## The Mathematics and Statistics Majors and Minors

Below are the most recent major/minor requirements. You can follow the requirements below or the requirements that were available when you entered Wash U. See the appropriate Washington University Bulletin Archive. The material found in 2018-2019 Bulletin will probably apply to most interested students. You can also read the most current Washington University Bulletin.

Students may declare at most one major or minor in the Department of Mathematics and Statistics (including any majors or minors that are joint with another department).

### Updated Major and Minor Requirements

Below are the most recent major and minor requirements. All students may follow the new requirements. Some students may be able to follow the old requirements if they desire.

- Students who entered Wash U before Fall 2020 can follow the old requirements for a Major in Mathematics. These requirements can be found in the 2018-2019 Washington University Bulletin.
- Students who entered Wash U before Fall 2021 can follow the old requirements for a Minor in Mathematics. These requirements can be found in the 2018-2019 Washington University Bulletin.
- At this link, you may read the most current Washington University Bulletin.

### Common courses for all majors and minors

The following are required for all majors in the Math/Stat Department. 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

### How to declare your major or minor

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. See below for the list of such courses.

## The Major in Mathematics & Computer Science

### About the Major

The School of Engineering & Applied Science (SEAS) and the College of Arts & Sciences (A&S) developed a 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

### 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 350: Dynamical Systems
- Math 370: Introduction To Combinatorics
- Math 371: Graph Theory
- Math 4111: Introduction To Analysis
- Math 4121: Lesbesgue Integration
- Math 429: Linear Algebra
- Math 430: Modern 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 460: Multivariable 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 411A: AI and Society
- CSE 412A (or 511A): Artificial Intelligence
- CSE 416A: Analysis of Data Networks
- CSE 417T: Machine Learning I
- CSE 427S: Cloud Computing
- CSE 442T: Cryptography
- CSE 468T: Intro Quantum Computing
- 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 533T: Coding and Information Theory for Data Science
- 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 555T: Adversarial AI
- CSE 559A: Computer Vision
- CSE 581T: Approximation Algorithms
- CSE 584A: Algorithms for Biosequence Comparison
- CSE 587A: Algorithsm for Computational Biology

Approved Electives Outside of Math/Stat and CSE:

- ESE 403: Operations Research
- ESE 415: Optimization
- ESE 417: Intro to Machine Learning and Pattern Classification
- ESE 427: Financial Mathematics
- ESE 429: Basic Principles of Quantum Optics and Quantum Information
- ESE 520: Probability and Stochastic Processes
- BME 470: Mathematics of Imaging Science
- BIOL 5657: Biological Neural Computation
- Econ 4151: Applied Econometrics
- Econ 467: Game Theory

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

## Major in Mathematics and Economics

Not available until Fall 2021

### About the Major

Mathematics and statistics are essential in all aspects of economics. At the same time, Economics is a natural application outlet for statisticians and mathematicians. The joint major in Mathematics & Economics will allow students interested in both disciplines to efficiently combine them without pursuing them as two separate majors. Upon completion, majors will be able to follow career paths in economics that require solid quantitative training. The combination of the two fields could also provide a well-grounded basis to pursue doctoral studies in other areas in the social sciences and public policy, business, and law school

### Core Course Requirements

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

- Math 309: Matrix Algebra
- Math 3200 or Math 493: Elementary To Intermediate Statistics or Probability
- Math 310 or Math 310W: Foundations of Higher Mathematics (with writing)
- Econ 1011: Introduction to Microeconomics
- Econ 1021: Introduction to Macroeconomics
- Econ 4011: Intermediate Microeconomics
- Econ 4021: Intermediate Macroeconomics
- Econ 413 or Econ 413W: Introduction to Econometrics (with Writing)

### Electives

Majors must complete 7 electives, with no fewer than 3 in each department.

Possible Math Electives:

- Math 410: Introduction to Fourier Series and Integrals
- Math 415: Partial Differential Equations
- Math 416: Complex Analysis
- Math 4111: Introduction to Analysis
- Math 4121: Introduction to Lebesgue Integration
- Math 429: Linear Algebra
- Math 439: Linear Statistical Models
- Math 4392: Advanced 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 460: Multivariate Statistical Analysis
- Math 461: Time Series Analysis
- Math 462: Mathematical Foundations of Big Data
- Math 475: Statistical Computation
- Math 494: Mathematical Statistics
- Math 495: Stochastic Processes

Possible Econ Electives:

- Econ 404: Behavioral and Experimental Economics
- Econ 407: Market Design
- Econ 410: Macroeconomics of Inequality
- Econ 4151: Applied Econometrics
- Econ 429: Decision Under Risk and Time
- Econ 435: Open Economy Macroeconomics
- Econ 437: The Economics of Financial Intermediation
- Econ 452: Industrial Organization
- Econ 460: Urban Economics
- Econ 467: Game Theory
- Econ 471: Development Economics
- Econ 477: Topics in Financial Economics: Investments
- Econ 477: Topics in Financial Economics: Asset Pricing
- Econ 480: Labor Economics
- Econ 484: Computational Macroeconomics

## Major in Data Science

Not available until Fall 2021

### About the Major

We are living in an era of data revolution where an unprecedented amount of data is being collected in every field, including science, engineering, and business! Data Science provides analytical and computational tools to extract meaningful information from the data. The College of Arts & Sciences and the McKelvey School of Engineering developed a new major to address the burgeoning demand for data scientists in industry and academia by efficiently capturing the intersection of mathematics and statistics with computer science for data science. The Bachelor of Science in Data Science (BSDS) will give students the formal foundation needed to understand the applicability and consequences of the various approaches to analyzing data with a focus on statistical modeling and machine learning. This program of study is a collaboration between the Department of Mathematics and Statistics in Arts & Sciences and the Department of Computer Science & Engineering in the McKelvey School of Engineering.

### Core Course Requirements

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

- Math 309 Matrix Algebra
- Math 3211 Statistics for Data Science 1
- Math 439 Linear Models
- Math 4211 Statistics for Data Science 2
- CSE 247 Data Structures and Algorithms
- CSE 217A Introduction to Data Science
- CSE 314A Data Management and Manipulation
- Either CSE 417T: Introduction to Machine Learning OR Math 460: Statistical Learning

### Electives

Majors must complete 4 electives, at least one in Mathematics and Statistics and one in CSE.

**Allowed Electives in Mathematics and Statistics:**

- Math 322 Bio stats
- Math 4392 Advanced Linear Statistical Models
- Math 449 Numerical Applied Mathematics
- Math 450 Topics in Applied Mathematics
- Math 456 Financial Mathematics
- Math 459 Bayesian Statistics
- Math 460 Statistical Learning
- Math 461 Time Series Analysis
- Math 462 Foundations of Big Data
- Math 475 Statistical Computation
- Math 493 Probability
- Math 494 Mathematical Statistics
- Math 495 Stochastic Processes
- Math 5047 Diff Geometry
- Math 5061 Theory Of Statistics I
- Math 5062 Theory Of Statistics II
- Math 5071 Advanced Linear Model I
- Math 5072 Advanced Linear Model II

**Allowed electives in CSE:**

- CSE 237S Programming Tools and Techniques
- CSE 256A Introduction to Human-Centered Design
- CSE 311A Introduction to Intelligent Agents Using Science Fiction
- CSE 347 Analysis of Algorithms
- CSE 411A AI and Society
- CSE 416A Analysis of Network Data
- CSE 417T Introduction to Machine Learning (also possible in core)
- CSE 427S Cloud Computing
- CSE 457A Introduction to Visualization
- CSE 511A Intro to AI
- CSE 514A Data Mining
- CSE 515T Bayesian methods in ML
- CSE 517A Machine Learning
- CSE 518A Crowdsourcing Computing
- CSE 530S Database Management Systems
- CSE 534A Large-Scale Optimization for Data Science
- CSE 543T Algorithms for Nonlinear Optimization
- CSE 559A Computer Vision

**Allowed electives in ESE:**

- ESE 403 Operations Research
- ESE 415 Optimization

Majors must also complete 3 credits in Ethics and Professional Responsibility. You may select one of the following:

- E60 Engr 330: Amplifying Cyberdiversity: Real Humans in Virtual Spaces (3.0 Units)
- E60 Engr 4501: Engineering Ethics and Sustainability (1.0 Unit)
- E60 Engr 4502: Engineering Leadership and Team Building (1.0 Unit)
- E60 Engr 4503 Conflict Management and Negotiation (1.0 Unit)
- E60 Engr 4505: Publication Writing (3.0 Units)
- E60 Engr 450F: Engineers in the Community (Engineering Ethics, Leadership and Conflict Management)
- Presentation Skills for Scientists and Engineers (2.0 Units)

### Practicum

Students must enroll in a practicum course, usually taken in your junior or senior year. More details to appear here.

## The Minor in Mathematics

### Course Requirements

A total of at least 15 upper level credits (300 level or above) in the Math/Stats Department.

- CSE 131
- Math 131-132-233
- Math 309 or Math 429
- Math 3200 or Math 494
- Three upper level electives (any courses 300 level or above in the Math/Stats Department)

## The Minor in Statistics

Not available until Fall 2021.

### Course Requirements

A total of at least 15 upper level credits (300 level or above) in the Math/Stats Department.

- CSE 131
- Math 131-132-233
- Math 309 or Math 429
- Math 3200 or Math 494
- Three upper level statistics electives. See below for a list of statistics courses.

## Other Requirements and Restrictions for Majors and Minors

### Restrictions

- A student may declare at most one major or minor in any department. This includes joint majors such as Math+CS or Math+Econ.

### Additional Requirements

- All mathematics majors must fulfill Calculus I-II-III. 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 for a grade (not pass/fail) with a letter grade of C- or better.
- University College courses cannot be counted toward major requirements.
- No double-counting of upper level 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 most 3 units from a different department at Wash U can count toward the major requirements.
- Courses transferred from other accredited colleges and universities can be counted toward a major or minor with departmental approval.
- 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.
- A student can not declare more than one major or minor in the department.

### Course Substitutions and Notes

At most one approved substitution can be made using a course not home-based in the Department of Mathematics & Statistics. Please note the policy that at most one course from a different department at Wash U can count towards a major or minor.

- ESE 326 can be taken in place of Math 3200. ESE 326 and Math 3200 cannot both count towards a major or minor.
- Any course from another department that is cross-listed as a mathematics L24 course can count for an upper level elective. For example, L24-501C, L24-440C, or L24-403C. Such L24 courses always end with a "C."
- The following can count as an upper level mathematics elective:

Phil 401, Phil 403, Phil404

Econ 4151 (can count as a statistics elective)

ESE 319, ESE 403, ESE 411 - Math 3211: Statistics for Data Science I does not count as an upper level elective for any of the majors.

### Courses in Probability and Statistics

The Major and Minor in Statistics require electives in probability and statistics. Below is the list of allowed such courses.

- Math 3200: Elementary To Intermediate Statistics
- Math 322: Biostatistics
- Math 420: Experimental Design
- Math 434: Survival Analysis
- Math 439: Linear Statistical Models
- 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 493: Probability
- Math 494: Mathematical Statistics
- Math 495: Stochastic Processes
- Math 496: Topics In Statistics