mathematics

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.

Acceptance

To be accepted as a major in mathematics a student must complete MATH 221 Calculus and Analytic Geometry 1, MATH 222 Calculus and Analytic Geometry 2, and MATH 234 Calculus--Functions of Several Variables  with a grade point average of 2.500 or better in this sequence. However, a higher grade point average is advisable. 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
  • Breadth—Humanities/Literature/Arts: 6 credits
  • Breadth—Natural 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
  • Breadth—Social Studies: 3 credits
  • Communication Part A & Part B *
  • Ethnic Studies *
  • Quantitative Reasoning Part A & Part B *

* 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
  • Humanities, 12 credits: 6 of the 12 credits must be in literature
  • Social Sciences, 12 credits
  • Natural Sciences, 12 credits: must include 6 credits in biological science; and must include 6 credits in physical science
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.

Requirements for the Major

There are two tracks: Option I or Option II. Both are flexible, so students should plan their programs with the advice of their math advisors. In particular, those following Option II must have their programs formally approved by their mathematics advisors. 

Option I

The Option I package requires exposure to at least two areas of mathematics at the advanced undergraduate level. This package 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.

The Option I major requires a minimum of seven mathematics courses numbered 307–699.1

Linear Algebra
Select one of the following: 1
Elementary Matrix and Linear Algebra
Linear Algebra
Topics in Multi-Variable Calculus and Linear Algebra
Calculus, Topology, Algebra
Select two of the following:
Analysis I
Modern Algebra
Elementary Topology
Additional Math 500 or higher
Select one course from Math 500-679 (see course list A below)
Select additional courses to reach 7 courses in the major (see course list B below)
1

 Only one of these courses will count towards the major.

Course list A

MATH/​COMP SCI  513 Numerical Linear Algebra3
MATH/​COMP SCI  514 Numerical Analysis3
MATH 519 Ordinary Differential Equations3
MATH 521 Analysis I3
MATH 522 Analysis II3
MATH/​COMP SCI/​I SY E/​STAT  525 Linear Programming Methods3
MATH 531 Probability Theory3
MATH 541 Modern Algebra3
MATH 542 Modern Algebra3
MATH 551 Elementary Topology3
MATH 552 Elementary Geometric and Algebraic Topology3
MATH 561 Differential Geometry3
MATH 567 Elementary Number Theory3
MATH 570 Fundamentals of Set Theory3
MATH/​PHILOS  571 Mathematical Logic3
MATH 605 Stochastic Methods for Biology3
MATH/​B M I/​BIOCHEM/​BMOLCHEM  606 Mathematical Methods for Structural Biology3
MATH 607 Topics in Mathematics Study Abroad1-5
MATH 608 Mathematical Methods for Continuum Modeling in Biology3
MATH/​B M I/​BIOCHEM/​BMOLCHEM  609 Mathematical Methods for Systems Biology3
MATH 619 Analysis of Partial Differential Equations3
MATH 621 Analysis III3
MATH 623 Complex Analysis3
MATH 627 Introduction to Fourier Analysis3
MATH 629 Introduction to Measure and Integration3
MATH/​I SY E/​OTM/​STAT  632 Introduction to Stochastic Processes3
MATH/​I SY E/​OTM  633 Queuing Theory and Stochastic Modeling3
MATH 635 An Introduction to Brownian Motion and Stochastic Calculus3
MATH/​E C E  641 Introduction to Error-Correcting Codes3

Course list B1

MATH/​STAT  309 Introduction to Probability and Mathematical Statistics I3
MATH/​STAT  310 Introduction to Probability and Mathematical Statistics II3
MATH 319 Techniques in Ordinary Differential Equations3
MATH 321 Applied Mathematical Analysis3
MATH 322 Applied Mathematical Analysis3
MATH 331 An Introduction to Probability and Markov Chain Models3
MATH 341 Linear Algebra3
MATH 376 Topics in Multi-Variable Calculus and Differential Equations5
MATH 407 Topics in Mathematics Study Abroad1-5
MATH 415 Applied Dynamical Systems, Chaos and Modeling3
MATH/​COMP SCI/​I SY E  425 Introduction to Combinatorial Optimization 23
MATH/​STAT  431 Introduction to the Theory of Probability3
MATH/​COMP SCI/​E C E  435 Introduction to Cryptography3
MATH 441 Introduction to Modern Algebra3
MATH 443 Applied Linear Algebra3
MATH 461 College Geometry I3
MATH/​HIST SCI  473 History of Mathematics3
MATH/​COMP SCI/​STAT  475 Introduction to Combinatorics3
MATH 491 Topics in Undergraduate Mathematics3
MATH/​COMP SCI  513 Numerical Linear Algebra3
MATH/​COMP SCI  514 Numerical Analysis3
MATH 519 Ordinary Differential Equations3
MATH 521 Analysis I3
MATH 522 Analysis II3
MATH/​COMP SCI/​I SY E/​STAT  525 Linear Programming Methods3
MATH 531 Probability Theory3
MATH 541 Modern Algebra3
MATH 542 Modern Algebra3
MATH 551 Elementary Topology3
MATH 552 Elementary Geometric and Algebraic Topology3
MATH 561 Differential Geometry3
MATH 567 Elementary Number Theory3
MATH 570 Fundamentals of Set Theory3
MATH/​PHILOS  571 Mathematical Logic3
MATH 605 Stochastic Methods for Biology3
MATH/​B M I/​BIOCHEM/​BMOLCHEM  606 Mathematical Methods for Structural Biology3
MATH 607 Topics in Mathematics Study Abroad1-5
MATH 608 Mathematical Methods for Continuum Modeling in Biology3
MATH/​B M I/​BIOCHEM/​BMOLCHEM  609 Mathematical Methods for Systems Biology3
MATH 619 Analysis of Partial Differential Equations3
MATH 621 Analysis III3
MATH 623 Complex Analysis3
MATH 627 Introduction to Fourier Analysis3
MATH 629 Introduction to Measure and Integration3
MATH/​I SY E/​OTM/​STAT  632 Introduction to Stochastic Processes3
MATH/​I SY E/​OTM  633 Queuing Theory and Stochastic Modeling3
MATH 635 An Introduction to Brownian Motion and Stochastic Calculus3
MATH/​E C E  641 Introduction to Error-Correcting Codes3
MATH 681 Senior Honors Thesis3
MATH 682 Senior Honors Thesis3
MATH 691 Undergraduate Thesis2-4
MATH 692 Undergraduate Thesis2-4
1

 There are two subgroups within this course list where only one course from each subgroup will count towards the major:

  1. Differential Equations: MATH 319, MATH 376
  2. Probability: MATH/​STAT  309, MATH 331, MATH/​STAT  431, STAT 311
2

 This course will only count if taken after Summer 2015.

Option II

This option allows students to focus on mathematics associated to one specific area or application. Students interested in a focused mathematics program (i.e., actuary mathematics, elementary education, etc.) or a dual major program often choose this option.

Mathematics Core

Linear Algebra
Select one of the following: 1
Linear Algebra and Differential Equations
Elementary Matrix and Linear Algebra
Linear Algebra
Topics in Multi-Variable Calculus and Linear Algebra
Advanced Courses
Select two courses from MATH 500 - 679 (see course list A below)
Intermediate Courses
Select three courses from MATH 307- 692 (see course list B below)
1

 Only one of these courses will count towards the major.

Course List A

MATH/​COMP SCI  513 Numerical Linear Algebra3
MATH/​COMP SCI  514 Numerical Analysis3
MATH 519 Ordinary Differential Equations3
MATH 521 Analysis I3
MATH 522 Analysis II3
MATH/​COMP SCI/​I SY E/​STAT  525 Linear Programming Methods3
MATH 531 Probability Theory3
MATH 541 Modern Algebra3
MATH 542 Modern Algebra3
MATH 551 Elementary Topology3
MATH 552 Elementary Geometric and Algebraic Topology3
MATH 561 Differential Geometry3
MATH 567 Elementary Number Theory3
MATH 570 Fundamentals of Set Theory3
MATH/​PHILOS  571 Mathematical Logic3
MATH 605 Stochastic Methods for Biology3
MATH/​B M I/​BIOCHEM/​BMOLCHEM  606 Mathematical Methods for Structural Biology3
MATH 607 Topics in Mathematics Study Abroad1-5
MATH 608 Mathematical Methods for Continuum Modeling in Biology3
MATH/​B M I/​BIOCHEM/​BMOLCHEM  609 Mathematical Methods for Systems Biology3
MATH 619 Analysis of Partial Differential Equations3
MATH 621 Analysis III3
MATH 623 Complex Analysis3
MATH 627 Introduction to Fourier Analysis3
MATH 629 Introduction to Measure and Integration3
MATH/​I SY E/​OTM/​STAT  632 Introduction to Stochastic Processes3
MATH/​I SY E/​OTM  633 Queuing Theory and Stochastic Modeling3
MATH 635 An Introduction to Brownian Motion and Stochastic Calculus3
MATH/​E C E  641 Introduction to Error-Correcting Codes3

Course List B1

MATH/​STAT  309 Introduction to Probability and Mathematical Statistics I3
MATH/​STAT  310 Introduction to Probability and Mathematical Statistics II3
MATH 319 Techniques in Ordinary Differential Equations3
MATH 320 Linear Algebra and Differential Equations3
MATH 321 Applied Mathematical Analysis3
MATH 322 Applied Mathematical Analysis3
MATH 331 An Introduction to Probability and Markov Chain Models3
MATH 340 Elementary Matrix and Linear Algebra3
MATH 341 Linear Algebra3
MATH 375 Topics in Multi-Variable Calculus and Linear Algebra5
MATH 376 Topics in Multi-Variable Calculus and Differential Equations5
MATH 407 Topics in Mathematics Study Abroad1-5
MATH 415 Applied Dynamical Systems, Chaos and Modeling3
MATH 421 The Theory of Single Variable Calculus3
MATH/​COMP SCI/​I SY E  425 Introduction to Combinatorial Optimization3
MATH/​STAT  431 Introduction to the Theory of Probability3
MATH/​COMP SCI/​E C E  435 Introduction to Cryptography3
MATH 441 Introduction to Modern Algebra3
MATH 443 Applied Linear Algebra3
MATH 461 College Geometry I3
MATH/​CURRIC  471 Mathematics for Secondary School Teachers3
MATH/​HIST SCI  473 History of Mathematics3
MATH/​COMP SCI/​STAT  475 Introduction to Combinatorics3
MATH/​COMP SCI  513 Numerical Linear Algebra3
MATH/​COMP SCI  514 Numerical Analysis3
MATH 519 Ordinary Differential Equations3
MATH 521 Analysis I3
MATH 522 Analysis II3
MATH/​COMP SCI/​I SY E/​STAT  525 Linear Programming Methods3
MATH 531 Probability Theory3
MATH 541 Modern Algebra3
MATH 542 Modern Algebra3
MATH 551 Elementary Topology3
MATH 552 Elementary Geometric and Algebraic Topology3
MATH 561 Differential Geometry3
MATH 567 Elementary Number Theory3
MATH 570 Fundamentals of Set Theory3
MATH/​PHILOS  571 Mathematical Logic3
MATH 605 Stochastic Methods for Biology3
MATH/​B M I/​BIOCHEM/​BMOLCHEM  606 Mathematical Methods for Structural Biology3
MATH 607 Topics in Mathematics Study Abroad1-5
MATH 608 Mathematical Methods for Continuum Modeling in Biology3
MATH/​B M I/​BIOCHEM/​BMOLCHEM  609 Mathematical Methods for Systems Biology3
MATH 619 Analysis of Partial Differential Equations3
MATH 621 Analysis III3
MATH 623 Complex Analysis3
MATH 627 Introduction to Fourier Analysis3
MATH 629 Introduction to Measure and Integration3
MATH/​I SY E/​OTM/​STAT  632 Introduction to Stochastic Processes3
MATH/​I SY E/​OTM  633 Queuing Theory and Stochastic Modeling3
MATH 635 An Introduction to Brownian Motion and Stochastic Calculus3
MATH/​E C E  641 Introduction to Error-Correcting Codes3
1

 There are two subgroups within this course list where only one course from each subgroup will count towards the major:

  1. Differential Equations: MATH 319, MATH 376
  2. Probability: MATH/​STAT  309, MATH 331, MATH/​STAT  431, STAT 311

Applied Concentration Area

Select 4 courses from one of the concentrated areas. Note that math courses may fulfill the requirements in the concentration, but cannot count for the Intermediate Courses requirement listed above Students are strongly urged to consult their major advisor to develop an area of applied focus that is intellectually coherent.

Actuarial Mathematics

ACT SCI/​MATH  303 Theory of Interest and Life Insurance3
ACT SCI 652 Loss Models I3
Select two of the following:
ACT SCI 650 Actuarial Mathematics I3
ACT SCI 651 Actuarial Mathematics II3
or ACT SCI 653 Loss Models II

Astronomy

ASTRON 310 Stellar Astrophysics3
Select three from the following:
ASTRON 320 The Interstellar Medium3
or ASTRON 335 Cosmology
PHYSICS 415 Thermal Physics3
PHYSICS 448 Atomic and Quantum Physics3
PHYSICS 449 Atomic and Quantum Physics3
PHYSICS/​E C E/​N E  525 Introduction to Plasmas3
PHYSICS 531 Introduction to Quantum Mechanics3
PHYSICS 535 Introduction to Particle Physics3
PHYSICS 545 Introduction to Atomic Structure3
PHYSICS 551 Solid State Physics3

Atmospheric & Oceanic Studies

ATM OCN 310 Dynamics of the Atmosphere and Ocean I3
ATM OCN 311 Dynamics of the Atmosphere and Ocean II3
ATM OCN 330 Physics of the Atmosphere and Ocean I3
PHYSICS 208 General Physics5
or PHYSICS 248 A Modern Introduction to Physics

Bio-Informatics

B M I/​COMP SCI  576 Introduction to Bioinformatics3
COMP SCI 300 Programming II3
COMP SCI 302 Introduction to Programming3
COMP SCI 367 Introduction to Data Structures3
COMP SCI 400 Programming III3
GENETICS 466 Principles of Genetics3

Bio-Statistics

STAT 333 Applied Regression Analysis3
STAT/​M E  424 Statistical Experimental Design3
STAT 575 Statistical Methods for Spatial Data3
STAT/​B M I  641 Statistical Methods for Clinical Trials3
or STAT/​B M I  642 Statistical Methods for Epidemiology
STAT/​B M I  541 Introduction to Biostatistics3

Business (Operations Research)

MATH/​COMP SCI/​I SY E/​STAT  525 Linear Programming Methods3
OTM 410 Operations Research I3
Select two from the following:
GEN BUS 301 Business Law3
OTM 451 Service Operations Management3
OTM 411 Operations Research II3
OTM/​I SY E/​MATH  633 Queuing Theory and Stochastic Modeling3
OTM 654 Production Planning and Control3

Chemical Engineering

CBE/​B M E  320 Introductory Transport Phenomena4
CBE 326 Momentum and Heat Transfer Operations3
CBE 426 Mass Transfer Operations3
CBE 470 Process Dynamics and Control3

Chemistry

CHEM 327 Fundamentals of Analytical Science4
or CHEM 329 Fundamentals of Analytical Science
CHEM 561 Physical Chemistry3
CHEM 562 Physical Chemistry3
PHYSICS 208 General Physics5

Civil and Environmental Engineering

CIV ENGR 310 Fluid Mechanics3
CIV ENGR 311 Hydroscience3
CIV ENGR 340 Structural Analysis I4
Select one of the following:
CIV ENGR 440 Structural Analysis II3
CIV ENGR 442 Wood Structures I3
CIV ENGR 445 Steel Structures I3
CIV ENGR 447 Concrete Structures I3

Computer Sciences

COMP SCI 300 Programming II3
COMP SCI/​E C E  352 Digital System Fundamentals3
COMP SCI 367 Introduction to Data Structures3
COMP SCI 412 Introduction to Numerical Methods3
COMP SCI/​E C E/​MATH  435 Introduction to Cryptography3
COMP SCI/​MATH/​STAT  475 Introduction to Combinatorics3
COMP SCI/​MATH  513 Numerical Linear Algebra3
COMP SCI 520 Introduction to Theory of Computing3
COMP SCI/​I SY E/​MATH/​STAT  525 Linear Programming Methods3
COMP SCI/​E C E/​M E  532 Theory and Applications of Pattern Recognition3
COMP SCI/​E C E  533 Image Processing3
COMP SCI 538 Introduction to the Theory and Design of Programming Languages3
COMP SCI 540 Introduction to Artificial Intelligence3
COMP SCI 545 Natural Language and Computing3
COMP SCI 547 Computer Systems Modeling Fundamentals3
COMP SCI/​I SY E/​M E  558 Introduction to Computational Geometry3
COMP SCI 559 Computer Graphics3
COMP SCI/​B M I  576 Introduction to Bioinformatics3
COMP SCI 577 Introduction to Algorithms4

Cryptography

COMP SCI 300 Programming II3
COMP SCI 302 Introduction to Programming3
COMP SCI 367 Introduction to Data Structures3
COMP SCI 400 Programming III3
E C E/​COMP SCI/​M E  532 Theory and Applications of Pattern Recognition3-4
or COMP SCI 537 Introduction to Operating Systems
E C E/​MATH  641 Introduction to Error-Correcting Codes3

Ecology

COMP SCI 412 Introduction to Numerical Methods3
ENVIR ST/​A A E/​F&W ECOL  652 Decision Methods for Natural Resource Managers3-4
ZOOLOGY 504 Modeling Animal Landscapes3-5
ZOOLOGY/​BOTANY/​F&W ECOL  460 General Ecology4
ZOOLOGY 535 Ecosystem Analysis3
ZOOLOGY/​ENTOM  540 Theoretical Ecology3

Economics, Version 1

ECON 311 Intermediate Microeconomic Theory - Advanced Treatment3
ECON 312 Intermediate Macroeconomic Theory - Advanced Treatment3
Select two of the following:
ECON 101 Principles of Microeconomics4
or ECON 102 Principles of Macroeconomics
or ECON 111 Principles of Economics-Accelerated Treatment
ECON 410 Introductory Econometrics4
ECON 468 Industrial Organization and Imperfect Competition3-4
ECON 521 Game Theory and Economic Analysis3-4
ECON 666 Issues in International Finance3-4
MATH 415 Applied Dynamical Systems, Chaos and Modeling3
MATH/​COMP SCI/​I SY E/​STAT  525 Linear Programming Methods3
MATH/​I SY E/​OTM/​STAT  632 Introduction to Stochastic Processes3
STAT/​MATH  310 Introduction to Probability and Mathematical Statistics II3

Economics, Version 2

ECON 301 Intermediate Microeconomic Theory4
ECON 302 Intermediate Macroeconomic Theory4
Select two of the following:
ECON 410 Introductory Econometrics4
ECON 468 Industrial Organization and Imperfect Competition3-4
ECON 521 Game Theory and Economic Analysis3-4
ECON 666 Issues in International Finance3-4
MATH 415 Applied Dynamical Systems, Chaos and Modeling3
MATH/​COMP SCI/​I SY E/​STAT  525 Linear Programming Methods3
MATH/​I SY E/​OTM/​STAT  632 Introduction to Stochastic Processes3
STAT/​MATH  310 Introduction to Probability and Mathematical Statistics II3

Electrical and Computer Engineering

E C E 220 Electrodynamics I3
E C E 230 Circuit Analysis4
E C E/​COMP SCI  352 Digital System Fundamentals3
Select one of the following:
E C E/​COMP SCI/​MATH  435 Introduction to Cryptography3
E C E/​N E/​PHYSICS  525 Introduction to Plasmas3
E C E/​COMP SCI  533 Image Processing3

Engineering Mechanics and Astronautics

E M A 201 Statics3
E M A 202 Dynamics3
E M A 303 Mechanics of Materials3
E M A 542 Advanced Dynamics3
or E M A 545 Mechanical Vibrations

Finance

ECON 310 Statistics: Measurement in Economics4
ECON 410 Introductory Econometrics4
FINANCE/​ECON  300 Introduction to Finance3
FINANCE/​ECON  320 Investment Theory3

Forestry

F&W ECOL 300 Forest Biometry4
F&W ECOL 410 Principles of Silviculture3
F&W ECOL/​A A E/​ENVIR ST  652 Decision Methods for Natural Resource Managers3-4
F&W ECOL 635 Forest Stand Dynamics1-2

Genetics

GENETICS 466 Principles of Genetics3
GENETICS/​MD GENET  565 Human Genetics3
GENETICS/​BOTANY/​MD GENET  629 Evolutionary Genetics3
Select one of the following:
ZOOLOGY/​BIOLOGY  101 Animal Biology3
or ZOOLOGY/​BIOLOGY/​BOTANY  151 Introductory Biology

Industrial Engineering

I SY E 315 Production Planning and Control3
I SY E 320 Simulation and Probabilistic Modeling3
I SY E 321 Simulation Modeling Laboratory1
I SY E/​COMP SCI/​MATH  425 Introduction to Combinatorial Optimization3
I SY E 516 Introduction to Decision Analysis3
I SY E/​COMP SCI/​MATH/​STAT  525 Linear Programming Methods3
I SY E/​COMP SCI  526 Advanced Linear Programming3-4
I SY E/​COMP SCI/​M E  558 Introduction to Computational Geometry3
I SY E 575 Introduction to Quality Engineering3
I SY E 615 Production Systems Control3
I SY E/​OTM  620 Simulation Modeling and Analysis3
I SY E 624 Stochastic Modeling Techniques3
I SY E/​COMP SCI  635 Tools and Environments for Optimization3
I SY E/​M E  643 Performance Analysis of Manufacturing Systems3

Mechanical Engineering

M E 340 Introduction to Dynamic Systems3
M E 361 Thermodynamics3
M E 363 Fluid Dynamics3
M E 364 Elementary Heat Transfer3

Metallurgical Engineering or Materials Sciences & Engineering

M S & E 330 Thermodynamics of Materials4
M S & E 331 Transport Phenomena in Materials3
M S & E 351 Materials Science-Structure and Property Relations in Solids3

Nuclear Engineering an Engineering Physics

N E 305 Fundamentals of Nuclear Engineering3
N E 405 Nuclear Reactor Theory3
N E 408 Ionizing Radiation3
N E 411 Nuclear Reactor Engineering3

Physics

PHYSICS 311 Mechanics3
PHYSICS 322 Electromagnetic Fields3
Select two from the following:
PHYSICS 415 Thermal Physics3
PHYSICS 448 Atomic and Quantum Physics3
PHYSICS 449 Atomic and Quantum Physics3
PHYSICS/​E C E/​N E  525 Introduction to Plasmas3
PHYSICS 531 Introduction to Quantum Mechanics3
PHYSICS 535 Introduction to Particle Physics3
PHYSICS 545 Introduction to Atomic Structure3
PHYSICS 551 Solid State Physics3

Secondary Education

COMP SCI 300 Programming II3
COMP SCI 302 Introduction to Programming3
COMP SCI 400 Programming III3
MATH/​CURRIC  471 Mathematics for Secondary School Teachers3
MATH/​HIST SCI  473 History of Mathematics3
MATH/​STAT  310 Introduction to Probability and Mathematical Statistics II3
PHYSICS 207 General Physics5
PHYSICS 208 General Physics5

Statistics, Version 1

STAT 333 Applied Regression Analysis3
STAT/​M E  424 Statistical Experimental Design3
Select two from the following:
STAT 349 Introduction to Time Series3
STAT 351 Introductory Nonparametric Statistics3
STAT 411 An Introduction to Sample Survey Theory and Methods3
STAT 421 Applied Categorical Data Analysis3
STAT/​B M I  641 Statistical Methods for Clinical Trials3

Statistics, Version 2

STAT/​MATH  309 Introduction to Probability and Mathematical Statistics I3
STAT/​MATH  310 Introduction to Probability and Mathematical Statistics II3
STAT 333 Applied Regression Analysis3
STAT/​M E  424 Statistical Experimental Design3

Structural Biology

MATH/​B M I/​BIOCHEM/​BMOLCHEM  606 Mathematical Methods for Structural Biology3
CHEM 327 Fundamentals of Analytical Science4
or CHEM 329 Fundamentals of Analytical Science
CHEM 561 Physical Chemistry3
CHEM 562 Physical Chemistry3

Systems Biology

MATH 320 Linear Algebra and Differential Equations3
or BIOCHEM 501 Introduction to Biochemistry
CHEM 341 Elementary Organic Chemistry3
or CHEM 343 Introductory Organic Chemistry
BIOCHEM 601 Protein and Enzyme Structure and Function2
BIOCHEM/​GENETICS/​MICROBIO  612 Prokaryotic Molecular Biology3
BIOCHEM/​GENETICS/​MD GENET  620 Eukaryotic Molecular Biology3
BIOCHEM/​BOTANY  621 Plant Biochemistry3
BIOCHEM 624 Mechanisms of Enzyme Action2
BIOCHEM/​PHMCOL-M/​ZOOLOGY  630 Cellular Signal Transduction Mechanisms3

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 Mathematics 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 a B.A. or B.S. with Honors in the Major in Mathematics students must satisfy both the requirements for the major (above) and the following additional requirements:

  • Earn a 3.300 overall 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:
Analysis I (Taken for Honors)
Analysis II (Taken for Honors)
Modern Algebra (Taken for Honors)
Modern Algebra (Taken for Honors)
Select at least two more courses above 500, the following will usually be one of the courses: 1
Elementary Topology
Select one of the following Capstone projects: 1
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 1
1

Chosen in consultation with the Mathematics Honors advisor.

At least one of the two sequences (MATH 521 Analysis IMATH 522 Analysis II or MATH 541 Modern AlgebraMATH 542 Modern Algebra) must be completed prior to enrollment in the Capstone project.

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.
  1. Students will be able to 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.
  2. Students will be able to construct and evaluate mathematical proofs and arguments.
  3. Students will acquire a diverse set of skills and strategies in mathematical reasoning/problem solving.
  4. Students will use mathematics to model and analyze phenomena in other disciplines.
  5. Students will be able to write, explain, and present mathematics to both experts and non-­experts.

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.

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:

MATH 341 Linear Algebra3
or MATH 375 Topics in Multi-Variable Calculus and Linear Algebra
MATH 521 Analysis I3
MATH 522 Analysis II3
MATH 541 Modern Algebra3
MATH 542 Modern Algebra3
MATH 551 Elementary Topology3
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.

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)