# The Mathematics Major

This page has a few notes that may be helpful to mathematics majors.

For details about math major requirements, please see the current edition of YCPS.

For more information, take a look at the Math major FAQ.

In summary:

Math majors must take a total of 10 courses in mathematics numbered 200 or above.

Pure mathematics majors can include up to two courses from related departments, such as the courses listed below that do not have a math number. Joint majors may not substitute courses from other departments - a course to be counted toward the math requirements must have a math number. [Reasons for this decisions are explained in our FAQ.]

Vector Analysis and Linear Algebra (either 120-225-250, or 230a-231b) are required. Students who have completed multivariable calculus / linear algebra can speak with the DUS for permission to substitute a higher level course for Math 120 / 225. Exceptionally well prepared students can take an exam in August to place out of 230-231. For details, please see the Math major FAQ.

Each Mathematics Major must take the senior seminar, Math 480a or b, or complete the senior essay, Math 475. One section of Math 480 each year is especially designed for Mathematics-Economics majors.

The remaining requirement for the Bachelor of Arts consists of 7 elective courses selected from the 5 categories below. At least two courses must be selected from three of the five categories. Brief descriptions of their contents and structure may be found in the current edition of the Yale College Program of Studies.

Majors are required to take courses from at least two of the three core areas (all three are recommended): Algebra (Math 350 or higher), Real Analysis (Math 300 or 301 or higher) and Complex Analysis (Math 310 or higher). These courses form the core of the undergraduate major. Their companion second semesters, Math 370, 305, and 315, are also highly recommended.

The requirements for the Degree of Bachelor of Science in Mathematics include those for the B.A. degree, plus two additional advanced science courses approved by the DUS.

**Categories**

Below is a list of courses that tend to belong to each category, with pre-requisites in brackets. Some of these courses are not offered every year, new ones may be added, and our offering may change in other ways in any given year. For a current list of courses that count toward a particular category, with up-to-date prerequisites, we encourage you to use the attribute search on OCS.

### Algebra, Combinatorics, and Number Theory

Math 350 and Math 370 are often taken as a 2-term sequence. Math 380 may also be taken for graduate credit.

222 or 225 Linear Algebra I

230 Vector calculus and linear algebra

235 Reflection groups

240 Advanced linear algebra

244 Discrete Mathematics

350 Introduction to Abstract Algebra (231 or 250)

353 Introduction to Representation Theory (350)

[354] Number Theory (350)

370* Fields and Galois Theory (350)

[373] Algebraic number theory

380 Modern Algebra I (350, 370)

### Logic and Foundations

Math 270 Set Theory (120)

Phil 267 Mathematical Logic (may count for pure math major only, with limit oas noted above)

Phil 427 Computability and Logic (may count for pure math major only, with limit as noted above)

### Analysis

Math 301-305, Math 320-325 and Math 310-315 are generally taken as two term sequences; Math 315, 320, and 325 may also be taken for graduate credit.

231 Vector calculus and linear algebra II

246 Ordinary Differential Equations (120)

250 Vector analysis

260 Basic Analysis in Function Spaces (222 or 225, 246)

300 Topics in Analysis (250)

301* Introduction,to Analysis (231)

305 Real Analysis (301)

310 Introduction to Complex Analysis

315* Intermediate Complex Analysis (310)

320* Measure Theory and Integration (305)

325* Introduction to Functional Analysis (320)

### Geometry and Topology

430 and 435 are generally offered in alternate years.

[430 ] Introduction to Algebraic Topology

[435 ] Differential Geometry (231 or 250)

360 Introduction to Lie Theory (301, 350)

544 Introduction to algebraic topology

[This is the only graduate course that carries an attribute.]

### Applied Mathematics

241 Probability Theory

242 Theory of Statistics

244 Discrete Mathematics

246 Ordinary Differential Equations (120)

251 Stochastic Processes

260 Basic Analysis in Function Spaces (222 or 225, 246)

330 Advanced probability

345 Modern combinatorics

### Other courses that may be of interest

As noted above, these only count for pure math majors (not joint-math), and there is a maximum of two that may be counted. They carry no attributes.

AMTH 437 Optimization Techniques

CPSC 365 or 366 (Intensive) Algorithms

ECON 135 or 136 (these may not be counted along with MATH 241 or 242)

ECON 351 Mathematical economics: game theory

S&DS 364 Information theory

S&DS 410 Statistical inference