MathGA 2130: Algebra I, Thu. 7:10pm
Office hours:
 Thu 5pm6pm or by appointment
Syllabus:
 Basic notions of algebra: groups, rings, and fields
 Symmetric groups, linear groups
 Structure theorems, Sylow subgroups
 Algebraic number fields, finite fields, field extensions
 Galois theory
 Polynomial rings, unique factorization
 Geometry of Numbers, ideals, ideal class groups, units
 Rings, algebraic integers, ideals
Grading:
 Homework: 20%
 Midterm October 18: 30%
 Final December 13: 50%
Recommended books:
 M. Artin, Algebra, Pearson Education
 A. ChambertLoir, A Field guide to Algebra, Springer
Homework:

Elementary number theory: Euclidean algorithm, divisibility, primes, congruences, Euler function, residues
(due September 20)

Residues, basic group theory
(due September 27)

Group theory
(due October 4)

Invariant theory
(due October 11)

Galois theory
(due November 1)

Fields
(due November 8)

Rings, ideals
(due November 15)

Class groups
(due November 29)