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 CalculusFunctions 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 
* 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 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. View a comparison of the degree requirements here.
Bachelor of Arts degree requirements
Mathematics  Fulfilled with completion of University General Education requirements Quantitative Reasoning a (QR A) and Quantitative Reasoning b (QR B) coursework. Please note that some majors may require students to complete additional math coursework beyond the B.A. mathematics requirement. 
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 
UWMadison 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}
Code  Title  Credits 

Linear Algebra  
Select one of the following: ^{1}  
Elementary Matrix and Linear Algebra  
Linear Algebra  
Topics in MultiVariable 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 500679 (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
Code  Title  Credits 

MATH/COMP SCI 513  Numerical Linear Algebra  3 
MATH/COMP SCI 514  Numerical Analysis  3 
MATH 519  Ordinary Differential Equations  3 
MATH 521  Analysis I  3 
MATH 522  Analysis II  3 
MATH/COMP SCI/I SY E/STAT 525  Linear Programming Methods  3 
MATH 531  Probability Theory  3 
MATH 541  Modern Algebra  3 
MATH 542  Modern Algebra  3 
MATH 551  Elementary Topology  3 
MATH 552  Elementary Geometric and Algebraic Topology  3 
MATH 561  Differential Geometry  3 
MATH 567  Elementary Number Theory  3 
MATH 570  Fundamentals of Set Theory  3 
MATH/PHILOS 571  Mathematical Logic  3 
MATH 605  Stochastic Methods for Biology  3 
MATH/B M I/BIOCHEM/BMOLCHEM 606  Mathematical Methods for Structural Biology  3 
MATH 607  Topics in Mathematics Study Abroad  15 
MATH 608  Mathematical Methods for Continuum Modeling in Biology  3 
MATH/B M I/BIOCHEM/BMOLCHEM 609  Mathematical Methods for Systems Biology  3 
MATH 619  Analysis of Partial Differential Equations  3 
MATH 621  Analysis III  3 
MATH 623  Complex Analysis  3 
MATH 627  Introduction to Fourier Analysis  3 
MATH 629  Introduction to Measure and Integration  3 
MATH/I SY E/OTM/STAT 632  Introduction to Stochastic Processes  3 
MATH/I SY E/OTM 633  Queuing Theory and Stochastic Modeling  3 
MATH 635  An Introduction to Brownian Motion and Stochastic Calculus  3 
MATH/E C E 641  Introduction to ErrorCorrecting Codes  3 
Course list B^{1}
Code  Title  Credits 

MATH/STAT 309  Introduction to Probability and Mathematical Statistics I  3 
MATH/STAT 310  Introduction to Probability and Mathematical Statistics II  3 
MATH 319  Techniques in Ordinary Differential Equations  3 
MATH 321  Applied Mathematical Analysis  3 
MATH 322  Applied Mathematical Analysis  3 
MATH 331  An Introduction to Probability and Markov Chain Models  3 
MATH 341  Linear Algebra  3 
MATH 376  Topics in MultiVariable Calculus and Differential Equations  5 
MATH 407  Topics in Mathematics Study Abroad  15 
MATH 415  Applied Dynamical Systems, Chaos and Modeling  3 
MATH/COMP SCI/I SY E 425  Introduction to Combinatorial Optimization ^{2}  3 
MATH/STAT 431  Introduction to the Theory of Probability  3 
MATH/COMP SCI/E C E 435  Introduction to Cryptography  3 
MATH 441  Introduction to Modern Algebra  3 
MATH 443  Applied Linear Algebra  3 
MATH 461  College Geometry I  3 
MATH/HIST SCI 473  History of Mathematics  3 
MATH/COMP SCI/STAT 475  Introduction to Combinatorics  3 
MATH 491  Topics in Undergraduate Mathematics  3 
MATH/COMP SCI 513  Numerical Linear Algebra  3 
MATH/COMP SCI 514  Numerical Analysis  3 
MATH 519  Ordinary Differential Equations  3 
MATH 521  Analysis I  3 
MATH 522  Analysis II  3 
MATH/COMP SCI/I SY E/STAT 525  Linear Programming Methods  3 
MATH 531  Probability Theory  3 
MATH 541  Modern Algebra  3 
MATH 542  Modern Algebra  3 
MATH 551  Elementary Topology  3 
MATH 552  Elementary Geometric and Algebraic Topology  3 
MATH 561  Differential Geometry  3 
MATH 567  Elementary Number Theory  3 
MATH 570  Fundamentals of Set Theory  3 
MATH/PHILOS 571  Mathematical Logic  3 
MATH 605  Stochastic Methods for Biology  3 
MATH/B M I/BIOCHEM/BMOLCHEM 606  Mathematical Methods for Structural Biology  3 
MATH 607  Topics in Mathematics Study Abroad  15 
MATH 608  Mathematical Methods for Continuum Modeling in Biology  3 
MATH/B M I/BIOCHEM/BMOLCHEM 609  Mathematical Methods for Systems Biology  3 
MATH 619  Analysis of Partial Differential Equations  3 
MATH 621  Analysis III  3 
MATH 623  Complex Analysis  3 
MATH 627  Introduction to Fourier Analysis  3 
MATH 629  Introduction to Measure and Integration  3 
MATH/I SY E/OTM/STAT 632  Introduction to Stochastic Processes  3 
MATH/I SY E/OTM 633  Queuing Theory and Stochastic Modeling  3 
MATH 635  An Introduction to Brownian Motion and Stochastic Calculus  3 
MATH/E C E 641  Introduction to ErrorCorrecting Codes  3 
MATH 681  Senior Honors Thesis  3 
MATH 682  Senior Honors Thesis  3 
MATH 691  Undergraduate Thesis  24 
MATH 692  Undergraduate Thesis  24 
^{1}  There are two subgroups within this course list where only one course from each subgroup will count towards the major:

^{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. A mathematics advisor must approve the collection of courses used to complete major requirements prior to major declaration.
Mathematics Core
Code  Title  Credits 

Linear Algebra  
Select one of the following: ^{1}  
Linear Algebra and Differential Equations  
Elementary Matrix and Linear Algebra  
Linear Algebra  
Topics in MultiVariable Calculus and Linear Algebra  
Advanced Courses  
Select two courses from MATH 500  679 (see course list A below). These courses must be approved by a mathematics advisor.  
Intermediate Courses  
Select three courses from MATH 307 692 (see course list B below). These courses must be approved by a mathematics advisor. 
^{1}  Only one of these courses will count towards the major. 
Course List A
Code  Title  Credits 

MATH/COMP SCI 513  Numerical Linear Algebra  3 
MATH/COMP SCI 514  Numerical Analysis  3 
MATH 519  Ordinary Differential Equations  3 
MATH 521  Analysis I  3 
MATH 522  Analysis II  3 
MATH/COMP SCI/I SY E/STAT 525  Linear Programming Methods  3 
MATH 531  Probability Theory  3 
MATH 541  Modern Algebra  3 
MATH 542  Modern Algebra  3 
MATH 551  Elementary Topology  3 
MATH 552  Elementary Geometric and Algebraic Topology  3 
MATH 561  Differential Geometry  3 
MATH 567  Elementary Number Theory  3 
MATH 570  Fundamentals of Set Theory  3 
MATH/PHILOS 571  Mathematical Logic  3 
MATH 605  Stochastic Methods for Biology  3 
MATH/B M I/BIOCHEM/BMOLCHEM 606  Mathematical Methods for Structural Biology  3 
MATH 607  Topics in Mathematics Study Abroad  15 
MATH 608  Mathematical Methods for Continuum Modeling in Biology  3 
MATH/B M I/BIOCHEM/BMOLCHEM 609  Mathematical Methods for Systems Biology  3 
MATH 619  Analysis of Partial Differential Equations  3 
MATH 621  Analysis III  3 
MATH 623  Complex Analysis  3 
MATH 627  Introduction to Fourier Analysis  3 
MATH 629  Introduction to Measure and Integration  3 
MATH/I SY E/OTM/STAT 632  Introduction to Stochastic Processes  3 
MATH/I SY E/OTM 633  Queuing Theory and Stochastic Modeling  3 
MATH 635  An Introduction to Brownian Motion and Stochastic Calculus  3 
MATH/E C E 641  Introduction to ErrorCorrecting Codes  3 
Course List B^{1}
Code  Title  Credits 

MATH/STAT 309  Introduction to Probability and Mathematical Statistics I  3 
MATH/STAT 310  Introduction to Probability and Mathematical Statistics II  3 
MATH 319  Techniques in Ordinary Differential Equations  3 
MATH 320  Linear Algebra and Differential Equations  3 
MATH 321  Applied Mathematical Analysis  3 
MATH 322  Applied Mathematical Analysis  3 
MATH 331  An Introduction to Probability and Markov Chain Models  3 
MATH 340  Elementary Matrix and Linear Algebra  3 
MATH 341  Linear Algebra  3 
MATH 375  Topics in MultiVariable Calculus and Linear Algebra  5 
MATH 376  Topics in MultiVariable Calculus and Differential Equations  5 
MATH 407  Topics in Mathematics Study Abroad  15 
MATH 415  Applied Dynamical Systems, Chaos and Modeling  3 
MATH 421  The Theory of Single Variable Calculus  3 
MATH/COMP SCI/I SY E 425  Introduction to Combinatorial Optimization  3 
MATH/STAT 431  Introduction to the Theory of Probability  3 
MATH/COMP SCI/E C E 435  Introduction to Cryptography  3 
MATH 441  Introduction to Modern Algebra  3 
MATH 443  Applied Linear Algebra  3 
MATH 461  College Geometry I  3 
MATH/CURRIC 471  Mathematics for Secondary School Teachers  3 
MATH/HIST SCI 473  History of Mathematics  3 
MATH/COMP SCI/STAT 475  Introduction to Combinatorics  3 
MATH/COMP SCI 513  Numerical Linear Algebra  3 
MATH/COMP SCI 514  Numerical Analysis  3 
MATH 519  Ordinary Differential Equations  3 
MATH 521  Analysis I  3 
MATH 522  Analysis II  3 
MATH/COMP SCI/I SY E/STAT 525  Linear Programming Methods  3 
MATH 531  Probability Theory  3 
MATH 541  Modern Algebra  3 
MATH 542  Modern Algebra  3 
MATH 551  Elementary Topology  3 
MATH 552  Elementary Geometric and Algebraic Topology  3 
MATH 561  Differential Geometry  3 
MATH 567  Elementary Number Theory  3 
MATH 570  Fundamentals of Set Theory  3 
MATH/PHILOS 571  Mathematical Logic  3 
MATH 605  Stochastic Methods for Biology  3 
MATH/B M I/BIOCHEM/BMOLCHEM 606  Mathematical Methods for Structural Biology  3 
MATH 607  Topics in Mathematics Study Abroad  15 
MATH 608  Mathematical Methods for Continuum Modeling in Biology  3 
MATH/B M I/BIOCHEM/BMOLCHEM 609  Mathematical Methods for Systems Biology  3 
MATH 619  Analysis of Partial Differential Equations  3 
MATH 621  Analysis III  3 
MATH 623  Complex Analysis  3 
MATH 627  Introduction to Fourier Analysis  3 
MATH 629  Introduction to Measure and Integration  3 
MATH/I SY E/OTM/STAT 632  Introduction to Stochastic Processes  3 
MATH/I SY E/OTM 633  Queuing Theory and Stochastic Modeling  3 
MATH 635  An Introduction to Brownian Motion and Stochastic Calculus  3 
MATH/E C E 641  Introduction to ErrorCorrecting Codes  3 
^{1}  There are two subgroups within this course list where only one course from each subgroup will count towards the major:

Applied Concentration Area
Select four additional courses. These courses may be from any department and should be appropriate for the focused nature of the option II major. The following concentration areas have been preapproved and may be useful for planning purposes, though any collection of four courses approved by a mathematics advisor can be used to fulfill this program requirement. Note that math courses may fulfill the requirements in the concentration, but cannot also count for the core mathematics course requirements listed above.
Actuarial Mathematics
Code  Title  Credits 

ACT SCI/MATH 303  Theory of Interest and Life Insurance  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 
Astronomy
Code  Title  Credits 

Select two from the following:  
ASTRON 310  Stellar Astrophysics  3 
ASTRON 320  The Interstellar Medium  3 
ASTRON 335  Cosmology  3 
Any two 3credit PHYSICS courses numbered 400 and above excluding labs 
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 
BioInformatics
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 
BioStatistics
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 
or STAT/B M I 642  Statistical Methods for Epidemiology 
Business
Code  Title  Credits 

MATH/COMP SCI/I SY E/STAT 525  Linear Programming Methods  3 
OTM 410  Operations Research I  3 
Select two from the following:  
GEN BUS 306  Business Analytics I  3 
GEN BUS 307  Business Analytics II  3 
OTM 451  Service Operations Management  3 
OTM 411  Operations Research II  3 
OTM/I SY E/MATH 633  Queuing Theory and Stochastic Modeling  3 
OTM 654  Production Planning and Control  3 
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 
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 
Civil and Environmental Engineering
Code  Title  Credits 

CIV ENGR 310  Fluid Mechanics  3 
CIV ENGR 311  Hydroscience  3 
CIV ENGR 340  Structural Analysis I  4 
Select one of the following:  
CIV ENGR 440  Structural Analysis II  3 
CIV ENGR 442  Wood Structures I  3 
CIV ENGR 445  Steel Structures I  3 
CIV ENGR 447  Concrete Structures I  3 
Computer Sciences (Computational Methods)
Code  Title  Credits 

Select four of the following:  
COMP SCI/E C E 352  Digital System Fundamentals  3 
COMP SCI 400  Programming III  3 
COMP SCI 412  Introduction to Numerical Methods  3 
COMP SCI/E C E/MATH 435  Introduction to Cryptography  3 
COMP SCI/MATH/STAT 475  Introduction to Combinatorics  3 
COMP SCI/MATH 513  Numerical Linear Algebra  3 
COMP SCI/MATH 514  Numerical Analysis  3 
COMP SCI/I SY E/MATH/STAT 525  Linear Programming Methods  3 
COMP SCI/E C E 533  Image Processing  3 
COMP SCI 540  Introduction to Artificial Intelligence  3 
COMP SCI 545  Natural Language and Computing  3 
COMP SCI/I SY E/M E 558  Introduction to Computational Geometry  3 
COMP SCI 559  Computer Graphics  3 
Computer Sciences (Cryptography)
Code  Title  Credits 

COMP SCI 300  Programming II  3 
COMP SCI 400  Programming III  3 
Select two of the following:  
Introduction to Operating Systems  
Introduction to Information Security  
Digital System Fundamentals  
Introduction to ErrorCorrecting Codes 
Computer Sciences (Theory)
Code  Title  Credits 

COMP SCI 520  Introduction to Theory of Computing  3 
COMP SCI 577  Introduction to Algorithms  4 
Select two of the following:  
Digital System Fundamentals  
Programming III  
Introduction to Numerical Methods  
Introduction to Cryptography  
Introduction to Combinatorics  
Numerical Linear Algebra  
Numerical Analysis  
Linear Programming Methods  
Image Processing  
Introduction to Artificial Intelligence  
Natural Language and Computing  
Introduction to Computational Geometry  
Computer Graphics 
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  34 
ZOOLOGY 504  Modeling Animal Landscapes  35 
ZOOLOGY/BOTANY/F&W ECOL 460  General Ecology  4 
ZOOLOGY 535  Ecosystem Analysis  3 
ZOOLOGY/ENTOM 540  Theoretical Ecology  3 
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 
Select two of the following:  
ZOOLOGY/BOTANY/F&W ECOL 460  General Ecology  4 
ZOOLOGY 504  Modeling Animal Landscapes  35 
ZOOLOGY/ENTOM 540  Theoretical Ecology  3 
F&W ECOL 300  Forest Biometry  4 
F&W ECOL 410  Principles of Silviculture  3 
F&W ECOL/BOTANY/ZOOLOGY 460  General Ecology  4 
F&W ECOL/A A E/ECON 531  Natural Resource Economics  3 
F&W ECOL/A A E/ENVIR ST 652  Decision Methods for Natural Resource Managers  34 
F&W ECOL 655  Animal Population Dynamics  3 
Economics
Code  Title  Credits 

ECON 301  Intermediate Microeconomic Theory  34 
or ECON 311  Intermediate Microeconomic Theory  Advanced Treatment  
ECON 302  Intermediate Macroeconomic Theory  34 
or ECON 312  Intermediate Macroeconomic Theory  Advanced Treatment  
Select two of the following:  
ECON 410  Introductory Econometrics  4 
ECON 475  Economics of Growth  34 
ECON 503  Markets with Frictions  34 
ECON 521  Game Theory and Economic Analysis  34 
ECON 525  Economics of Education: Theory and Measurement  3 
ECON 666  Issues in International Finance  34 
MATH 415  Applied Dynamical Systems, Chaos and Modeling  3 
MATH/I SY E/OTM/STAT 632  Introduction to Stochastic Processes  3 
STAT/MATH 310  Introduction to Probability and Mathematical Statistics II  3 
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 
Select one of the following:  
E C E/COMP SCI/MATH 435  Introduction to Cryptography  3 
E C E/N E/PHYSICS 525  Introduction to Plasmas  3 
E C E/COMP SCI 533  Image Processing  3 
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 
Select one of the following:  
E M A 521  Aerodynamics  3 
E M A 542  Advanced Dynamics  3 
E M A 545  Mechanical Vibrations  3 
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 
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  34 
F&W ECOL 635  Forest Stand Dynamics  12 
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 
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 ResearchDeterministic Modeling  3 
Select one of the following:  
I SY E/COMP SCI/MATH 425  Introduction to Combinatorial Optimization  3 
I SY E 516  Introduction to Decision Analysis  3 
I SY E/COMP SCI/MATH/STAT 525  Linear Programming Methods  3 
I SY E/COMP SCI 526  Advanced Linear Programming  34 
I SY E/COMP SCI/M E 558  Introduction to Computational Geometry  3 
I SY E 575  Introduction to Quality Engineering  3 
I SY E 615  Production Systems Control  3 
I SY E/OTM 620  Simulation Modeling and Analysis  3 
I SY E 624  Stochastic Modeling Techniques  3 
I SY E/COMP SCI 635  Tools and Environments for Optimization  3 
I SY E/M E 643  Performance Analysis of Manufacturing Systems  3 
Mechanical Engineering
Code  Title  Credits 

M E 340  Introduction to Dynamic Systems  3 
M E 361  Thermodynamics  3 
M E 363  Fluid Dynamics  3 
M E 364  Elementary Heat Transfer  3 
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 ScienceStructure and Property Relations in Solids  3 
Select one of the following:  
Introduction to Chemical Process Modeling  
Programming II  
Problem Solving Using Computers  
Circuit Analysis  
Electrical and Electronic Circuits  
Introduction to RealTime Digital Signal Processing  
Electric Circuits and Electronics  
Statistical Experimental Design 
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 
Select one of the following:  
Nuclear Reactor Engineering  
Electric Circuits and Electronics  
Electromagnetic Fields  
Electrical and Electronic Circuits  
Radiological Physics and Dosimetry 
Physics
Code  Title  Credits 

PHYSICS 311  Mechanics  3 
PHYSICS 322  Electromagnetic Fields  3 
Any two 3credit physics course above the 400 level (excluding labs)  
Select two from the following:  
PHYSICS 415  Thermal Physics  3 
PHYSICS 448  Atomic and Quantum Physics  3 
PHYSICS 449  Atomic and Quantum Physics  3 
PHYSICS/E C E/N E 525  Introduction to Plasmas  3 
PHYSICS 531  Introduction to Quantum Mechanics  3 
PHYSICS 535  Introduction to Particle Physics  3 
PHYSICS 545  Introduction to Atomic Structure  3 
PHYSICS 551  Solid State Physics  3 
Secondary Education
Code  Title  Credits 

MATH/CURRIC 471  Mathematics for Secondary School Teachers  3 
MATH/HIST SCI 473  History of Mathematics  3 
Select two from the following:  
Programming II  
The Theory of Single Variable Calculus  
Introduction to Combinatorics  
Differential Geometry  
Elementary Number Theory  
General Physics 
Statistics
Code  Title  Credits 

STAT 333  Applied Regression Analysis  3 
STAT/M E 424  Statistical Experimental Design  3 
Select two from the following:  
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 
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 
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 
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 ^{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:
Code  Title  Credits 

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 upperlevel 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 I–MATH 522 Analysis II or MATH 541 Modern Algebra–MATH 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. 
 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.
 Students will be able to construct and evaluate mathematical proofs and arguments.
 Students will acquire a diverse set of skills and strategies in mathematical reasoning/problem solving.
 Students will use mathematics to model and analyze phenomena in other disciplines.
 Students will be able to write, explain, and present mathematics to both experts and nonexperts.
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 dropin 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 dropin advising, students should contact one of the advisors to set up an appointment.
For advice on college algebra, precalculus, 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 MultiVariable 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 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.
Faculty
Professors Angenent, Arinkin, Assadi, Bolotin, Boston, Caldararu, Craciun, Denissov, Ellenberg, Feldman, Gong, Jin, Lempp, MariBeffa, 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), BenguriaAndrews (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)