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 Programming and Computing 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 | |
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. The course and credits will only count once toward the course/credit requirements for the major.
| Code | Title | Credits |
|---|---|---|
| MATH 341 | Linear Algebra | 3 |
| or MATH 375 | Topics in Multi-Variable Calculus and Linear Algebra | |
| MATH 421 | The Theory of Single Variable Calculus | 3 |
| MATH 467 | Introduction to Number Theory | 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:
| Code | Title | Credits |
|---|---|---|
| MATH/COMP SCI 514 | Numerical Analysis | 3 |
| MATH 521 | Analysis I | 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/PHILOS 571 | Mathematical Logic | 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 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 567 | Modern Number Theory | 3 |
| MATH 570 | Fundamentals of Set Theory | 3 |
| MATH/PHILOS 571 | Mathematical Logic | 3 |
| MATH 616 | Data-Driven Dynamical Systems, Stochastic Modeling and Prediction | 3 |
| MATH 619 | Analysis of Partial Differential Equations | 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 319 | Techniques in Ordinary Differential Equations | 3 |
| or MATH 376 | Topics in Multi-Variable Calculus and Differential Equations | |
| 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 STAT/MATH 309 | Introduction to Probability and Mathematical Statistics I | |
At most one course in Introductory Probability (STAT/MATH 309 and MATH/STAT 431) may be used to fulfill the course/credit requirements for the major. | ||
| MATH/COMP SCI/E C E 435 | Introduction to Cryptography | 3 |
| MATH 443 | Applied Linear Algebra | 3 |
| MATH 444 | Graphs and Networks in Data Science | 3 |
| MATH 467 | Introduction to Number Theory | 3 |
| MATH/COMP SCI/STAT 475 | Introduction to Combinatorics | 3 |
Programming and Computations 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 the following:
| Code | Title | Credits |
|---|---|---|
| COMP SCI 300 | Programming II | 3 |
| COMP SCI 400 | Programming III | 3 |
Programming and Computations 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 |
|---|---|---|
| COMP SCI 412 | Introduction to Numerical Methods | 3 |
| COMP SCI/I SY E/MATH 425 | Introduction to Combinatorial Optimization | 3 |
| COMP SCI/E C E/MATH 435 | Introduction to Cryptography | 3 |
| COMP SCI/STAT 471 | Introduction to Computational Statistics | 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 520 | Introduction to Theory of Computing | 3 |
| COMP SCI/E C E/I SY E 524 | Introduction to Optimization | 3 |
| COMP SCI/I SY E/MATH/STAT 525 | Linear Optimization | 3 |
| COMP SCI/I SY E 526 | Advanced Linear Programming | 3 |
| COMP SCI/E C E/M E 532 | Matrix Methods in Machine Learning | 3 |
| COMP SCI/E C E 533 | Image Processing | 3 |
| COMP SCI 538 | Introduction to the Theory and Design of Programming Languages | 3 |
| COMP SCI/E C E/M E 539 | Introduction to Artificial Neural Networks | 3 |
| COMP SCI 540 | Introduction to Artificial Intelligence | 3 |
| COMP SCI 541 | Theory & Algorithms for Data Science | 3 |
| COMP SCI 559 | Computer Graphics | 3 |
| COMP SCI/B M I 567 | Biomedical Image Analysis | 3 |
| COMP SCI/B M I 576 | Introduction to Bioinformatics | 3 |
| COMP SCI 577 | Introduction to Algorithms | 4 |
| COMP SCI 642 | Introduction to Information Security | 3 |
| I SY E 623 | Advanced Optimization Modeling | 3 |
Residence and Quality of Work
- 2.000 GPA on 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
- Additional 300/400-level MATH courses as needed
- Required Advanced MATH course
- Additional 500/600-level MATH courses
| 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 Required Linear Algebra | 3 |
| Humanities Breadth | 3 | Transition to Advanced Math | 3 |
| Communication B | 3 | COMP SCI 200 | 3 |
| Physical Science Breadth | 3 | Humanities Breadth | 3 |
| Elective | 3 | Physical Science Breadth | 3 |
| 16 | 15 | ||
| Junior | |||
| Fall | Credits | Spring | Credits |
| 300/400-level MATH elective | 3 | 300/400-level MATH elective | 3 |
| COMP SCI 300 | 3 | COMP SCI 400 | 3 |
| Social Sciences Breadth | 3 | Social Sciences Breadth | 3 |
| Biological Sciences Breadth | 3 | Biological Sciences Breadth | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Senior | |||
| Fall | Credits | Spring | Credits |
| Required Advanced MATH | 3 | 500/600-level MATH elective | 3 |
| Elective Programming/Computations Course | 3 | Elective Programming/Computations Course | 3 |
| Social Science Breadth | 3 | Social Science Breadth | 3 |
| Elective | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Total Credits 120 | |||
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Students should declare the major upon the successful completion of this course