Yale University

The Mathematics Major

Math majors must take a total of 10 courses in mathematics or related departments (see below) numbered 222 or above. Vector Analysis and Linear Algebra (either 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. Some substitutions are possible and may be made with the concurrence of the DUS.

Majors (beginning with the class of 2012) 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 350a and Math 370b are often taken as a 2-term sequence. Math 380a and 381b may also be taken for graduate credit, as well as Math 500a and 501b.

222 or 225 Linear Algebra

244 Discrete Mathematics

350 a Introduction to Abstract Algebra (222 or 225)

353a Introduction to Representation Theory

[354b] Number Theory (350a)

370b* Fields and Galois Theory (350)

380a Modern Algebra I (350a, 370)

381b Modern Algebra II (380)

 

Logic and Foundations

270 a Set Theory (120)

Phil 267a a Logical Theory I

Phil 268b Logical Theory II

Analysis

Math 30la-305b, Math 320a-325b and Math 310a-315b are generally taken as two term sequences; Math 315b, 320a, and 325b may also be taken for graduate credit, as Math 515b, 520a, and 525b.

246 a,b Ordinary Differential Equations (120)

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

300b Topics in Analysis (250)

301a* Introduction,to Analysis (230)

305b Real Analysis (301)

310a Introduction to Complex Analysis (301)

315b* Intermediate Complex Analysis (310)

320a* Measure Theory and Integration (305)

325b* Introduction to Functional Analysis (320)

Geometry and Topology

430b and 435b are generally offered in alternate years.

228b From Euclid to Einstein

290 b Fractal Geometry; Concepts and Applications

[430 b] Introduction to Algebraic Topology

[435 a]} Differential Geometry (230 or 250)

360b Introduction to Lie Theory (301, 350)

Applied Mathematics

CPSC 201 a,b Introduction to Computer Science

Stat 230 b/Math 235 b Introductory Data Analysis

OPRS 235 b Optimization I

Math/Stat 241 a Probability Theory

Math/Stat 242 b Theory of Statistics

Math 244 Discrete Mathematics

246 a,b Ordinary Differential Equations (120)

Math/Stat 251 Stochastic Processes

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

290 b Fractal Geometry; Concepts and Applications

400a Introduction to Mathematical Mechanics

CPSC 440 a Numerical Computation I

CPSC 467a Foundations of Cryptography