MATH 205A: Real Analysis
Basic measure theory and the theory of Lebesgue integration. Prerequisite: 171 or equivalent.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
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

Grading: Letter or Credit/No Credit
Instructors:
Vasy, A. (PI)
MATH 205C: Real Analysis
Continuation of 205B.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Vasy, A. (PI)
MATH 210A: Modern Algebra I
Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, canonical forms and Jordan decomposition. Prerequisite: 122 or equivalent.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Taylor, R. (PI)
MATH 210B: Modern Algebra II
Continuation of 210A. Topics in field theory, commutative algebra, algebraic geometry, and finite group representations. Prerequisites: 210A, and 121 or equivalent.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Vakil, R. (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 for credit

Grading: Letter or Credit/No Credit
Instructors:
Bump, D. (PI)
MATH 215A: Algebraic Topology
Topics: fundamental group and covering spaces, basics of homotopy theory, homology and cohomology (simplicial, singular, cellular), products, introduction to topological manifolds, orientations, Poincare duality. Prerequisites: 113, 120, and 171.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Kerckhoff, S. (PI)
MATH 215B: Differential Topology
Topics: Basics of differentiable manifolds (tangent spaces, vector fields, tensor fields, differential forms), embeddings, tubular neighborhoods, integration and Stokes¿ Theorem, deRham cohomology, intersection theory via Poincare duality, Morse theory. Prerequisite: 215A
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
MATH 215C: Differential Geometry
This course will be an introduction to Riemannian Geometry. Topics will include the LeviCivita connection, Riemann curvature tensor, Ricci and scalar curvature, geodesics, parallel transport, completeness, geodesics and Jacobi fields, and comparison techniques. Prerequisites 146 or 215B
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Hershkovits, O. (PI)
MATH 216A: Introduction to Algebraic Geometry
Algebraic curves, algebraic varieties, sheaves, cohomology, RiemannRoch theorem. Classification of algebraic surfaces, moduli spaces, deformation theory and obstruction theory, the notion of schemes. May be repeated for credit. Prerequisites: 210ABC or equivalent.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Conrad, B. (PI)
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