printer friendly pageMATH 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
Instructors:
Taylor, R. (PI)
;
Landesman, A. (TA)
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
5 times
(up to 15 units total)
Instructors:
Tsai, C. (PI)
;
Fayyazuddin Ljungberg, B. (TA)
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
Instructors:
Cohen, R. (PI)
;
Fauteux-Chapleau, F. (TA)
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
Instructors:
Varolgunes, U. (PI)
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
Instructors:
Luk, J. (PI)
;
Fauteux-Chapleau, F. (TA)
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
MATH 216B: Introduction to Algebraic Geometry
Continuation of 216A. May be repeated for credit.
Last offered: Winter 2018
| Repeatable
for credit
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