## MATH 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.

Last offered: Autumn 2013
| UG Reqs: GER:DB-Math

## MATH 120: Groups and Rings

Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 109 but altered content and more theoretical orientation. 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

## 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:
Yun, Z. (PI)
;
Rosengarten, Z. (TA)

## MATH 122: Modules and Group Representations

Modules over PID. Tensor products over fields. 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:
Wilson, J. (PI)
;
Wolf, A. (TA)

## 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

## MATH 132: Partial Differential Equations II

Laplace's equation and properties of harmonic functions. Green's functions. Distributions and Fourier transforms. Eigenvalue problems and generalized Fourier series. Numerical solutions. Prerequisite: 131P.

Last offered: Spring 2015
| UG Reqs: GER:DB-Math

## 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:
Zheng, T. (PI)
;
Jafarov, J. (TA)

## MATH 137: Mathematical Methods of Classical Mechanics

Newtonian mechanics. Lagrangian formalism. E. Noether's theorem. Oscillations. Rigid bodies. Introduction to symplectic geometry. Hamiltonian formalism. Legendre transform. Variational principles. Geometric optics. Introduction to the theory of integrable systems. Prerequisites: 51, 52, 53, or 51H, 52H, 53H.

Last offered: Winter 2013
| UG Reqs: GER:DB-Math

## MATH 138: Celestial Mechanics

Mathematically rigorous introduction to the classical N-body problem: the motion of N particles evolving according to Newton's law. Topics include: the Kepler problem and its symmetries; other central force problems; conservation theorems; variational methods; Hamilton-Jacobi theory; the role of equilibrium points and stability; and symplectic methods. Prerequisites: 53, and 115 or 171.

Last offered: Autumn 2014
| UG Reqs: GER:DB-Math

## MATH 142: Hyperbolic Geometry

An introductory course in hyperbolic geometry. Topics may include: different models of hyperbolic geometry, hyperbolic area and geodesics, Isometries and Mobius transformations, conformal maps, Fuchsian groups, Farey tessellation, hyperbolic structures on surfaces and three manifolds, limit sets.nnPrerequisites: some familiarity with the basic concepts of differential geometrynand the topology of surfaces and manifolds is strongly recommended

Terms: Win
| Units: 3

Instructors:
Mirzakhani, M. (PI)
;
Dozier, B. (TA)

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