The Mathematics for the Physical and Biological Sciences program requires 10 distinct courses for at least 30 credits as described below.  While a single courses may be used to fulfill more than one requirement, it will only contribute once to the total course count.  Finally, only one course from each of the following groupings may be used to fulfill course and credit requirements: Intro Linear Algebra (MATH 320MATH 340MATH 341MATH 375), Intro Differential Equations (MATH 319MATH 320 or MATH 376), and Intro Probability (MATH/​STAT  309 or MATH/​STAT  431).

Core Math Requirement (minimum of six distinct MATH courses for at least 18 credits) 1
Linear Algebra3-5
Linear Algebra and Differential Equations
Elementary Matrix and Linear Algebra
Linear Algebra
Topics in Multi-Variable Calculus and Linear Algebra
Differential Equations0-5
Techniques in Ordinary Differential Equations
Linear Algebra and Differential Equations
Topics in Multi-Variable Calculus and Differential Equations
Intermediate Mathematics Requirement (complete at one)0-6
Applied Mathematical Analysis
and Applied Mathematical Analysis
Topics in Multi-Variable Calculus and Linear Algebra
Linear Algebra
The Theory of Single Variable Calculus
Advanced Mathematics Requirement (complete one)3
Numerical Analysis
Ordinary Differential Equations
Analysis I
Probability Theory
Linear Algebra II
Modern Algebra
Elementary Topology
Differential Geometry
Analysis of Partial Differential Equations
Complex Analysis
MATH Elective to reach six courses and 18 credits3-9
At least one from: 1
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 Systems Biology
Analysis of Partial Differential Equations
Complex Analysis
Introduction to Fourier Analysis
Introduction to Measure and Integration
Introduction to Stochastic Processes
An Introduction to Brownian Motion and Stochastic Calculus
Remaining courses/credits may be from:
Introduction to Probability and Mathematical Statistics II
Applied Mathematical Analysis
Applied Mathematical Analysis
Applied Dynamical Systems, Chaos and Modeling
The Theory of Single Variable Calculus
Introduction to Combinatorial Optimization
Introduction to the Theory of Probability
Introduction to Probability and Mathematical Statistics I
Applied Linear Algebra
Introduction to Combinatorics
Natural/Biological Sciences Requirement (Four courses distinct from the above for at least 12 credits) 112-16
A Modern Introduction to Physics
General Physics
General Physics
Statics
A Modern Introduction to Physics
General Physics
General Physics
Two additional courses from the following: 2
Stellar Astrophysics
The Interstellar Medium
Dynamics of the Atmosphere and Ocean I
Dynamics of the Atmosphere and Ocean II
Science of Climate Change
Physics of the Atmosphere and Ocean I
Physics of the Atmosphere and Ocean II
Cellular Biology
Physical Chemistry
Biophysical Chemistry
Physical Chemistry
Programming II
Problem Solving Using Computers
Data Programming II
Programming III
Introduction to Combinatorial Optimization
Introduction to Combinatorics
Numerical Linear Algebra
Numerical Analysis
Linear Optimization
Introduction to Geophysics: The Dynamic Earth
Practical Applications of GPS Surveying
Quantitative Methods for Geoscience
Introduction to Applied Geophysics
Hydrogeology
A Modern Introduction to Physics
Introduction to Modern Physics
Modern Physics for Engineers
Mechanics
Electric Circuits and Electronics
Electromagnetic Fields
Electromagnetic Fields
Optics
Scientific Background to Global Environmental Problems
Radiological Physics and Dosimetry
Introduction to Plasmas
Solid State Physics
Radionuclides in Medicine and Biology
Electronic Aids to Measurement
Applied Optics
Introduction to Probability and Mathematical Statistics II
Introduction to Theory and Methods of Mathematical Statistics II
Applied Regression Analysis
Introduction to Time Series
Introductory Nonparametric Statistics
An Introduction to Sample Survey Theory and Methods
Applied Categorical Data Analysis
Statistical Experimental Design
Introduction to the Theory of Probability
Introduction to Probability and Mathematical Statistics I
Introduction to Theory and Methods of Mathematical Statistics I
Applied Multivariate Analysis
Financial Statistics
Introduction to Computational Statistics
Introduction to Combinatorics
Linear Optimization
Introduction to Stochastic Processes
Computational Modeling of Biological Systems
Mathematical Methods for Structural Biology
Mathematical Methods for Systems Biology
Plant Biochemistry
Mechanisms of Enzyme Action
Cellular Signal Transduction Mechanisms
Engineering Principles for Biological Systems
Quantitative Techniques for Biological Systems
Structural Design for Agricultural Facilities
Engineering Properties of Food and Biological Materials
Measurements and Instrumentation for Biological Systems
Rheology of Foods and Biomaterials
Engineering Principles of Agricultural Machinery
Bioinstrumentation
Biomechanics
Introductory Transport Phenomena
Applied Statistics for Biomedical Engineers
Engineering Principles of Molecules, Cells, and Tissues
Radiological Physics and Dosimetry
Biofluidics
Stem Cell Bioengineering
Medical Imaging Systems
Introduction to Energy-Tissue Interactions
Systems Biology: Mammalian Signaling Networks
Biochemical Engineering
Physics of Radiotherapy
The Physics of Diagnostic Radiology
Medical Image Science: Mathematical and Conceptual Foundations
Tissue Mechanics
Introduction to Chemical Process Modeling
Chemical Process Thermodynamics
Introductory Transport Phenomena
Momentum and Heat Transfer Operations
Engineering Principles of Molecules, Cells, and Tissues
Fluid Mechanics
Hydroscience
Environmental Engineering Processes
Structural Analysis I
Transportation Engineering
Uncertainty Analysis for Engineers
Electrodynamics I
Circuit Analysis
Introduction to Solid State Electronics
Electrodynamics II
Signals and Systems
Introduction to Cryptography
Introduction to Error-Correcting Codes
Dynamics
Dynamics
Mechanics of Materials
Mechanics of Materials
Practicum in Finite Elements
Intermediate Problem Solving for Engineers
Engineering Analysis I
Engineering Analysis II
Astrodynamics
Simulation and Probabilistic Modeling
Operations Research-Deterministic Modeling
Uncertainty Analysis for Engineers
Introduction to Decision Analysis
Introduction to Optimization
Linear Optimization
Advanced Linear Programming
Thermodynamics of Materials
Transport Phenomena in Materials
Macroprocessing of Materials
Introduction to Thin-Film Deposition Processes
Introduction to Computational Materials Science and Engineering
Computer-Aided Engineering
Dynamic Systems
Introduction to Feedback Control for Mechanical Engineers
Thermodynamics
Statistical Experimental Design
Fundamentals of Nuclear Engineering
Introduction to Plasmas
Methods for Probabilistic Risk Analysis of Nuclear Power Plants
Radiological Physics and Dosimetry
Medical Imaging Systems
Introduction to Energy-Tissue Interactions
Radionuclides in Medicine and Biology
The Physics of Diagnostic Radiology
Health Physics and Biological Effects
Total Credits30

Residency and quality of Work

  • 2.000 GPA for all MATH courses and courses eligible for the major.3
  • 2.000 GPA on at least 15 credits of upper level credit in the major.4
  • 15 credits in MATH in the major taken on the UW-Madison campus.5

 Footnotes

Sample Four-Year Plan

This Sample Four-Year Plan is a tool to assist students and their advisor(s). Students should use it—along with their DARS report, the Degree Planner, and Course Search & Enroll tools—to make their own four-year plan based on their placement scores, credit for transferred courses and approved examinations, and individual interests. As students become involved in athletics, honors, research, student organizations, study abroad, volunteer experiences, and/or work, they might adjust the order of their courses to accommodate these experiences. Students will likely revise their own four-year plan several times during college.

In general, your four year plan in mathematics should be organized along the following sequence: 1) Calculus, 2) Linear Algebra, 3) Required Intermediate level course, 4) Additional intermediate level courses as needed, 5) Required advanced level course, 6) Additional advanced level courses.

Freshman
FallCreditsSpringCredits
MATH 2215MATH 2224
Literature Breadth3Literature Breadth3
Communication A3Ethnic Studies3
Foreign Language if required4Foreign Language (if required)4
 15 14
Sophomore
FallCreditsSpringCredits
MATH 23414MATH 3213
MATH 3203Humanities Breadth3
Humanities Breadth3Elective6
Communication B3 
Elective3 
 16 12
Junior
FallCreditsSpringCredits
MATH 3223Intermediate MATH elective3
PHYSICS 247, 207, 201, or E M A 2015PHYSICS 248, 208, or 2025
Social Sciences Breadth3Social Science Breadth3
Biological Sciences Breadth3Biological Sciences Breadth3
Elective3Elective3
 17 17
Senior
FallCreditsSpringCredits
Required Advanced MATH3Advanced MATH3
Natural/Biological requirement elective3Natural/Biological requirement elective3
Social Science Breadth3Social Science Breadth3
Elective6Elective5
 15 14
Total Credits 120

 footnotes