# The Mathematics Major

This page has a few notes that may be helpful to mathematics majors. Other useful sources of information:

- For details about math major requirements, please see the current edition of YCPS.
- For more information, take a look at our extensive Math major FAQ.
- For detailed information about introductory courses and assistance choosing your path through them, please visit our first year student resources site.
- A list of recent textbooks for our courses is available.

In summary:

The introductory sequence into the mathematics major consists of linear algebra (Math 225 or 226), analysis (Math 255 or 256), and multvariable analysis / calculus (Math 302 or 120).

Each Mathematics Major must take the senior seminar, Math 480 or Math 481, or the senior essay, Math 475.

In total, mathematics majors must complete ten mathematics courses numbered 200 or higher (counting the introductory sequence and the senior seminar).

There are two distributional requirements, categories and core areas.

There are five categories: algebra, combinatorics and number theory; logic and foundations; analysis; geometry and topology; applied mathematics. From three of the five categories, at least two courses in each must be completed. Yale course search provides current listing and descriptions of the courses. It lists the attributes for each course, and can be used to search for courses with a particular attribute. (A sample list of courses that could be offered, by category, can be found below.)

For the second distributional requirement, students 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 305 or higher) and Complex Analysis (Math 310 or higher). These courses form the core of the undergraduate major.

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. A list of approved courses can be found in the Math major FAQ.

Pure mathematics majors can count up to two courses from related departments. Some of these courses are listed below; a full list can be found in the Math major FAQ. (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 policy are explained in our Math major FAQ.)

**Categories**

Below is a list of courses that tend to belong to each category. 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 YCS.

### 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, by students who have a graduate course requirement in the intensive major or the B.S./M.S. program. )

225 or 226 Linear Algebra

244 Discrete Mathematics

340 Advanced linear algebra

345 Modern Combinatorics

350 Introduction to Abstract Algebra (also carries core area algebra attribute)

353 Introduction to Representation Theory (typically offered every other year)

354 Number Theory

370 Fields and Galois Theory (also carries core area algebra attribute)

373 Algebraic number theory (typically offered every other year)

380 Modern Algebra (also carries core area algebra attribute)

440 Introduction to Algebraic Geometry (typically offered every other year)

### Logic and Foundations

Math 270 Set Theory

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

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

### Analysis

(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, by students who have a graduate course requirement in the intensive major or the B.S./M.S. program.)

255 or 256 Analysis I

246 Ordinary Differential Equations

302 Multivariable Analysis

305 Real Analysis (also carries core area real analysis attribute)

310 Introduction to Complex Analysis (also carries core area complex analysis attribute)

315 Intermediate Complex Analysis (also carries core area complex analysis attribute)

320 Measure Theory and Integration (also carries core area real analysis attribute)

325 Introduction to Functional Analysis (also carries core area real analysis attribute)

447 Partial differential equations (typically offered every other year)

### Geometry and Topology

360 Introduction to Lie Groups

430 Introduction to Algebraic Topology (typically offered every other year)

435 Differential Geometry (typically offered every other year)

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

247 Partial Differential Equations

251 Stochastic Processes

310 Complex Analysis

330 Advanced probability

345 Modern combinatorics

421 Mathematics of Data Science (typically offered every other year)

447 Partial differential equations (typically offered every other year)

### 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. For the full list of courses that can be counted as outside electives for pure math majors, please see the math major FAQ.

AMTH 437 Optimization Techniques

CPSC 365 or 366 (Intensive) Algorithms

(and other CPSC classes, such as 267, 427, 440, 460, 468)

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