Basic Courses
Click here for rules regarding basic courses
See Syllabi for Basic First-year Courses
Forms:
| Course # | Course Title | Semester | Description |
|---|---|---|---|
| 60210 | Algebra I | Fall | Groups, rings, modules |
| 60220 | Algebra II | Spring | Fields, Galois theory, and topics chosen from modules, multilinear algebra, homological algebra, commutative algebra, and noncommutative algebra. This course is sequential to 60210. |
| 60350 | Real Analysis I | Fall | Calculus, Lebesgue measure, general measure theory |
| 60360 | Spring | Functional Analysis or topics chosen at the discretion of the instructor. This course is sequential to 60350. | |
| 60370 | Complex Analysis I | Fall | Analytic functions, Cauchy integral theorems and formulas, applications. |
| 60380 | Complex Analysis II | Spring | Topics from complex manifolds, Riemann surfaces. This course is sequential to 60370. |
| 60330 | Basic Geometry & Topology | Fall | Quick review of point set topology, fundamental groups and covering spaces, manifolds. |
| 60440 | Basic Topology II | Spring | Algebraic topology, homology, cohomology, duality theorems. This course is sequential to 60330. |
| 60510 | Logic I | Fall | Model theory and some set theory. |
| 60520 | Logic II | Spring | Computability theory and more set theory. |
| 60610 | Discrete Mathematics | Enumeration, graph theory, error correcting codes, and other topics at discretion of the instructor | |
| 60620 | Optimization | Convex sets, theorems of Caratheodory, Radon, Helly, and Krein-Milman. Facial structure of convex sets. Extreme points. Separation Theorem. Optimality conditions for convex programming problems. Introduction to subdifferential calculus. Chebyshev approximations. | |
| 60650 | Basic PDE | Linear partial differential equations, including transport, Laplace, heat, and wave equations. Nonlinear differential equations. This course is sequential to 60350. | |
| 60670 | Basic Differential Geometry | Spring | Connections, Riemannian geometry, topics chosen from Kahler geometry, symplectic geometry, contact geometry. This course is sequential to 60330. |
| 60850 | Probability | An introduction to probability theory, including elements of measure and integration, random variables, central limit theorems, and other topics. This course is sequential to 60350. | |
| 70220 | Lie Groups and Lie Algebras | Spring |