printer friendly pageMATH 122: Modules and Group Representations
Modules over PID. Tensor algebra. Group representations and group rings. Maschke's theorem and character theory. Character tables, construction of representations. Prerequisite:
Math 120. Also recommended: 113.
Terms: Spr
| Units: 3
Instructors:
Venkatesh, A. (PI)
MATH 131P: Partial Differential Equations I
An introduction to PDE; particularly suitable for non-Math majors. Topics include physical examples of PDE's, method of characteristics, D'Alembert's formula, maximum principles, heat kernel, Duhamel's principle, separation of variables, Fourier series, Harmonic functions, Bessel functions, spherical harmonics. Students who have taken
MATH 171 should consider taking
MATH 173 rather than 131p. Prerequisite: 53.
Terms: Aut, Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Ignatova, M. (PI)
;
Menz, G. (PI)
MATH 136: Stochastic Processes (STATS 219)
Introduction to measure theory, Lp spaces and Hilbert spaces. Random variables, expectation, conditional expectation, conditional distribution. Uniform integrability, almost sure and Lp convergence. Stochastic processes: definition, stationarity, sample path continuity. Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales. Construction and basic properties of Brownian motion. Prerequisite:
STATS 116 or
MATH 151 or equivalent. Recommended:
MATH 115 or equivalent.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Dembo, A. (PI)
;
Zheng, T. (PI)
MATH 143: Differential Geometry
Geometry of curves and surfaces in three-space and higher dimensional manifolds. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces.
Last offered: Winter 2013
| UG Reqs: GER:DB-Math
MATH 144: Riemannian Geometry
Smooth manifolds, tensor fields, geometry of Riemannian and Lorentz metrics, the Levi-Civita connection and curvature tensor, Ricci curvature, scalar curvature, and Einstein manifolds, spaces of constant curvature. Prerequisites:
Math 51, 52, and 53.
Terms: Win
| Units: 3
Instructors:
Schoen, R. (PI)
MATH 145: Algebraic Geometry
Hilbert's nullstellensatz, complex affine and projective curves, Bezout's theorem, the degree/genus formula, blow-up, Riemann-Roch theorem. Prerequisites: 120, and 121 or knowledge of fraction fields. Recommended: familiarity with surfaces equivalent to 143, 146, 147, or 148.
Last offered: Winter 2012
| UG Reqs: GER:DB-Math
MATH 146: Analysis on Manifolds
Differentiable manifolds, tangent space, submanifolds, implicit function theorem, differential forms, vector and tensor fields. Frobenius' theorem, DeRham theory. Prerequisite: 52 or 52H.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
MATH 147: Differential Topology
Smooth manifolds, transversality, Sards' theorem, embeddings, degree of a map, Borsuk-Ulam theorem, Hopf degree theorem, Jordan curve theorem. Prerequisite: 115 or 171.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Berwick-Evans, D. (PI)
MATH 148: Algebraic Topology
Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.
Last offered: Winter 2013
| UG Reqs: GER:DB-Math
MATH 149: Applied Algebraic Topology
Introduction to algebraic topology and its applications, in particular persistent homology as a tool for shape and pattern recognition from high dimensional data sets, with examples analyzed using state-of-the-art software. Prerequisite: linear algebra.
Terms: Win
| Units: 3
Instructors:
Carlsson, G. (PI)
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