printer friendly pageMATH 205A: Real Analysis
Basic measure theory and the theory of Lebesgue integration. Prerequisite: 171 or equivalent.
Terms: Aut
| Units: 3
Instructors:
Ryzhik, L. (PI)
MATH 205B: Real Analysis
Point set topology, basic functional analysis, Fourier series, and Fourier transform. Prerequisites: 171 and 205A or equivalent.
Terms: Win
| Units: 3
Instructors:
Vasy, A. (PI)
MATH 210A: Modern Algebra I
Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, introduction to representation theory. Prerequisite: 122 or equivalent.
Terms: Aut
| Units: 3
Instructors:
Vakil, R. (PI)
MATH 210B: Modern Algebra II
Continuation of 210A. Topics in Galois theory, commutative algebra, and algebraic geometry. Prerequisites: 210A, and 121 or equivalent.
Terms: Win
| Units: 3
Instructors:
Yun, Z. (PI)
MATH 210C: Lie Theory
Topics in Lie groups, Lie algebras, and/or representation theory. Prerequisite:
math 210B. May be repeated for credit.
Terms: Spr
| Units: 3
| Repeatable
5 times
(up to 15 units total)
Instructors:
Bump, D. (PI)
MATH 215A: Complex Analysis, Geometry, and Topology
Analytic functions, complex integration, Cauchy's theorem, residue theorem, argument principle, conformal mappings, Riemann mapping theorem, Picard's theorem, elliptic functions, analytic continuation and Riemann surfaces.
Terms: Aut
| Units: 3
Instructors:
Ionel, E. (PI)
MATH 215B: Complex Analysis, Geometry, and Topology
Topics: fundamental group and covering spaces, homology, cohomology, products, basic homotopy theory, and applications. Prerequisites: 113, 120, and 171, or equivalent; 215A is not a prerequisite for 215B.
Terms: Win
| Units: 3
Instructors:
Galatius, S. (PI)
MATH 215C: Complex Analysis, Geometry, and Topology
Differentiable manifolds, transversality, degree of a mapping, vector fields, intersection theory, and Poincare duality. Differential forms and the DeRham theorem. Prerequisite: 215B or equivalent.
Terms: Spr
| Units: 3
Instructors:
Miller, J. (PI)
MATH 217A: Differential Geometry
Smooth manifolds and submanifolds, tensors and forms, Lie and exterior derivative, DeRham cohomology, distributions and the Frobenius theorem, vector bundles, connection theory, parallel transport and curvature, affine connections, geodesics and the exponential map, connections on the principal frame bundle. Prerequisite: 215C or equivalent.
Terms: Aut
| Units: 3
Instructors:
Yang, T. (PI)
MATH 217C: Complex Differential Geometry
Complex structures, almost complex manifolds and integrability, Hermitian and Kahler metrics, connections on complex vector bundles, Chern classes and Chern-Weil theory, Hodge and Dolbeault theory, vanishing theorems, Calabi-Yau manifolds, deformation theory.
Terms: Win
| Units: 3
| Repeatable
2 times
(up to 6 units total)
Instructors:
Ionel, E. (PI)
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