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# 41 - 50 of 77 results for: all courses

## 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 | Grading: Letter or Credit/No Credit
Instructors: Vakil, R. (PI)

## MATH 131P:Partial Differential Equations

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: Win | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit
Instructors: Wang, Y. (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/math-136/
Terms: Win | Units: 3 | UG Reqs: GER:DB-Math | 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: Spr | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## 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.
Terms: not given this year, last offered Autumn 2014 | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## 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.
Terms: Spr | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## MATH 145:Algebraic Geometry

An introduction to the methods and concepts of algebraic geometry. The point of view and content will vary over time, but include: affine varieties, Hilbert basis theorem and Nullstellensatz, projective varieties, algebraic curves. Required: 120. Strongly recommended: additional mathematical maturity via further basic background with fields, point-set topology, or manifolds.
Terms: Aut, alternate years, not given next year | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## MATH 146:Analysis on Manifolds

Differentiable manifolds, tangent space, submanifolds, implicit function theorem, differential forms, vector and tensor fields. Frobenius' theorem, DeRham theory. Prerequisite: 62CM or 52 and familiarity with linear algebra and analysis arguments at the level of 113 and 115 respectively.
Terms: Aut | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## 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, last offered Spring 2018 | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## MATH 148:Algebraic Topology

Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.
Terms: Win, alternate years, not given next year | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit
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