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81 - 90 of 161 results for: MATH

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 | Grading: Letter or Credit/No Credit
Instructors: Conrad, B. (PI)

MATH 215A: Complex Analysis, Geometry, and Topology

Analytic functions, complex integration, Cauchy's theorem, residue theorem, argument principle, conformal mappings, Riemann mapping theorem, Picard's theorem, elliptic functions, analytic continuation and Riemann surfaces.
Terms: Aut | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: Ryzhik, L. (PI)

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 | Grading: Letter or Credit/No Credit
Instructors: Li, Z. (PI)

MATH 216B: Introduction to Algebraic Geometry

Continuation of 216A. May be repeated for credit.
Terms: Win | Units: 3 | Repeatable for credit | Grading: Letter or Credit/No 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 | Grading: Letter or Credit/No Credit
Instructors: Vakil, R. (PI)

MATH 217A: Differential Geometry

Smooth manifolds and submanifolds, tensors and forms, Lie and exterior derivative, DeRham cohomology, distributions and the Frobenius theorem, vector bundles, connection theory, parallel transport and curvature, affine connections, geodesics and the exponential map, connections on the principal frame bundle. Prerequisite: 215C or equivalent.
Terms: Spr | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: Mazzeo, R. (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: foundation in multivariable calculus and ordinary differential equations.
Terms: Aut | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: Ryzhik, L. (PI)

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 l-1 minimization. Fast algorithms and their implementation.
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: Ryzhik, L. (PI)

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 high-frequency, 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: Spr | Units: 3 | Grading: Letter or Credit/No Credit

MATH 222: Computational Methods for Fronts, Interfaces, and Waves

High-order methods for multidimensional systems of conservation laws and Hamilton-Jacobi equations (central schemes, discontinuous Galerkin methods, relaxation methods). Level set methods and fast marching methods. Computation of multi-valued solutions. Multi-scale analysis, including wavelet-based methods. Boundary schemes (perfectly matched layers). Examples from (but not limited to) geometrical optics, transport equations, reaction-diffusion equations, imaging, and signal processing.
Terms: not given this year | Units: 3 | Grading: Letter or Credit/No Credit
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