---|---|
| Fall | Credits | Spring | Credits |
| MATH 2211,2,3 | 5 | MATH 2222,3 | 4 |
| Communication-A (must be completed in first year) | 3 | Ethnic Studies (must be completed in first 60 credits) | 3 |
| Foreign Language if required | 4 | Foreign Language if required | 4 |
| L&S Breadth | 3 | L&S Breadth | 3 |
| 15 | 14 | ||
| Sophomore | |||
| Fall | Credits | Spring | Credits |
| MATH Prerequisite (234)2,3 | 4 | MATH Linear Algebra4 | 3 |
| Communication-B | 3-5 | Intermediate MATH5,6 | 3 |
| L&S Breadth | 3 | L&S Breadth | 3 |
| L&S Breadth | 3 | L&S Breadth | 3 |
| Elective | 3 | Elective | 3 |
| 16-18 | 15 | ||
| Junior | |||
| Fall | Credits | Spring | Credits |
| Intermediate MATH6 | 3 | Intermediate MATH6 | 3 |
| L&S Breadth | 3 | Advanced MATH7 | 3 |
| L&S Breadth | 3 | L&S Breadth | 3 |
| Elective | 3 | L&S Breadth | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Senior | |||
| Fall | Credits | Spring | Credits |
| Advanced MATH7 | 3 | L&S Breadth | 3 |
| L&S Breadth | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| Elective | 3 | Advanced MATH7 | 3 |
| 15 | 15 | ||
| Total Credits 120-122 | |||
Focused Mathematics Major - Bachelor of Arts/Science Degree
Note: approval of math and application courses required.
| Freshman | |||
|---|---|---|---|
| Fall | Credits | Spring | Credits |
| MATH 2211,2,3 | 5 | MATH 2222,3 | 4 |
| MATH Option 2 Applied Concentration Area Course Prerequisite or L&S Bredth | 3 | MATH Major Option 2 Applied Concentration Area Course Prerequisite or L&S Breadth | 3 |
| Communication-A (must be completed in first year) | 3 | Ethnic Studies (must be completed in first 60 credits) | 3 |
| Foreign Language if required | 4 | Foreign Language if required for the BA | 4 |
| 15 | 14 | ||
| Sophomore | |||
| Fall | Credits | Spring | Credits |
| MATH 2342,3 | 4 | MATH Linear Algebra4 | 3 |
| MATH Option 2 Applied Concentration Area Course Prerequisite or L&S Breadth | 3 | Intermediate MATH5,6 | 3 |
| Communication-B | 3-5 | MATH Major Option 2 Applied Concentration Area Course Prerequisite or L&S Breadth | 3 |
| L&S Breadth | 3 | L&S Breadth | 3 |
| Elective | 3 | L&S Breadth | 3 |
| 16-18 | 15 | ||
| Junior | |||
| Fall | Credits | Spring | Credits |
| Intermediate MATH6 | 3 | Intermediate MATH6 | 3 |
| MATH Major Option 2 Applied Concentration Area Course8 | 3 | MATH Major Option 2 Applied Concentration Area Course8 | 3 |
| L&S Breadth | 3 | L&S Breadth | 3 |
| L&S Breadth | 3 | L&S Breadth | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Senior | |||
| Fall | Credits | Spring | Credits |
| Advanced MATH7 | 3 | Advanced MATH7 | 3 |
| MATH Major Option 2 Applied Concentration Area Course8 | 3 | MATH Major Option 2 Applied Concentration Area Course8 | 3 |
| L&S Breadth or Elective | 3 | L&S Breadth or Elective | 3 |
| L&S Breadth or Elective | 3 | L&S Breadth or Elective | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Total Credits 120-122 | |||
L&S requires all students to complete at least 60 credits at the Intermediate or Advanced level.
Students must declare a major by the time they reach Senior standing (86 credits).
Please refer to the Requirements tab in Guide for additional College of Letters & Science Breadth and Degree Requirements as well as Residence and Quality of Work requirements for the major.
| 1 | Math majors will naturally complete Quantitative Reasoning requirements with the introductory calculus courses required to declare the major. |
| 2 | This course counts for the Natural Science L&S Breadth requirement for the Bachelor of Arts (BA) degree. |
| 3 | 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. |
| 4 | E.g., MATH 320 Linear Algebra and Differential Equations, MATH 340 Elementary Matrix and Linear Algebra, or MATH 341 Linear Algebra. |
| 5 | MATH 321 Applied Mathematical Analysis or MATH 421 The Theory of Single Variable Calculus strongly recommended |
| 6 | An intermediate level math course is any numbered above 306 excluding MATH 320 Linear Algebra and Differential Equations, MATH 340 Elementary Matrix and Linear Algebra, or MATH 341 Linear Algebra, or MATH/CURRIC 471 Mathematics for Secondary School Teachers. |
| 7 | An advanced level MATH course is any numbered above 500. |
| 8 | Discuss options for these courses with a mathematics major advisor. |
Advising
Students who are interested in the math major should visit a faculty advisor. During the fall and spring semesters several faculty advisors have regular drop-in office hours. The current list of advisors and the schedule of the office hours can be found at the Math advising page. During the winter break and the summer semester there is no drop-in advising, students should contact one of the advisors to set up an appointment.
For advice on college algebra, pre-calculus, and calculus, see the placement advising pages of the department.
Transition courses
Students are strongly recommended to include one of the following courses in their major program before moving into MATH 500 and higher.
| Code | Title | Credits |
|---|---|---|
| Linear Algebra | ||
| Topics in Multi-Variable Calculus and Linear Algebra | ||
| The Theory of Single Variable Calculus |
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 | 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
SuccessWorks at the College of Letters & Science helps students leverage the academic skills learned in their major, certificates, and liberal arts degree; explore and try out different career paths; participate in internships; prepare for the job search and/or graduate school applications; and network with professionals in the field (alumni and employers). In short, SuccessWorks helps students in the College of Letters & Science discover themselves, find opportunities, and develop the skills they need for success after graduation.
SuccessWorks can also assist students in career advising, résumé and cover letter writing, networking opportunities, and interview skills, as well as course offerings for undergraduates to begin their career exploration early in their undergraduate career.
Students should set up their profiles in Handshake to take care of everything they need to explore career events, manage their campus interviews, and apply to jobs and internships from 200,000+ employers around the country.
- SuccessWorks
- Set up a career advising appointment
- INTER-LS 210 L&S Career Development: Taking Initiative (1 credit, targeted to first- and second-year students)—for more information, see Inter-LS 210: Career Development, Taking Initiative
- INTER-LS 215 Communicating About Careers (3 credits, fulfills Com B General Education Requirement)
- Handshake
- Learn how we’re transforming career preparation: L&S Career Initiative
Faculty
Professors Angenent, Arinkin, Assadi, Bolotin, Boston, Caldararu, Craciun, Denissov, Ellenberg, Feldman, Gong, Jin, Lempp, Mari-Beffa, Maxim, Miller, Mitchell, Paul, Roch, Seeger, Seppalainen, Smith, Terwilliger, Thiffeault, Valko, Viaclovsky, Waleffe, Yang.
Associate Professors Anderson, Gurevich, Stechmann, Street, Kent.
Assistant Professors Andrews, Dymarz, Erman, Kim, Marshall, Sam, Spagnolie, Stovall, Tran, B. Wang, L. Wang, M. Matchett Wood, P. Matchett Wood, Li.
Academic staff
Anzaldo (Precalculus Coordinator), Benguria-Andrews (Calculus Coordinator), Hanhart (Associate Director of Undergraduate Studies), Kwon (Math 13X Coordinator), Malekpour (Director of the Instructional Excellence Program, WISCEL), Rivard (Placement and Enrollment Coordinator)