This course is an introduction to abstract algebra. It covers material related to
fundamental concepts such as groups, rings and fields:
o Groups, subgroups, cyclic groups, isomorphism, generators and relations, permutation groups, cosets,
Lagrange's theorem,
homomorphisms and factor groups, direct products, finitely generated abelian groups, symmetries and
isometries, groups acting on sets.
o Rings and fields, integral domains, Fermat's and Euler's theorems, field of quotients, rings of
polynomials, factorization of polynomials over a field, ideals, ring homomorphisms and factor rings,
prime and maximal ideals.
o Field extensions, vector spaces over fields, algebraic extensions, finite fields.
Approximate schedule of the course:
Week of:
Aug. 30: Sec. 0,1,2,3
Sep. 6: Sec. 4, 5, 6
Sep. 13: Sec. 7, 8
Sep. 20: Sec. 9, 10
Sep. 27: Sec. 11, 12
Oct. 4: Sec. 13, 14
Oct. 11: Sec. 15, 16
Oct. 18: Sec. 17, 18
Oct. 25: Sec. 19, 20
Nov. 1: Sec. 21, 22
Nov. 8: Sec. 23, 26
Nov. 15: Sec. 27, 29
Nov. 22: Thanksgiving
Nov. 29: Sec. 30, 31
Dec. 6: Sec. 33 and review