MATH 6310 - Algebra

Nicolas Templier, fall 2016.

MATH 6310-MATH 6320 are the core algebra courses in the mathematics graduate program.

MATH 6310 covers group theory, especially finite groups; rings and modules; ideal theory in commutative rings; arithmetic and factorization in principal ideal domains and unique factorization domains; introduction to field theory; tensor products and multilinear algebra. (Optional topic: introduction to affine algebraic geometry.)

Prerequisite

Familiarity with material covered in a standard undergraduate course in abstract algebra.

Textbooks

The main text is I. M. Isaacs, Algebra, a graduate course, 1994 — free electronic access provided by the Cornell Math Library

Additional references (optional) include:

David S. Dummit & Richard M. Foote, Abstract Algebra, 3rd ed., John Wiley & Sons, 2004
S. Lang, Algebra, 3rd edition, 2002 — free electronic access provided by the Cornell Math Library
S. C. Coutinho, A primer of algebraic D-modules, London Mathematical Society Student Texts, 33. 1995; — free electronic access provided by the Cornell Math Library
N. Jacobson, Basic algebra, two volumes, 2nd edition, 1985–1989;
T. W. Hungerford, Algebra, 1974 — free electronic access provided by the Cornell Math Library