## MATH 216A: Introduction to Algebraic Geometry

Algebraic curves, algebraic varieties, sheaves, cohomology, Riemann-Roch theorem. Classification of algebraic surfaces, moduli spaces, deformation theory and obstruction theory, the notion of schemes. May be repeated for credit. Prerequisites: 210ABC or equivalent.

Terms: Aut
| Units: 3
| Repeatable for credit

Instructors:
Vakil, R. (PI)

## MATH 216B: Introduction to Algebraic Geometry

Continuation of 216A. May be repeated for credit.

Terms: Win
| Units: 3
| Repeatable for credit

Instructors:
Vakil, R. (PI)

## MATH 216C: Introduction to Algebraic Geometry

Continuation of 216B. May be repeated for credit.

Terms: Spr
| Units: 3
| Repeatable for credit

Instructors:
Kemeny, M. (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:
Ryzhik, L. (PI)
;
Liu, F. (TA)

## MATH 226: Numerical Solution of Partial Differential Equations (CME 306)

Hyperbolic partial differential equations: stability, convergence and qualitative properties; nonlinear hyperbolic equations and systems; combined solution methods from elliptic, parabolic, and hyperbolic problems. Examples include: Burger's equation, Euler equations for compressible flow, Navier-Stokes equations for incompressible flow. Prerequisites:
MATH 220A or
CME 302.

Terms: Spr
| Units: 3

Instructors:
Ying, L. (PI)

## MATH 228: Stochastic Methods in Engineering (CME 308, MS&E 324)

The basic limit theorems of probability theory and their application to maximum likelihood estimation. Basic Monte Carlo methods and importance sampling. Markov chains and processes, random walks, basic ergodic theory and its application to parameter estimation. Discrete time stochastic control and Bayesian filtering. Diffusion approximations, Brownian motion and an introduction to stochastic differential equations. Examples and problems from various applied areas. Prerequisites: exposure to probability and background in analysis.

Terms: Spr
| Units: 3

Instructors:
Glynn, P. (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: 116,
MATH 171.

Terms: Aut
| Units: 2-4

## MATH 230B: Theory of Probability II (STATS 310B)

Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,n(v) ergodic theory. Prerequisite: 310A or
MATH 230A.

Terms: Win
| Units: 2-3

## MATH 230C: Theory of Probability III (STATS 310C)

Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or
MATH 230B.
http://statweb.stanford.edu/~adembo/stat-310c/

Terms: Spr
| Units: 2-4

## MATH 231: Mathematics and Statistics of Gambling (STATS 334)

Probability and statistics are founded on the study of games of chance. Nowadays, gambling (in casinos, sports and the Internet) is a huge business. This course addresses practical and theoretical aspects. Topics covered: mathematics of basic random phenomena (physics of coin tossing and roulette, analysis of various methods of shuffling cards), odds in popular games, card counting, optimal tournament play, practical problems of random number generation. Prerequisites: Statistics 116 and 200.

Terms: Spr
| Units: 3

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