Fall 2022

Time and venue:  TR 2:20–3:35 p.m., BLOC 163

First day hand-out

Office hours (BLOC 301b):
Office hours (ZOOM meeting): Office hours during the finals (ZOOM meeting):
  • Friday, December 9, 5:00–6:00 p.m.
  • Monday, December 12, 5:00–6:00 p.m.
  • by appointment

Office hours during the finals (BLOC 301b):
  • Tuesday, December 13, 11:00 a.m.–1:00 p.m.
  • Wednesday, December 14, 10:30 a.m.–12:30 p.m.

Homework assignment #1 (due Thursday, September 8)

Homework assignment #2 (due Thursday, September 15)

Homework assignment #3 (due Thursday, September 22)

Homework assignment #4 (due Thursday, September 29)

Exam 1: Thursday, October 6 (Sample problems)

Homework assignment #5 (due Thursday, October 13)

Homework assignment #6 (due Thursday, October 20)

Homework assignment #7 (due Thursday, October 27)

Homework assignment #8 (due Thursday, November 3)

Exam 2: Thursday, November 10 (Sample problems)

Homework assignment #9 (due Thursday, November 17)

Homework assignment #10 (due Friday, November 25)

Homework assignment #11 (due Monday, December 5)

Final exam: Wednesday, December 14, 1:00-3:00 p.m. (Sample problems)

Course outline:

Part I: Basic group theory


Fraleigh/Brand: Chapters I and II

Lecture 1: Preliminaries from set theory. Cardinality of a set.
Lecture 2: Cardinality of a set (continued). Binary operations.
Lecture 3: Isomorphism of binary structures. Groups.
Lecture 4: Basic properties of groups. Semigroups.
Lecture 5: Subgroups. Order of an element in a group. Cyclic groups.
Lecture 6: Cyclic groups (continued). Cayley graphs. Permutations.
Lecture 7: Cycle decomposition. Order and sign of a permutation.
Lecture 8: Sign of a permutation (continued). Classical definition of the determinant. Cosets. Lagrange's theorem.

Part II: More advanced group theory


Fraleigh/Brand: Chapters II and III

Lecture 9: Direct product of groups. Factor groups.
Lecture 10: Homomorphisms of groups.
Lecture 11: Classification of groups. Transformation groups.
Lecture 12: Review for Exam 1.
Lecture 13: Transformation groups (continued). Group actions.

Part III: Basic theory of rings and fields


Fraleigh/Brand: Chapters V and VI

Lecture 14: Rings and fields.
Lecture 15: Fields (continued). Advanced algebraic structures.
Lecture 16: Some examples of rings. Field of quotients.
Lecture 17: Modular arithmetic.
Lecture 18: Public key encryption. Rings of polynomials. Division of polynomials.
Lecture 19: Factorization of polynomials.
Lecture 20: Review for Exam 2.

Part IV: More advanced ring theory


Fraleigh/Brand: Chapter VI

Lecture 21: Subrings and ideals. Factor rings.
Lecture 22: Homomorphisms of rings.
Lecture 23: Prime and maximal ideals. Ideals in polynomial rings.
Lecture 24: Factorization in integral domains. Principal ideal domains.
Lecture 25: Euclidean algorithm. Chinese remainder theorem.
Lecture 26: Review for the final exam.