## MATH 158: Basic Probability and Stochastic Processes with Engineering Applications (CME 298)

Calculus of random variables and their distributions with applications. Review of limit theorems of probability and their application to statistical estimation and basic Monte Carlo methods. Introduction to Markov chains, random walks, Brownian motion and basic stochastic differential equations with emphasis on applications from economics, physics and engineering, such as filtering and control. Prerequisites: exposure to basic probability.

Terms: Spr
| Units: 3

Instructors:
Ying, L. (PI)

## MATH 159: Discrete Probabilistic Methods

Modern discrete probabilistic methods suitable for analyzing discrete structures of the type arising in number theory, graph theory, combinatorics, computer science, information theory and molecular sequence analysis. Prerequisite:
STATS 116/
MATH 151 or equivalent. Typically in alternating years.

Terms: Spr
| Units: 3
| UG Reqs: WAY-FR

Instructors:
Kwan, M. (PI)

## MATH 161: Set Theory

Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations. The Zermelo-Fraenkel axiom system and the special role of the axiom of choice and its various equivalents. Well-orderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite: students should be comfortable doing proofs.

Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Sommer, R. (PI)

## 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: 61CM or 61DM or 115 or consent of the instructor. WIM

Terms: Aut, Spr, Sum
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

## MATH 172: Lebesgue Integration and Fourier Analysis

Similar to 205A, but for undergraduate Math majors and graduate students in other disciplines. Topics include Lebesgue measure on Euclidean space, Lebesgue integration, L^p spaces, the Fourier transform, the Hardy-Littlewood maximal function and Lebesgue differentiation. Prerequisite: 171 or consent of instructor.

Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
La, J. (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. In years when
Math 173 is not offered,
Math 220 is a recommended alternative (with similar content but a different emphasis). Prerequisite: 171 or equivalent.

Terms: Win
| Units: 3
| UG Reqs: WAY-FR

Instructors:
Kleinhenz, P. (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.

Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Vasy, A. (PI)
;
Stavrianidi, A. (TA)

## MATH 177: Geometric Methods in the Theory of Ordinary Differential Equations

Hamiltonian systems and their geometry. First order PDE and Hamilton-Jacobi equation. Structural stability and hyperbolic dynamical systems. Completely integrable systems. Perturbation theory.

Last offered: Spring 2018

## 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.

Last offered: Autumn 2019
| Repeatable
5 times
(up to 5 units total)

## 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
3 times
(up to 9 units total)

Instructors:
Chodosh, O. (PI)
;
Conrad, B. (PI)
;
Cook, N. (PI)
;
Dembo, A. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
;
Huh, J. (PI)
;
Kachru, S. (PI)
;
Kojima, F. (PI)
;
Luk, J. (PI)
;
Mazzeo, R. (PI)
;
Montanari, A. (PI)
;
Papanicolaou, G. (PI)
;
Ryzhik, L. (PI)
;
Soundararajan, K. (PI)
;
Taylor, R. (PI)
;
Vakil, R. (PI)
;
Vasy, A. (PI)
;
Vondrak, J. (PI)

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