The Mathematics major’s named options allow students to develop a deep understanding of how the subject relates to other areas of human inquiry. The requirements for these options feature mathematics courses with topics inspired by and commonly applied to problems in these associated fields. Though often paired with a second major in a related area, these programs function well alone and are suited to any mathematics student with a variety of interests. Students interested in a named option are recommended to meet with an advisor to navigate the various plans and courses available to them. Advising information can be found on the BA or BS pages.
The named options do not support Honors in the Major.
Requirements
The Mathematics for the Physical and Biological Sciences program requires at least 10 courses for at least 30 credits as described below.
Core Math Requirement
Complete at least six MATH courses for at least 18 credits.
Linear Algebra
Complete one course from the list below. Only one of these courses will be used to fulfill minimum course/credit requirements for the major.
| Code | Title | Credits |
|---|---|---|
| MATH 341 | Linear Algebra | 3-5 |
| or MATH 320 | Linear Algebra and Differential Equations | |
| or MATH 340 | Elementary Matrix and Linear Algebra | |
| or MATH 345 | Linear Algebra and Optimization | |
| or MATH 375 | Topics in Multi-Variable Calculus and Linear Algebra | |
Differential Equations
Complete one course from the list below. At most one course in Introductory Differential Equations (MATH 319, MATH 320, and MATH 376) may be used to fulfill the course/credit requirements for the major. If a student takes MATH 320 to complete the Linear Algebra requirement, they may also use that course for this requirement. The course and credits will count only once toward the course/credit requirements for the major.
| Code | Title | Credits |
|---|---|---|
| MATH 319 | Techniques in Ordinary Differential Equations | 3-5 |
| or MATH 320 | Linear Algebra and Differential Equations | |
| or MATH 376 | Topics in Multi-Variable Calculus and Differential Equations | |
| MATH 322 | Applied Mathematical Analysis 2: Partial Differential Equations | 3 |
| MATH 415 | Applied Dynamical Systems, Chaos and Modeling | 3 |
| MATH 519 | Ordinary Differential Equations | 3 |
Transition to Advanced Mathematics
Complete one course or sequence from the list below. If a student takes MATH 341 or MATH 375 to complete the Linear Algebra requirement, they may also use that course for this requirement. If a student takes MATH 322 to complete the Differential Equations requirement, they may also use that course for this requirement in sequence with MATH 321. In these situations, the course and credits will count only once toward the course/credit requirements for the major.
| Code | Title | Credits |
|---|---|---|
| MATH 341 | Linear Algebra | 3-5 |
| or MATH 375 | Topics in Multi-Variable Calculus and Linear Algebra | |
| MATH 421 | The Theory of Single Variable Calculus | 3 |
| MATH 321 & MATH 322 | Applied Mathematical Analysis 1: Vector and Complex Calculus and Applied Mathematical Analysis 2: Partial Differential Equations | 6 |
Advanced Mathematics Requirement
Complete one course from the list below. If a student takes MATH 519 to complete the Differential Equations requirement, they may use that course to complete this requirement as well. The course and credits will count only once toward the course/credit requirements for the major.
| Code | Title | Credits |
|---|---|---|
| MATH/COMP SCI 514 | Numerical Analysis | 3 |
| MATH 519 | Ordinary Differential Equations | 3 |
| MATH 521 | Analysis I | 3 |
| MATH 531 | Probability Theory | 3 |
| MATH 540 | Linear Algebra II | 3 |
| MATH 541 | Modern Algebra 1 | 3 |
| MATH 551 | Point-Set Topology | 3 |
| MATH 561 | Differential Geometry | 3 |
| MATH 619 | Analysis of Partial Differential Equations | 3 |
| MATH 623 | Complex Analysis | 3 |
MATH Electives
Complete at least six MATH courses for at least 18 credits to satisfy the overall requirements of the major by choosing additional MATH courses from the lists below.
At least one MATH elective must be chosen from the list of Advanced MATH Elective courses. The course chosen for the Advanced MATH Elective must be distinct from the course used for the Advanced Mathematics requirement.
The remaining courses required to reach the required minimum courses and credits may be chosen from either the list of Advanced MATH Elective courses or the Additional MATH Electives.
Advanced MATH Elective
| 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 Optimization | 3 |
| MATH 531 | Probability Theory | 3 |
| MATH 535 | Mathematical Methods in Data Science | 3 |
| MATH 540 | Linear Algebra II | 3 |
| MATH 541 | Modern Algebra 1 | 3 |
| MATH 542 | Modern Algebra 2 | 3 |
| MATH 551 | Point-Set Topology | 3 |
| MATH 552 | Introduction to Algebraic Topology | 3 |
| MATH 561 | Differential Geometry | 3 |
| MATH 567 | Modern Number Theory | 3 |
| MATH 570 | Fundamentals of Set Theory | 3 |
| MATH/PHILOS 571 | Mathematical Logic | 3 |
| MATH/B M I/BIOCHEM/BMOLCHEM 609 | Mathematical Methods for Systems Biology | 3 |
| MATH 616 | Data-Driven Dynamical Systems, Stochastic Modeling and Prediction | 3 |
| MATH 619 | Analysis of Partial Differential Equations | 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 635 | An Introduction to Brownian Motion and Stochastic Calculus | 3 |
Additional MATH Electives
| Code | Title | Credits |
|---|---|---|
| MATH/STAT 310 | Introduction to Probability and Mathematical Statistics II | 3 |
| MATH 321 | Applied Mathematical Analysis 1: Vector and Complex Calculus | 3 |
| MATH 322 | Applied Mathematical Analysis 2: Partial Differential Equations | 3 |
| 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 |
| or MATH/STAT 309 | Introduction to Probability and Mathematical Statistics I | |
At most one course in Introductory Probability (MATH/STAT 309 and MATH/STAT 431) may be used to fulfill the course/credit requirements for the major. | ||
| MATH 443 | Applied Linear Algebra | 3 |
| MATH 444 | Graphs and Networks in Data Science | 3 |
| MATH/COMP SCI/STAT 475 | Introduction to Combinatorics | 3 |
Natural/Biological Sciences Requirement
Complete at least four courses for at least 12 credits. Each course that satisfies this requirement must be distinct from those satisfying any part of the Core Math requirement. Courses below may have prerequisites outside of the requirements for this named option.
Complete two courses from:
| Code | Title | Credits |
|---|---|---|
| PHYSICS 247 | A Modern Introduction to Physics | 3-5 |
| or PHYSICS 207 | General Physics | |
| or PHYSICS 201 | General Physics | |
| or E M A 201 | Statics | |
| PHYSICS 248 | A Modern Introduction to Physics | 5 |
| or PHYSICS 208 | General Physics | |
| or PHYSICS 202 | General Physics | |
Natural/Biological Sciences Electives
To reach the four courses and 12 credits required, students may complete additional courses from the MATH electives lists above or any of the following courses.
Approved Electives
| Code | Title | Credits |
|---|---|---|
| ASTRON 310 | Stellar Astrophysics | 3 |
| ASTRON 320 | The Interstellar Medium | 3 |
| 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 |
| ATM OCN 340 | Physics of the Atmosphere and Ocean II | 3 |
| BIOCORE 383 | Cellular Biology | 3 |
| CHEM 561 | Physical Chemistry I | 3 |
| or CHEM 665 | Biophysical Chemistry | |
| CHEM 562 | Physical Chemistry II | 3 |
| COMP SCI 300 | Programming II | 3 |
| COMP SCI 310 | Problem Solving Using Computers | 3 |
| COMP SCI 320 | Data Science Programming II | 4 |
| COMP SCI 400 | Programming III | 3 |
| COMP SCI/I SY E/MATH 425 | Introduction to Combinatorial Optimization | 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 Optimization | 3 |
| GEOSCI/G L E 350 | Introduction to Geophysics: The Dynamic Earth | 3 |
| GEOSCI/CIV ENGR/ENVIR ST/G L E 444 | Practical Applications of GPS Surveying | 2 |
| GEOSCI/G L E 537 | Quantitative Methods for Geoscience | 3 |
| GEOSCI/G L E 594 | Introduction to Applied Geophysics | 3 |
| GEOSCI/G L E 627 | Hydrogeology | 3-4 |
| PHYSICS 249 | A Modern Introduction to Physics | 4 |
| or PHYSICS 241 | Introduction to Modern Physics | |
| or PHYSICS 205 | Modern Physics for Engineers | |
| PHYSICS 311 | Mechanics | 3 |
| PHYSICS 321 | Electric Circuits and Electronics | 4 |
| PHYSICS 322 | Electromagnetic Fields | 3 |
| PHYSICS 323 | Electromagnetic Fields | 3 |
| PHYSICS 325 | Optics | 4 |
| PHYSICS/B M E/H ONCOL/MED PHYS 501 | Radiation Physics and Dosimetry | 3 |
| PHYSICS/E C E/N E 525 | Introduction to Plasmas | 3 |
| PHYSICS 551 | Solid State Physics | 3 |
| PHYSICS 623 | Electronic Aids to Measurement | 4 |
| PHYSICS 625 | Applied Optics | 4 |
| STAT/MATH 310 | Introduction to Probability and Mathematical Statistics II | 3 |
| or STAT 312 | Introduction to Theory and Methods of Mathematical Statistics II | |
| STAT 333 | Applied Regression Analysis | 3 |
| STAT 349 | Introduction to Time Series | 3 |
| STAT 351 | Introductory Nonparametric Statistics | 3 |
| STAT 411 | An Introduction to Sample Survey Theory and Methods | 3 |
| STAT 421 | Applied Categorical Data Analysis | 3 |
| STAT 424 | Statistical Experimental Design | 3 |
| STAT/MATH 431 | Introduction to the Theory of Probability | 3 |
| or STAT/MATH 309 | Introduction to Probability and Mathematical Statistics I | |
| or STAT 311 | Introduction to Theory and Methods of Mathematical Statistics I | |
| STAT 456 | Applied Multivariate Analysis | 3 |
| STAT 461 | Financial Statistics | 3 |
| STAT/COMP SCI 471 | Introduction to Computational Statistics | 3 |
| STAT/COMP SCI/MATH 475 | Introduction to Combinatorics | 3 |
| STAT/COMP SCI/I SY E/MATH 525 | Linear Optimization | 3 |
| STAT/I SY E/MATH/OTM 632 | Introduction to Stochastic Processes | 3 |
| BIOCHEM/B M I/BMOLCHEM/MATH 609 | Mathematical Methods for Systems Biology | 3 |
| BIOCHEM/BOTANY 621 | Plant Biochemistry | 3 |
| BSE 249 | Engineering Principles for Biological Systems | 3 |
| BSE 349 | Quantitative Techniques for Biological Systems | 3 |
| BSE 364 | Engineering Properties of Food and Biological Materials | 3 |
| BSE 365 | Measurements and Instrumentation for Biological Systems | 3 |
| BSE/M E 475 | Engineering Principles of Agricultural Machinery | 3 |
| B M E 310 | Bioinstrumentation | 3 |
| B M E 315 | Biomechanics | 3 |
| B M E 325 | Applied Statistics for Biomedical Engineers | 3 |
| B M E 330 | Engineering Principles of Molecules, Cells, and Tissues | 4 |
| B M E/H ONCOL/MED PHYS/PHYSICS 501 | Radiation Physics and Dosimetry | 3 |
| B M E/M E 505 | Biofluidics | 3 |
| B M E 520 | Stem Cell Bioengineering | 3 |
| B M E/MED PHYS 535 | Introduction to Energy-Tissue Interactions | 3 |
| B M E 556 | Systems Biology: Mammalian Signaling Networks | 3 |
| B M E/MED PHYS 566 | Physics of Radiotherapy | 3 |
| B M E/MED PHYS 573 | Mathematical Methods in Medical Physics | 3 |
| B M E/M E 615 | Tissue Mechanics | 3 |
| CBE 255 | Introduction to Chemical Process Modeling | 3 |
| CBE 310 | Chemical Process Thermodynamics | 3 |
| CBE 320 | Introductory Transport Phenomena | 4 |
| CBE 326 | Momentum and Heat Transfer Operations | 3 |
| CIV ENGR 310 | Fluid Mechanics | 3 |
| CIV ENGR 311 | Hydroscience | 3 |
| CIV ENGR 322 | Environmental Engineering Processes | 3 |
| CIV ENGR 340 | Structural Analysis I | 3 |
| CIV ENGR 370 | Transportation Engineering | 3 |
| E C E 220 | Electrodynamics I | 3 |
| E C E 230 | Circuit Analysis | 4 |
| E C E/PHYSICS 235 | Introduction to Solid State Electronics | 3 |
| E C E 320 | Electrodynamics II | 3 |
| E C E 330 | Signals and Systems | 3 |
| E C E/COMP SCI/MATH 435 | Introduction to Cryptography | 3 |
| E C E/M E 441 | Kinematics, Dynamics, and Control of Robotic Manipulators | 3 |
| E M A 202 | Dynamics | 3 |
| E M A 303 | Mechanics of Materials | 3 |
| E M A 405 | Practicum in Finite Elements | 3 |
| E M A 450 | Orbital Mechanics | 3 |
| E M A/E P 471 | Intermediate Problem Solving for Engineers | 3 |
| E M A/E P 547 | Engineering Analysis I | 3 |
| E M A/E P 548 | Engineering Analysis II | 3 |
| I SY E 320 | Simulation and Probabilistic Modeling | 3 |
| I SY E 323 | Operations Research-Deterministic Modeling | 3 |
| I SY E 516 | Introduction to Decision Analysis | 3 |
| I SY E/COMP SCI/E C E 524 | Introduction to Optimization | 3 |
| I SY E/COMP SCI/MATH/STAT 525 | Linear Optimization | 3 |
| I SY E/COMP SCI 526 | Advanced Linear Programming | 3 |
| I SY E 623 | Advanced Optimization Modeling | 3 |
| M S & E 330 | Thermodynamics of Materials | 4 |
| M S & E 331 | Transport Phenomena in Materials | 3 |
| M S & E 332 | Macroprocessing of Materials | 3 |
| M S & E 434 | Introduction to Thin-Film Deposition Processes | 3 |
| M S & E 460 | Introduction to Computational Materials Science and Engineering | 3 |
| M E 331 | Computer-Aided Engineering | 3 |
| M E 340 | Dynamic Systems | 3 |
| M E 361 | Thermodynamics | 3 |
| M E 446 | Introduction to Feedback Control | 3 |
| M E 536 | Machine Learning for Data-Driven Engineering Design | 3 |
| N E 305 | Fundamentals of Nuclear Engineering | 3 |
| N E/E C E/PHYSICS 525 | Introduction to Plasmas | 3 |
| N E/I SY E 574 | Methods for Probabilistic Risk Analysis of Nuclear Power Plants | 3 |
| MED PHYS/B M E/H ONCOL/PHYSICS 501 | Radiation Physics and Dosimetry | 3 |
| MED PHYS/B M E 535 | Introduction to Energy-Tissue Interactions | 3 |
| MED PHYS/N E 569 | Health Physics and Biological Effects | 3-4 |
Residence and Quality of Work
- 2.000 GPA for all MATH courses and courses eligible for the major.
- This includes all MATH courses (including those cross-listed with MATH), regardless of appearing in the requirements of the program, and any non-MATH course that meets a requirement in the program.
- 2.000 GPA on at least 15 credits of upper level credit in the major.
- This includes all MATH courses numbered 307 and above (including those cross-listed with MATH), regardless of appearing in the requirements of the program, and any non-MATH courses that meet a requirement in the program and carry the Advanced level designation.
- 15 credits in MATH in the major taken on the UW-Madison campus.
- This includes all MATH courses numbered 307 and above (including those cross-listed with MATH), regardless of appearing in the requirements of the program.
Four-Year Plan
This Four-Year Plan is only one way a student may complete an L&S degree with this major. Many factors can affect student degree planning, including placement scores, credit for transferred courses, credits earned by examination, and individual scholarly interests. In addition, many students have commitments (e.g., athletics, honors, research, student organizations, study abroad, work and volunteer experiences) that necessitate they adjust their plans accordingly. Informed students engage in their own unique Wisconsin Experience by consulting their academic advisors, Guide, DARS, and Course Search & Enroll for assistance making and adjusting their plan.
In general, your four year plan in mathematics should be organized along the following sequence:
- Calculus
- Linear Algebra
- Transition to Advanced Mathematics course (or sequence)
- Additional 300/400-level courses as needed
- Required Advanced Math course
- Additional 500/600-level course(s)
| Freshman | |||
|---|---|---|---|
| Fall | Credits | Spring | Credits |
| MATH 221 | 5 | MATH 222 | 4 |
| Literature Breadth | 3 | Literature Breadth | 3 |
| Communication A | 3 | Ethnic Studies | 3 |
| Language (if required) | 4 | Language (if required) | 4 |
| 15 | 14 | ||
| Sophomore | |||
| Fall | Credits | Spring | Credits |
| MATH 2341 | 4 | MATH 321 | 3 |
| MATH 320 | 3 | Humanities Breadth | 3 |
| Humanities Breadth | 3 | Social Sciences Breadth | 3 |
| Communication B | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| 16 | 15 | ||
| Junior | |||
| Fall | Credits | Spring | Credits |
| 300/400-level MATH elective | 3 | MATH 322 | 3 |
| PHYSICS 247, 207, 201, or E M A 201 | 5 | PHYSICS 248, 208, or 202 | 5 |
| Social Sciences Breadth | 3 | Biological Sciences Breadth | 3 |
| Biological Sciences Breadth | 3 | INTER-LS 210 | 1 |
| Elective | 3 | ||
| 14 | 15 | ||
| Senior | |||
| Fall | Credits | Spring | Credits |
| Required Advanced MATH | 3 | 500/600-level MATH elective | 3 |
| Natural/Biological requirement elective | 3 | Natural/Biological requirement elective | 3 |
| Social Sciences Breadth | 3 | Social Sciences Breadth | 3 |
| Elective | 4 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| 16 | 15 | ||
| Total Credits 120 | |||
Footnotes
- 1
Students should declare their major upon the successful completion of this course