MATH 216B: Introduction to Algebraic Geometry
Continuation of 216A. May be repeated for credit.
Terms: not given this year, last offered Winter 2018

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 216C: Introduction to Algebraic Geometry
Continuation of 216B. May be repeated for credit.
Terms: not given this year, last offered Spring 2018

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 217C: Complex Differential Geometry
Complex structures, almost complex manifolds and integrability, Hermitian and Kahler metrics, connections on complex vector bundles, Chern classes and ChernWeil theory, Hodge and Dolbeault theory, vanishing theorems, CalabiYau manifolds, deformation theory.
Terms: not given this year, last offered Winter 2015

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 220: Partial Differential Equations of Applied Mathematics (CME 303)
Firstorder 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 proofbased treatment of the material as in
Math 171 or
Math 61CM (formerly
Math 51H).
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Vasy, A. (PI)
;
Sarkar, R. (TA)
MATH 221A: Mathematical Methods of Imaging (CME 321A)
Image denoising and deblurring with optimization and partial differential equations methods. Imaging functionals based on total variation and l1 minimization. Fast algorithms and their implementation.
Terms: alternate years, given next year, last offered Winter 2014

Units: 3

Grading: Letter or Credit/No Credit
MATH 221B: Mathematical Methods of Imaging (CME 321B)
Array imaging using Kirchhoff migration and beamforming, resolution theory for broad and narrow band array imaging in homogeneous media, topics in highfrequency, variable background imaging with velocity estimation, interferometric imaging methods, the role of noise and inhomogeneities, and variational problems that arise in optimizing the performance of array imaging algorithms.
Terms: not given this year, last offered Spring 2016

Units: 3

Grading: Letter or Credit/No Credit
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, NavierStokes equations for incompressible flow. Prerequisites:
MATH 220 or
CME 302.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Gerritsen, M. (PI)
;
Orozco Bohorquez, C. (TA)
MATH 227: Partial Differential Equations and Diffusion Processes
Parabolic and elliptic partial differential equations and their relation to diffusion processes. First order equations and optimal control. Emphasis is on applications to mathematical finance. Prerequisites:
MATH 136/
STATS 219 (or equivalents) and
MATH 131P +
MATH 115/171 or
MATH 173 or
MATH 220.
Terms: not given this year, last offered Winter 2015

Units: 3

Grading: Letter or Credit/No Credit
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

Grading: Letter or Credit/No Credit
MATH 228A: Probability, Stochastic Analysis and Applications
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 basic stochastic differential equations. Examples and problems from various applied areas. Prerequisites: exposure to probability and background in analysis.
Terms: not given this year, last offered Spring 2016

Units: 3

Grading: Letter or Credit/No Credit
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