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61 - 70 of 138 results for: MATH

MATH 205A: Real Analysis

Basic measure theory and the theory of Lebesgue integration. Prerequisite: 171 or equivalent.
Terms: Aut | Units: 3

MATH 205B: Real Analysis

Point set topology, basic functional analysis, Fourier series, and Fourier transform. Prerequisites: 171 and 205A or equivalent.
Terms: Win | Units: 3
Instructors: Mazzeo, R. (PI)

MATH 205C: Real Analysis

Continuation of 205B.
Last offered: Spring 2018

MATH 210A: Modern Algebra I

Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, canonical forms and Jordan decomposition. Prerequisite: 122 or equivalent.
Terms: Aut | Units: 3

MATH 210B: Modern Algebra II

Continuation of 210A. Topics in field theory, commutative algebra, algebraic geometry, and finite group representations. Prerequisites: 210A, and 121 or equivalent.
Terms: Win | Units: 3
Instructors: Vakil, R. (PI)

MATH 210C: Lie Theory

Topics in Lie groups, Lie algebras, and/or representation theory. Prerequisite: math 210B. May be repeated for credit.
Terms: Spr | Units: 3 | Repeatable for credit

MATH 215A: Algebraic Topology

Topics: fundamental group and covering spaces, basics of homotopy theory, homology and cohomology (simplicial, singular, cellular), products, introduction to topological manifolds, orientations, Poincare duality. Prerequisites: 113, 120, and 171.
Terms: Aut | Units: 3

MATH 215B: Differential Topology

Topics: Basics of differentiable manifolds (tangent spaces, vector fields, tensor fields, differential forms), embeddings, tubular neighborhoods, integration and Stokes¿ Theorem, deRham cohomology, intersection theory via Poincare duality, Morse theory. Prerequisite: 215A
Terms: Win | Units: 3

MATH 215C: Differential Geometry

This course will be an introduction to Riemannian Geometry. Topics will include the Levi-Civita connection, Riemann curvature tensor, Ricci and scalar curvature, geodesics, parallel transport, completeness, geodesics and Jacobi fields, and comparison techniques. Prerequisites 146 or 215B
Terms: Spr | Units: 3

MATH 216A: Introduction to Algebraic Geometry

Algebraic curves, algebraic varieties, sheaves, cohomology, Riemann-Roch theorem. Classification of algebraic surfaces, moduli spaces, deformation theory and obstruction theory, the notion of schemes. May be repeated for credit. Prerequisites: 210ABC or equivalent.
Last offered: Autumn 2017 | Repeatable for credit
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