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: 3
| Repeatable
for credit
Instructors:
Borga, J. (PI)
;
Bump, D. (PI)
;
Chodosh, O. (PI)
;
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Ionel, E. (PI)
;
Luk, J. (PI)
;
Mazzeo, R. (PI)
;
Taylor, R. (PI)
MATH 205B: Real Analysis
Point set topology, basic functional analysis, Fourier series, and Fourier transform. Prerequisites: 171 and 205A or equivalent. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Win
| Units: 3
Instructors:
Luk, J. (PI)
;
Greilhuber, J. (TA)
MATH 210B: Modern Algebra II
Continuation of 210A. Topics in field theory, commutative algebra, algebraic geometry, and finite group representations. Prerequisites: 210A, and 121 or equivalent.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Win
| Units: 3
Instructors:
Zhu, X. (PI)
;
Iwasaki, H. (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: 215ANOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Win
| Units: 3
Instructors:
Abouzaid, M. (PI)
;
Yang, H. (TA)
MATH 216B: Introduction to Algebraic Geometry
Continuation of 216A. May be repeated for credit.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Win
| Units: 3
| Repeatable
for credit
Instructors:
Vakil, R. (PI)
;
Miagkov, K. (TA)
MATH 220B: Computational Methods of Applied Mathematics (CME 306)
Numerical methods for solving elliptic, parabolic, and hyperbolic partial differential equations. Algorithms for gradient and Hamiltonian systems. Algorithms for stochastic differential equations and Monte Carlo methods. Algorithms for computational harmonic analysis. Prerequisites: advanced undergraduate level PDE and advanced undergraduate level numerical analysis. Note: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Win
| Units: 3
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.
http://statweb.stanford.edu/~adembo/stat-310b. Prerequisite: 310A or
MATH 230A.
Terms: Win
| Units: 3
MATH 235: Modern Markov Chains (STATS 318)
Tools for understanding Markov chains as they arise in applications. Random walk on graphs, reversible Markov chains, Metropolis algorithm, Gibbs sampler, hybrid Monte Carlo, auxiliary variables, hit and run, Swedson-Wong algorithms, geometric theory, Poincare-Nash-Cheeger-Log-Sobolov inequalities. Comparison techniques, coupling, stationary times, Harris recurrence, central limit theorems, and large deviations.
Terms: Win
| Units: 3
MATH 236: Introduction to Stochastic Differential Equations
Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Random walk approximation of diffusions. Introduction to stochastic control and Bayesian filtering. Prerequisite:
Math 136 or equivalent and basic familiarity with parabolic partial differential equations. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such other courses taken.
Terms: Win
| Units: 3
Instructors:
Papanicolaou, G. (PI)
MATH 238: Mathematical Finance (STATS 250)
Stochastic models of financial markets. Risk neutral pricing for derivatives, hedging strategies and management of risk. Multidimensional portfolio theory and introduction to statistical arbitrage. Prerequisite:
Math 136 or equivalent. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as other courses taken.
Terms: Win
| Units: 3
Instructors:
Papanicolaou, G. (PI)
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