printer friendly pageMATH 118: Mathematics of Computation
Notions of analysis and algorithms central to modern scientific computing: continuous and discrete Fourier expansions, the fast Fourier transform, orthogonal polynomials, interpolation, quadrature, numerical differentiation, analysis and discretization of initial-value and boundary-value ODE, finite and spectral elements. Prerequisites:
MATH 51 and 53.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Ying, L. (PI)
MATH 120: Groups and Rings
Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and non-PID. Unique factorization domains. WIM.
Terms: Aut, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Li, Z. (PI)
;
Luu, M. (PI)
MATH 121: Galois Theory
Field of fractions, splitting fields, separability, finite fields. Galois groups, Galois correspondence, examples and applications. Prerequisite:
Math 120 and (also recommended) 113.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Conrad, B. (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 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
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