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 Secondary Education program requires at least eight courses for at least 24 credits as described below. Courses below may have prerequisites outside of this program.
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 | 3-5 |
| 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 |
Analysis
Complete one course from the list below. If a student takes MATH 421 to complete the Transition to Advanced Mathematics 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 421 | The Theory of Single Variable Calculus | 3 |
| MATH 521 | Analysis I | 3 |
Modern Algebra
Complete one course from:
| Code | Title | Credits |
|---|---|---|
| MATH 540 | Linear Algebra II | 3 |
| MATH 541 | Modern Algebra 1 | 3 |
Probability or Combinatorics
Complete one course from:
| Code | Title | Credits |
|---|---|---|
| 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 444 | Graphs and Networks in Data Science | 3 |
| MATH/COMP SCI/STAT 475 | Introduction to Combinatorics | 3 |
| MATH 531 | Probability Theory | 3 |
Statistics
Complete one course from:
| Code | Title | Credits |
|---|---|---|
| MATH/STAT 310 | Introduction to Probability and Mathematical Statistics II | 3 |
| STAT 301 | Introduction to Statistical Methods | 3 |
| STAT 312 | Introduction to Theory and Methods of Mathematical Statistics II | 3 |
| STAT 324 | Introduction to Statistics for Science and Engineering | 3 |
| ECON 310 | Statistics: Measurement in Economics | 4 |
History of Mathematics
Complete one course from:
| Code | Title | Credits |
|---|---|---|
| MATH/HIST SCI 473 | History of Mathematics | 3 |
Geometry
Complete one course from:
| Code | Title | Credits |
|---|---|---|
| MATH 461 | College Geometry I | 3 |
Capstone Course
Complete one course from:
| Code | Title | Credits |
|---|---|---|
| MATH/CURRIC 471 | Mathematics for Secondary School Teachers | 3 |
Advanced Mathematics
A student must complete at least two MATH courses numbered 500 or higher for this named option. If a student completes the requirements above with fewer such courses, they must complete a course from the list below. This course must be distinct from those used to complete the requirements above.
Approved Electives
| 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 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 561 | Differential Geometry | 3 |
| MATH 567 | Modern Number Theory | 3 |
| MATH 570 | Fundamentals of Set Theory | 3 |
| MATH/PHILOS 571 | Mathematical Logic | 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 |
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
- Required Transition to Advanced Mathematics course (The four-year plan assumes students will complete this by taking either MATH 341 for Linear Algebra or MATH 421 for Analysis.)
- Additional 300/400-level level courses as needed
- Required 500-level Algebra course
- Additional 500/600-level course
| 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 | MATH Required Probability or Combinatorics | 3 |
| Communication B | 3 | Humanities Breadth | 3 |
| Physical Sciences Breadth | 3 | Physical Sciences Breadth | 3 |
| Elective | 3 | Elective | 3 |
| 16 | 15 | ||
| Junior | |||
| Fall | Credits | Spring | Credits |
| MATH Required Analysis | 3 | MATH 461 | 3 |
| MATH Required Statistics | 3 | Social Sciences Breadth | 3 |
| Social Sciences Breadth | 3 | Biological Sciences Breadth | 3 |
| Biological Sciences Breadth | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Senior | |||
| Fall | Credits | Spring | Credits |
| MATH/HIST SCI 473 | 3 | MATH second Required 500/600-level course or Elective | 3 |
| MATH Required Algebra | 3 | MATH/CURRIC 471 (MATH second required 500/600-level course or Elective) | 3 |
| Social Sciences Breadth | 3 | Social Sciences Breadth | 3 |
| Elective | 3 | Elective | 3 |
| Elective | 3 | Elective | 3 |
| 15 | 15 | ||
| Total Credits 120 | |||
Footnotes
- 1
Students should declare their major upon the successful completion of this course
- 2
Taught only in odd-numbered springs. Take spring of junior year if graduating in an even-numbered spring.