## The Mathematics Major

All mathematics majors must complete one of five major tracks: traditional, probability/statistics, applied, mathematics for secondary education, or math (economics emphasis). The choice of track depends partly on your plans after graduation, but also on your tastes and abilities. Students typically choose their major track during their sophomore year.

Important note for the Class of 2018: Requirements for all major tracks were revised in fall 2015. Students who entered Washington University before fall 2015 should refer to the appropriate edition of the Washington University *Bulletin* for accurate major requirements.

### Common courses for all majors

Most math majors take all of the following courses:

- Math 131, 132, and 233 (Calculus I-III)
- Math 309 (Matrix Algebra)
- Math 318 (Calculus of Several Variables) or Math 308 (Mathematics for the Physical Sciences). Students cannot count both 318 and 308 toward major requirements.
- Math 310 (Foundations for Higher Mathematics)
- Math 3200 (Elementary to Intermediate Statistics with Data Analysis)

### Requirements and restrictions

The following applies to all five major tracks:

- All mathematics majors must complete Calculus I-II-III, in addition to track-specific course 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 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.

### 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.

## Track A: Traditional

### About the track

The traditional track 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 track is also a great choice for students who simply enjoy the rigor and beauty of more advanced mathematics.

### Course requirements

**Total 27 upper level mathematics units**

- Math 3200 or Math 493
- Math 310 or Math 310W
- Math 4111 and 4121
- Math 429 and 430
- Three other upper-level mathematics courses (These could include Math 309, Math 318 or 308. At least one upper-level elective must be at 400-level or higher.)

## Track B: Probability/Statistics

### About the track

This track 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

**Total 24 upper level mathematics units**

- CSE 131 (This should be taken as soon as possible. It is a prerequisite for some 400-level prob/stats courses. Students with a sufficient background in computing may use Math 475 to fulfill the computer science requirement in this track. But in that case Math 475 cannot also count as one of the required upper level electives.)
- Math 309
- Math 308 or 318
- Math 310 or Math 310W
- Math 3200
- Math 493 and 494
- Two other upper level prob/stat courses. This includes the following courses:

Math 322 Biostatistics

Math 408 Nonparametric Statistics

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 495 Stochastic Processes

## Track C: Applied

### About the track

The applied track can be done as a stand-alone major, but most students following this track combine it with substantial work in a math-related area such as physics, computer science, or engineering. With departmental approval, two substantially mathematical courses in a different department can be substituted for the physics or computer sciences requirement.

### Course requirements

**Total 24 upper level mathematics units**

- CSE 131 (This requirement should be completed as soon as possible. It is one of the prerequisites for Math 449.)
- Math 217 (a prerequisite for Math 308)
- Math 309
- Math 318 or Math 308
- Math 310 or Math 310W
- Math 3200 or Math 493
- Math 449 and 450
- Two other upper level electives, one of which is chosen from among Math 410, 415, 416, or 4111

## Track D: Mathematics for Secondary Education

### About the track

This track can be done only as a double major with secondary education. The courses required are typical of those required for certification as a secondary school mathematics teacher. Majors in this track should meet immediately with an advisor in the education department to understand its requirements and how to coordinate them with fulfilling the general education requirements of the College. Majors in this track need to finish the math major requirements by the end of the first semester of the senior year, since they will be student teaching and taking professionally-oriented education courses during their eighth semester.

### Required courses

**Total 24 upper level mathematics units**

- CSE 131 (This should be taken as soon as possible.)
- Math 309
- Math 318 or Math 308
- Math 310 or Math 310W
- Math 3200 or Math 493
- Math 302
- Math 331
- Two other upper level electives

## Track E: Mathematics (Economics Emphasis)

### About the track

This track provides a strong mathematics background that resembles the traditional track, but with less algebra and more probability/statistics. It was designed after consulting with the Department of Economics and Olin Business School and should be particularly useful as a second major to economics majors planning to go to graduate school in economics or to students planning to enter a graduate program in finance. The track could also be a good background for a career in investment banking, where pure math/economics candidates are sometimes attractive.

### Course requirements

**Total 24 upper level mathematics units + 3 economics courses**

- Economics 1011-1021
- One of Economics 4011, 4151, or 467
- Math 309
- Math 3200 or 493
- Math 310 or Math 310W
- Math 4111 and 4121
- Three additional upper level mathematics courses (One of these must be Math 429 or 493. The other two can be chosen from among Math 318 or 308, Math 456, or any 400-level probability/statistics course.)

## 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

- Math 131 | Calculus I (AP credit may satisfy this requirement), 3 credits
- Math 132 | Calculus II (AP credit may satisfy this requirement), 3 credits
- Math 233 | Calculus III, 3 credits
- CSE 131 | Introduction to Computer Science, 3 credits
- Math 310 | Foundations for Higher Mathematics or Math 310W | Foundations for Higher Mathematics with Writing or CSE 240 | Logic Discrete Mathematics, 3-4 credits
- CSE 247 | Data Structures and Algorithms, 3 credits
- Math 309 | Matrix Algebra, 3 credits
- Math 3200 | Elementary to Intermediate Statistics and Data Analysis or ESE 326 | Probability and Statistics for Engineering, 3 credits
- CSE 347 | Analysis of Algorithms, 3 credits

### Electives

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

- No fewer than three courses from each department
- Up to two preapproved courses from outside both departments
- 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

### Required Courses

- 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