## 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, canonical forms and Jordan decomposition. Prerequisite: 122 or equivalent.

Terms: Aut
| Units: 3

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

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

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

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

## MATH 215C: Differential Geometry

This course will be an introduction to Riemannian Geometry. Topics will include the Levi-Civita 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

Instructors:
Hershkovits, O. (PI)

## MATH 216A: Introduction to Algebraic Geometry

Algebraic varieties, and introduction to schemes, morphisms, sheaves, and the functorial viewpoint. May be repeated for credit. Prerequisites: 210AB or equivalent.

Terms: Aut
| Units: 3

Instructors:
Conrad, B. (PI)

## MATH 216B: Introduction to Algebraic Geometry

Continuation of 216A. May be repeated for credit.

Terms: Win
| Units: 3
| Repeatable for credit

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