## The Mathematics Major

Math majors must take a total of 10 courses in mathematics numbered 222 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 another department for any part of their math requirement. That is, the courses to be counted as math classes towards a joint major must be listed on OCS with a MATH number (they can be cross-listed with other departments, such as AMTH or S&DS, so long as MATH is one of them).

Vector Analysis and Linear Algebra (either 120-222-250, 225-250, or 230a-230b) are required although exceptionally well-prepared students can sometimes place out of them with DUS approval. Each Mathematics Major must take the senior seminar, Math 480a or b. 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. [1]Some substitutions are possible and may be made with the concurrence of the DUS.

Majors are required to take courses from at least two of the three core areas: 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.

**Algebra, Combinatorics, and Number Theory**

Math 350 and Math 370 are often taken as a 2-term sequence. Math 380 and 381 may also be taken for graduate credit, as well as Math 500 and 501.

222 or 225 Linear Algebra

244 Discrete Mathematics

350 Introduction to Abstract Algebra (222 or 225)

353 Introduction to Representation Theory

[354] Number Theory (350a)

370* Fields and Galois Theory (350)

380 Modern Algebra I (350a, 370)

381 Modern Algebra II (380)

**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 30l-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, as Math 515, 520, and 525.

246 Ordinary Differential Equations (120)

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

300 Topics in Analysis (250)

301* Introduction,to Analysis (230)

305 Real Analysis (301)

310 Introduction to Complex Analysis (301)

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.

228 From Euclid to Einstein

290 Fractal Geometry; Concepts and Applications

[430 ] Introduction to Algebraic Topology

[435 ] Differential Geometry (230 or 250)

360 Introduction to Lie Theory (301, 350)

**Applied Mathematics**

Math/Stat 241 Probability Theory

Math/Stat 242 Theory of Statistics

Math 244 Discrete Mathematics

246 Ordinary Differential Equations (120)

Math/Stat 251 Stochastic Processes

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

290 Fractal Geometry; Concepts and Applications

CPSC 365 Algorithms (may count for pure math major only, with limit as noted above, and it does not carry any attributes)

400 Introduction to Mathematical Mechanics

AMTH 437 Optimization Techniques (may count for pure math major only, with limit as ntoed above, and it does not carry any attributes)

CPSC 440 Numerical Computation (may count for pure math major only, with limit as noted above, and it does not carry any attributes)

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