## MATH 197: Senior Honors Thesis

Honors math major working on senior honors thesis under an approved advisor carries out research and reading. Satisfactory written account of progress achieved during term must be submitted to advisor before term ends. May be repeated 3 times for a max of 9 units. Contact department student services specialist to enroll.

Terms: Aut, Win, Spr, Sum
| Units: 1-6
| Repeatable for credit

Instructors:
Conrad, B. (PI)
;
Cook, N. (PI)
;
Dembo, A. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
;
Kachru, S. (PI)
;
Luk, J. (PI)
;
Soundararajan, K. (PI)
;
Taylor, R. (PI)
;
Vasy, A. (PI)
;
Vondrak, J. (PI)

## MATH 199: Reading Topics

For Math majors only. Undergraduates pursue a reading program under the direction of a Math faculty member; topics limited to those not in regular department course offerings. Credit can fulfill the elective requirement for Math majors. Departmental approval required; please contact the Student Services Specialist for the enrollment proposal form at least 2 weeks before the final study list deadline. May be repeated for credit. Enrollment beyond a third section requires additional approval.

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

## 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: 121 and 122 or equivalent.

Terms: Aut
| Units: 3

Instructors:
Taylor, R. (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 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 220: Partial Differential Equations of Applied Mathematics (CME 303)

First-order partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: Basic coursework in multivariable calculus and ordinary differential equations, and some prior experience with a proof-based treatment of the material as in
Math 171 or
Math 61CM (formerly
Math 51H).

Terms: Aut
| Units: 3

Instructors:
Luk, J. (PI)

## MATH 230A: Theory of Probability I (STATS 310A)

Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites:
STATS 116,
MATH 171.

Terms: Aut
| Units: 3

## MATH 233A: Topics in Combinatorics

A topics course in combinatorics and related areas. The topic will be announced by the instructor.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Sauermann, L. (PI)

## MATH 245A: Topics in Algebraic Geometry

Topics of contemporary interest in algebraic geometry. May be repeated for credit.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Larson, E. (PI)

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