## MATH 171: Fundamental Concepts of Analysis

Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 115 but altered content and more theoretical orientation. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite: 51H or 115 or consent of the instructor. WIM

| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Schoen, R. (PI)
;
Soundararajan, K. (PI)

## MATH 173: Theory of Partial Differential Equations

A rigorous introduction to PDE accessible to advanced undergraduates. Elliptic, parabolic, and hyperbolic equations in many space dimensions including basic properties of solutions such as maximum principles, causality, and conservation laws. Methods include the Fourier transform as well as more classical methods. The Lebesgue integral will be used throughout, but a summary of its properties will be provided to make the course accessible to students who have not had 172 or 205A. Prerequisite: 171 or equivalent.

Instructors:
Ignatova, M. (PI)

## MATH 175: Elementary Functional Analysis

Linear operators on Hilbert space. Spectral theory of compact operators; applications to integral equations. Elements of Banach space theory. Prerequisite: 115 or 171.

| UG Reqs: GER:DB-Math

Instructors:
Menz, G. (PI)

## MATH 193: Polya Problem Solving Seminar

Topics in mathematics and problem solving strategies with an eye towards the Putnam Competition. Topics may include parity, the pigeonhole principle, number theory, recurrence, generating functions, and probability. Students present solutions to the class. Open to anyone with an interest in mathematics.

| Repeatable for credit

Instructors:
Soundararajan, K. (PI)

## MATH 199: Independent Work

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.

| Repeatable for credit

Instructors:
Brendle, S. (PI)
;
Brumfiel, G. (PI)
;
Bump, D. (PI)
...
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Instructors:
Brendle, S. (PI)
;
Brumfiel, G. (PI)
;
Bump, D. (PI)
;
Camilier, I. (PI)
;
Candes, E. (PI)
;
Carlsson, G. (PI)
;
Church, T. (PI)
;
Cohen, R. (PI)
;
Conrad, B. (PI)
;
Dembo, A. (PI)
;
Diaconis, P. (PI)
;
Duffie, D. (PI)
;
Eliashberg, Y. (PI)
;
Feferman, S. (PI)
;
Finn, R. (PI)
;
Galatius, S. (PI)
;
Ionel, E. (PI)
;
Katznelson, Y. (PI)
;
Keller, J. (PI)
;
Kerckhoff, S. (PI)
;
Li, J. (PI)
;
Liu, T. (PI)
;
Lucianovic, M. (PI)
;
Mazzeo, R. (PI)
;
Milgram, R. (PI)
;
Mirzakhani, M. (PI)
;
Ornstein, D. (PI)
;
Osserman, R. (PI)
;
Papanicolaou, G. (PI)
;
Ryzhik, L. (PI)
;
Schoen, R. (PI)
;
Simon, L. (PI)
;
Soundararajan, K. (PI)
;
Toussaint, A. (PI)
;
Vakil, R. (PI)
;
Vasy, A. (PI)
;
Venkatesh, A. (PI)
;
White, B. (PI)
;
Wieczorek, W. (PI)
;
Ying, 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:
Mazzeo, R. (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:
Yun, Z. (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:
Conrad, B. (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:
Venkatesh, A. (PI)

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