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 
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. Please note that the following special degree programs are not considered majors so are not available to nonL&Sdegreeseeking 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 MultiVariable Calculus and Linear Algebra  
Analysis, Topology, Algebra (complete two):  6  
Analysis I  
Modern Algebra  
Elementary Topology  
Math 500699 (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 ErrorCorrecting 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 MultiVariable Calculus and Differential Equations  
Applied Mathematical Analysis  
Applied Mathematical Analysis  
Topics in Mathematics Study Abroad  
Applied Dynamical Systems, Chaos and Modeling  
The Theory of Single Variable Calculus  
Introduction to Combinatorial Optimization  
Introduction to Cryptography  
Introduction to Modern Algebra  
Applied Linear Algebra  
College Geometry I  
Introduction to Number Theory  
History of Mathematics  
Introduction to Combinatorics  
Undergraduate Seminar  
Topics in Undergraduate Mathematics  
Numerical Linear Algebra  
Numerical Analysis  
Ordinary Differential Equations  
Analysis I  
Analysis II  
Linear Optimization  
Probability Theory  
Mathematical Methods in Data Science  
Linear Algebra II  
Modern Algebra  
Modern Algebra  
Elementary Topology  
Elementary Geometric and Algebraic Topology  
Differential Geometry  
Modern Number Theory  
Fundamentals of Set Theory  
Mathematical Logic  
Stochastic Methods for Biology  
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 ErrorCorrecting 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 MultiVariable 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 500699 requirement and a course used to meet the MATH 500699 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 MultiVariable 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 MultiVariable Calculus and Linear Algebra  
Math 500699 (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 ErrorCorrecting 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 MultiVariable Calculus and Differential Equations  
Applied Mathematical Analysis  
Applied Mathematical Analysis  
Topics in Mathematics Study Abroad  
Applied Dynamical Systems, Chaos and Modeling  
The Theory of Single Variable Calculus  
Introduction to Combinatorial Optimization  
Introduction to Cryptography  
Introduction to Modern Algebra  
Applied Linear Algebra  
College Geometry I  
Introduction to Number Theory  
History of Mathematics  
Introduction to Combinatorics  
Undergraduate Seminar  
Topics in Undergraduate Mathematics  
Numerical Linear Algebra  
Numerical Analysis  
Ordinary Differential Equations  
Analysis I  
Analysis II  
Linear Optimization  
Probability Theory  
Mathematical Methods in Data Science  
Linear Algebra II  
Modern Algebra  
Modern Algebra  
Elementary Topology  
Elementary Geometric and Algebraic Topology  
Differential Geometry  
Modern Number Theory  
Fundamentals of Set Theory  
Mathematical Logic  
Stochastic Methods for Biology  
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 ErrorCorrecting 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 preapproved 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 subjectarea department.
PreApproved 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 3credit 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 
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 
Total Credits  12 
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 
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 ErrorCorrecting 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  34 
ZOOLOGY 504  Modeling Animal Landscapes  35 
ZOOLOGY/BOTANY/F&W ECOL 460  General Ecology  4 
ZOOLOGY/ENTOM 540  Theoretical Ecology  3 
Total Credits  1619 
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  34 
or ECON 311  Intermediate Microeconomic Theory  Advanced Treatment  
ECON 302  Intermediate Macroeconomic Theory  34 
or ECON 312  Intermediate Macroeconomic Theory  Advanced Treatment  
And two of the following:  68  
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  1216 
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  34 
F&W ECOL 635  Forest Stand Dynamics  12 
Total Credits  1113 
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 ResearchDeterministic 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 ScienceStructure 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 RealTime 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 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 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 upperlevel 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 nonexperts.
The Sample FourYear 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 FourYear 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 4year plan several times during college.
Traditional Mathematics Major  Bachelor of Arts/Science Degree
Freshman  

Fall  Credits  Spring  Credits 
MATH 221^{1,2,3}  5  MATH 222^{2,3}  4 
CommunicationA (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 Algebra^{4}  3 
CommunicationB  35  Intermediate MATH^{5,6}  3 
L&S Breadth  3  L&S Breadth  3 
L&S Breadth  3  L&S Breadth  3 
Elective  3  Elective  3 
1618  15  
Junior  
Fall  Credits  Spring  Credits 
Intermediate MATH^{6}  3  Intermediate MATH^{6}  3 
L&S Breadth  3  Advanced MATH^{7}  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 MATH^{7}  3  L&S Breadth  3 
L&S Breadth  3  Elective  3 
Elective  3  Elective  3 
Elective  3  Elective  3 
Elective  3  Advanced MATH^{7}  3 
15  15  
Total Credits 120122 
Focused Mathematics Major  Bachelor of Arts/Science Degree
Note: approval of math and application courses required.
Freshman  

Fall  Credits  Spring  Credits 
MATH 221^{1,2,3}  5  MATH 222^{2,3}  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 
CommunicationA (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 234^{2,3}  4  MATH Linear Algebra^{4}  3 
MATH Option 2 Applied Concentration Area Course Prerequisite or L&S Breadth  3  Intermediate MATH^{5,6}  3 
CommunicationB  35  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 
1618  15  
Junior  
Fall  Credits  Spring  Credits 
Intermediate MATH^{6}  3  Intermediate MATH^{6}  3 
MATH Major Option 2 Applied Concentration Area Course^{8}  3  MATH Major Option 2 Applied Concentration Area Course^{8}  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 MATH^{7}  3  Advanced MATH^{7}  3 
MATH Major Option 2 Applied Concentration Area Course^{8}  3  MATH Major Option 2 Applied Concentration Area Course^{8}  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 120122 
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 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.
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
 INTERLS 210 L&S Career Development: Taking Initiative (1 credit, targeted to first and secondyear students)—for more information, see InterLS 210: Career Development, Taking Initiative
 INTERLS 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, 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)