## MATH 199: Independent Work

For math majors only. Undergraduates pursue a reading program; topics limited to those not in regular department course offerings. Credit can fulfill the elective requirement for math majors. Approval of Undergraduate Affairs Committee is required to use credit for honors majors area requirement. Contact department student services specialist to enroll.

Terms: Aut, Win, Spr, Sum
| Units: 1-3
| Repeatable for credit

Instructors:
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
...
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Instructors:
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
;
Fredrickson, L. (PI)
;
Mazzeo, R. (PI)
;
Perlmutter, N. (PI)
;
Ryzhik, L. (PI)
;
Tsai, C. (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:
Luk, J. (PI)
;
Cote, L. (TA)

## 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:
Church, T. (PI)
;
Dore, D. (TA)

## MATH 210B: Modern Algebra II

Continuation of 210A. Topics in field theory, commutative algebra, and algebraic geometry. Prerequisites: 210A, and 121 or equivalent.

Terms: Win
| Units: 3

Instructors:
Li, J. (PI)
;
Fayyazuddin Ljungberg, B. (TA)

## 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:
Conrad, B. (PI)
;
Silliman, J. (TA)

## 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)
;
Arana Herrera, F. (TA)

## 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

Instructors:
Cohen, R. (PI)
;
Kuhn, N. (TA)

## 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)

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