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 initialvalue and boundaryvalue ODE, finite and spectral elements. Prerequisites:
MATH 51 and 53.
Terms: not given this year, last offered Winter 2018

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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 nonPID. Unique factorization domains. WIM.
Terms: Aut, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Diaconis, P. (PI)
;
Vakil, R. (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:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Tsai, C. (PI)
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

Grading: Letter or Credit/No Credit
Instructors:
Bump, D. (PI)
MATH 131P: Partial Differential Equations
An introduction to PDE; particularly suitable for nonMath 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: Win

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Fredrickson, L. (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.
http://statweb.stanford.edu/~adembo/math136/
Terms: Win

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Dembo, A. (PI)
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 61CM, 62CM, 63CM.
Terms: not given this year, last offered Spring 2019

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
MATH 138: Celestial Mechanics
Mathematically rigorous introduction to the classical Nbody 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; HamiltonJacobi theory; the role of equilibrium points and stability; and symplectic methods. Prerequisites: 53, and 115 or 171.
Terms: not given this year, last offered Autumn 2014

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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. Prerequisites: some familiarity with the basic concepts of differential geometrynand the topology of surfaces and manifolds is strongly recommended
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
MATH 143: Differential Geometry
Geometry of curves and surfaces in threespace and higher dimensional manifolds. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces.
Terms: Win

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Kerckhoff, S. (PI)
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