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41 - 50 of 136 results for: 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. http://statweb.stanford.edu/~adembo/math-136/
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

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: Math 53 and 147 or Math 62CM and 63CM.
Last offered: Spring 2019 | UG Reqs: GER:DB-Math, WAY-FR

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. Prerequisites: some familiarity with the basic concepts of differential geometryand the topology of surfaces and manifolds is strongly recommended
Last offered: Autumn 2021 | UG Reqs: WAY-FR

MATH 143: Differential Geometry

Geometry of curves and surfaces in three-space. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces. Prerequisite: Math 52.
Terms: Aut | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

MATH 144: Introduction to Topology and Geometry

Point set topology, including connectedness, compactness, countability and separation axioms. The inverse and implicit function theorems. Smooth manifolds, immersions and submersions, embedding theorems. Prerequisites: Math 61CM or both Math 113 and Math 171.
Terms: Win | Units: 4 | UG Reqs: WAY-FR

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: Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: Zhang, Z. (PI)

MATH 147: Differential Topology

Introduction to smooth methods in topology including tranvsersality, intersection number, fixed point theorems, as well as differential forms and integration. Prerequisites: Math 144 or equivalent.
Terms: Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: Chodosh, O. (PI)

MATH 148: Algebraic Topology

Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

MATH 151: Introduction to Probability Theory

A proof-oriented development of basic probability theory. Counting; axioms of probability; conditioning and independence; expectation and variance; discrete and continuous random variables and distributions; joint distributions and dependence; Central Limit Theorem and laws of large numbers. CS majors can petition to use Math 151 in place of CS 109, provided they expect to take either CS 228 or CS 229 as well. Prerequisite: Math 61CM, or Math 52 and either Math 56 or Math 115 (or equivalent).
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
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