printer friendly pageMATH 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.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Garapon, P. (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.
| UG Reqs: GER:DB-Math
Instructors:
Zuniga, J. (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.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Banchoff, T. (PI)
MATH 145: Algebraic Geometry
Real algebraic curves, Hilbert's nullstellensatz, complex affine and projective curves, Bezout's theorem, the degree/genus formula, Riemann surfaces, Riemann-Roch theorem. Prerequisites: 106 or 116, and 109 or 120. Recommended: familiarity with surfaces equivalent to 143, 146, 147, or 148.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Mirzakhani, M. (PI)
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.
Last offered: Winter 2009
| 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: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Kerckhoff, S. (PI)
MATH 151: Introduction to 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. Prerequisite: 52 or consent of instructor.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Kargin, V. (PI)
MATH 152: Elementary Theory of Numbers
Euclid's algorithm, fundamental theorems on divisibility; prime numbers; congruence of numbers; theorems of Fermat, Euler, Wilson; congruences of first and higher degrees; quadratic residues; introduction to the theory of binary quadratic forms; quadratic reciprocity; partitions.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Bump, D. (PI)
MATH 155: Analytic Number Theory
Topics in analytic number theory such as the distribution of prime numbers, the prime number theorem, twin primes and Goldbach's conjecture, the theory of quadratic forms, Dirichlet's class number formula, Dirichlet's theorem on primes in arithmetic progressions, and the fifteen theorem. Prerequisite: 152, or familiarity with the Euclidean algorithm, congruences, residue classes and reduced residue classes, primitive roots, and quadratic reciprocity.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Soundararajan, K. (PI)
MATH 159: Discrete Probabilistic Methods
Modern discrete probabilistic methods suitable for analyzing discrete structures of the type arising in number theory, graph theory, combinatorics, computer science, information theory and molecular sequence analysis. Prerequisite:
STATS 116/
MATH 151 or equivalent.
Terms: Aut
| Units: 3
Instructors:
Dembo, A. (PI)
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