## The Mathematics Majors

Starting Fall 2020, the department has brand new math major requirements. Students who entered Wash U before Fall 2020 can choose to follow these new requirements or follow the old requirements. The old requirements can be found at the appropriate Washington University *Bulletin*. The material found in 2019-2020 Bulletin will probably apply to most interested students.

### Common courses for all majors

Most math majors take the following courses. Many majors complete this requirement with AP credit or a waiver by taking the relevant course prior to coming to Washington University.

- Math 131: Calculus I
- Math 132: Calculus II
- Math 233: Calculus III
- CSE 131: Introduction to Computer Science

### Requirements and restrictions

The following applies to all majors:

- All mathematics majors must complete Calculus I-II-III, in addition to track-specific course requirements. There are other ways to fulfill this requirement including AP credit, Math 203-204 and some students get a waiver if they took similar courses before coming to Washington University.
- All required courses must be completed with a letter grade of C- or better.
- University College courses cannot be counted toward major requirements.
- No upper-level course used to satisfy a major requirement can also be counted to satisfy the requirements in any other major or minor (that is, no double-counting of courses between majors or minors is allowed).
- At most 3 units for independent study or research work can count toward the major requirements.
- A student can not declare more than one major or minor in the department.

### Transfer credits

With departmental approval, courses transferred from other accredited colleges and universities can be counted toward the major. Please note the following exceptions:

- Courses transferred from a 2-year college (such as a community college) cannot be used to satisfy upper-level requirements.
- At least half of the upper-level credits required in a mathematics major or minor program must be fulfilled by mathematics department courses taken at Washington University or WashU-approved overseas study programs.

### How to declare your major

To declare a major or second major in mathematics:

- Familiarize yourself with the requirements and options for a math major.
- Sign on to your WebStac account and use the Major Programs link to request a major in mathematics.
- Make an appointment for a 15-20 minute meeting with Blake Thornton.

## The Major in Mathematical Sciences

### About the Major

This is the basic math major, designed to fit with a wide variety of interests and career plans. It features a broad survey of mathematical thinking, problem solving, and numerical literacy, as well as an in-depth exploration of at least one of the main subfields of mathematics. While Mathematical Sciences can be a stand-alone major, we recommend that it be paired with a second major in another department. Students who will not have a second major should strongly consider one of the more specialized programs in Mathematics, Applied Mathematics, or Statistics.

### Course Requirements

**At least 24 upper level units in the Department of Mathematics and Statistics units, which must include the following:**

- Math 309: Matrix Algebra
- Math 310 or Math 310W: Foundation for Higher Mathematics
- Math 3200: Introductory to Intermediate Statistics

One of the following full-year 400 level sequences.

**Analysis.**Math 4111, Math 4121: Introduction to Analysis, Introduction to Lebesgue Integration**Topology.**Math 4171, Math 4181: Topology I, Topology II**Algebra.**Math 429, Math 430: Linear Algebra, Modern Algebra**Applied.**Math 449, Math 450: Numerical Applied Mathematics, Topics in Applied Mathematics**Statistics.**Math 494, Math 439: Mathematical Statistics, Linear Statistical Models**Education.**Math 302, Math 331: Elementary Geometry from an Advanced Point of View, Algebraic Systems

(This option is only allowed for students whose primary major is secondary education.)

At least one course from the following list (that hasn't been used above)

- Math 370: Introduction to Combinatorics
- Math 371: Graph Theory
- Math 410: Introduction to Fourier Series and Integrals
- Math 4111: Introduction to Analysis
- Math 415: Partial Differential Equations
- Math 416: Complex Variables
- Math 4171: Topology I
- Math 429: Linear Algebra
- Math 434: Survival Analysis
- Math 4351: Number Theory and Cryptography
- Math 439: Linear Statistical Models
- Math 449: Numerical Applied Mathematics

## The Major in Mathematics

### About the Major

The traditional math major is probably the best choice for students who plan on regularly using serious mathematics (for example, going to graduate school in mathematics or studying a heavily mathematical area of theoretical physics). Even if a student plans graduate work in statistics or "applied mathematics," a good graduate program will require a strong theoretical background. The traditional mathematics major is also a great choice for students who simply enjoy the rigor and beauty of more advanced mathematics.

### Course Requirements

**At least 30 upper level units in the Department of Mathematics and Statistics units, which must include the following:**

- Math 310 or Math 310W: Foundations For Higher Mathematics
- Math 4111: Introduction To Analysis
- Math 4121: Introduction To Lebesgue Integration
- Math 429: Linear Algebra
- Math 430: Modern Algebra
- Math 416: Complex Variables
- Math 4171: Topology I

At least one of the following:

- Math 407: An Introduction To Differential Geometry
- Math 415: Partial Differential Equations
- Math 4181: Topology II
- Math 4351: Number Theory And Cryptography

## The Major in Applied Mathematics

### About the Major

The Major in Applied Mathematics has much in common with the Major in Mathematics, but it places particular emphasis on those areas of mathematics that are important for applications in science, engineering, and computing. This is an excellent choice for students who plan to pursue graduate work in applied mathematics, as well as for those interested in pursuing career paths requiring a strong foundation in mathematical analysis and scientific computing.

### Course Requirements

**At least 30 upper level units in the Department of Mathematics and Statistics units, which must include the following:**

- Math 310 or Math 310W: Foundations For Higher Mathematics
- Math 4111: Introduction To Analysis
- Math 4121: Introduction To Lebesgue Integration
- Math 429: Linear Algebra
- Math 449: Numerical Applied Mathematics
- Math 450: Topics In Applied Mathematics:

At least two of the following:

- Math 410: Introduction To Fourier Series And Integrals
- Math 415: Partial Differential Equations
- Math 416: Complex Variables
- Math 4351: Number Theory And Cryptography

## The Major in Statistics

### About the Major

This major provides useful general knowledge about statistics for students who will be looking for a job after the undergraduate degree. In conjunction with some economics and finance courses, it provides an excellent background for entry into the actuarial profession. Students planning on graduate work in statistics should talk with their advisors about the possibility of also taking Math 4111-4121.

### Course Requirements

**At least 30 upper level units in the Department of Mathematics and Statistics units, which must include the following:**

- Math 309: Matrix Algebra
- Math 3200: Elementary To Intermediate Statistics
- Math 493: Probability
- Math 494: Mathematical Statistics
- Math 439: Linear Statistical Models
- Math 459 or Math 475: Bayesian Statistics, Statistical Computation

Two additional 400 level or above probability and/or statistics courses in the Department of Mathematics and Statistics. These courses include:

- Math 420: Experimental Design
- Math 434: Survival Analysis
- Math 4392: Advanced Linear Statistical Models
- Math 459: Bayesian Statistics
- Math 460: Multivariate Statistical Analysis
- Math 461: Time Series Analysis
- Math 462: Mathematical Foundations Of Big Data
- Math 475: Statistical Computation
- Math 495: Stochastic Processes
- Math 496: Topics In Statistics

## The Major in Mathematics & Computer Science

The School of Engineering & Applied Science (SEAS) and the College of Arts & Sciences (A&S) developed a new major that efficiently captures the intersection of the complementary studies of computer science and math.

SEAS students who declare this major must fulfill the distribution and all other requirements for the "Applied Science" degree in the School of Engineering & Applied Science. A&S students who declare this major must fulfill the distribution and all other requirements for an AB degree in addition to the specific requirements listed below.

### Core Course Requirements

In addition to Math 131, Math 132, Math 233, CSE 131, the following are also required:

- Math 310 or CSE 240: Foundations For Higher Mathematics, Discrete Math
- CSE 247: Data Structures and Algorithms
- Math 309: Matrix Algebra
- Math 3200 or ESE 326: Elementary To Intermediate Statistics, Probability and Statistics for Engineering
- CSE 347: Analysis of Algorithms

### Electives

**Eight upper-level approved courses from Math/Stat or CSE**

- No fewer than three courses from each department
- Up to two courses from outside Math/Stat or CSE.

Possible Math Electives:

- Math 370: Introduction To Combinatorics
- Math 371: Graph Theory
- Math 4111: Introduction To Analysis
- Math 429: Linear Algebra
- Math 4351: Number Theory And Cryptography
- Math 439: Linear Statistical Models
- Math 449: Numerical Applied Mathematics
- Math 450: Topics In Applied Mathematics:
- Math 456: Topics In Financial Mathematics
- Math 459: Bayesian Statistics
- Math 461: Time Series Analysis
- Math 462: Mathematical Foundations Of Big Data
- Math 470: Topics In Graph Theory
- Math 475: Statistical Computation
- Math 493: Probability
- Math 494: Mathematical Statistics
- Math 495: Stochastic Processes

Possible Computer Science electives

- CSE 217A: Introduction to Data Science
- CSE 341T: Parallel Algorithms
- CSE 416A: Analysis of Data Networks
- CSE 417T: Machine Learning I
- CSE 427S: Cloud Computing
- CSE 468T: Intro Quantum Computing
- CSE 511A: Artificial Intelligence
- CSE 513T: Theory Artificial Intelligence and Machine Learning
- CSE 514A: Data Mining
- CSE 515T: Bayesian Methods Machine Learning
- CSE 516A: Multiagent Systems
- CSE 517A: Machine Learning II
- CSE 518A: Human-in-the-Loop Computation
- CSE 541T: Advanced Algorithms
- CSE 543T: Algorithms for Nonlinear Optimization
- CSE 544T: Special topics
- CSE 546T: Computational Geometry
- CSE 547T: Formal Language and Automata
- CSE 554A: Geometric Computing for Medicine
- CSE 581T: Approximation Algorithms
- CSE 587A: Algorithsm for Computational Biology
- CSE 559A: Computer Vision

Approved Electives Outside of Math/Stat and CSE:

- ESE 403: Operations Research
- ESE 415: Optimization
- ESE 427: Financial Mathematics
- ESE 520: Probability and Stochastic Processes

A helpful spreadsheet of requirements can be found at Ron Cytron's Math+CS spreadsheet.

## The Mathematics Minor

### How to Declare a Minor

- Familiarize yourself with the requirements and options for a math minor
- Sign on to WebStac and use the Major Programs link to request a minor in mathematics

The Bulletin includes additional information about the Mathematics Minor

### Course Requirements

- CSE 131
- Math 131-132-233
- Math 309
- Math 318 or Math 308 (but not both)
- Math 3200
- Any additional upper-level elective mathematics course.

### Additional Requirements

- All required courses must be completed with a letter grade of C- or better.
- University College courses cannot be counted toward major requirements.
- No double-counting of courses between other majors or minors is allowed.
- At most 3 units for independent study or research work can count toward the major requirements.
- At least 6 of the 12 upper-level units required in a minor must be earned at Washington University or in a Washington University approved Overseas Study Program.
- Courses transferred from other accredited colleges and universities can be counted toward the minor with departmental approval.

### Approved Course Substitutions

At most one approved substitution can be made using a course not home-based in the Department of Mathematics & Statistics.

**Approved substitutions:**

- ESE 326 in place of Math 3200. ESE 326 and Math 3200 cannot both count towards a minor.
- For the upper-level elective: Any course from another department that is cross-listed as a mathematics L24 course: for example, L24-501C, L24-440C, or L24-403C. Such L24 courses always end with a "C."
- For the upper-level elective: Philosophy 401, 403 or 404
- For the upper-level elective: Econ 413 or Econ 4151
- For the upper-level elective: ESE 319 (but NOT ESE 318)
- For the upper-level elective: ESE 403
- For the upper-level elective: ESE 411