MATH 411-511: Abstract Algebra I

Office hours: Wednesday 12:45 PM to 1:35 PM at CAS 272, and Monday and Friday on Teams from 12:10 PM to 1:00 PM.

Textbook: Contemporary Abstract Algebra, 10th edition, by Joseph A. Gallian.

Homework:

• Homework 1: 4c, 5b, 7b of Chapter 2, and 2, 4, 12 of Chapter 3. 

• Homework 2: 3, 6, 9, 36, and 49 of Chapter 5. 

• Homework 3 : 30, 32, 38, and 56 of Chapter 5. 

• Homework 4: 2, 8, 34, 35, and 38 of Chapter 6. 

• Homework 5: 3, 5, 30, 38, and 44 of Chapter 12. 

• Homework 6:  11, 17, 25 of Chapter 16 and 13, 14, 23 of Chapter 17. 

Quizzes:

• Quiz 1: 

• Quiz 2: 

• Quiz 3: 

• Quiz 4:

• Quiz 5:

Midterms Tests and Final Exam:

• Test 1 (on Monday of Week 7)

• Test 2 (on Monday of Week 13)

• Comprehensive final exam: TBD

Recommended Problems:

• Chapter 1 - Introduction to groups: 3, 13, 21.

• Chapter 2 - Groups: 1, 4, 5, 7, 9, 12, 16, 17, 18, 19, 25, 27, 34 (for grads), 46 (for grads).

• Chapter 3 - Finite groups and subgroups: 1, 2, 4, 6, 10, 13, 14 (for grads), 18, 19, 20, 22, 23, 34, 36, 38, 40, 50, 60, 65, 71.

• Chapter 4 - Cyclic groups: 1, 3, 4, 5, 8, 10, 11, 19, 21, 22, 24, 30, 32, 63, 69, 71 (for grads).

• Chapter 5 - Permutation groups: 1-9, 11, 14, 15, 16, 19, 23, 24, 26, 29, 30, 32, 40, 43, 48.

• Chapter 6 - Isomorphisms: 1, 2, 3, 4, 5, 7, 8, 11, 13, 14, 15, 16, 17, 19, 21, 22, 24, 26, 28, 30, 32, 36, 37, 38, 39, 44, 45, 46.

• Chapter 7 - Cosets and Lagrange's Theorem: 1, 3, 4, 5, 6, 7, 9, 11 (for grads), 13 (for grads), 15, 16, 17, 21, 22, 26, 27, 28, 29, 30, 31, 33, 36, 39, 40, 41, 45, 46, 50, 51 (for grads).

• Chapter 12 - Rings: 2, 4, 6, 9, 12, 13, 16, 17, 18, 19, 20, 22, 28, 29, 31, 35, 39, 40 (for grads), 46, 49 (for grads).

• Chapter 13 - Integral domains: 3, 4, 5, 8, 11, 12, 15, 16, 18, 19, 21, 24, 25, 30, 32, 39, 44, 46, 56, 57.

• Chapter 15 - Ring homomorphisms: 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 21, 22, 23, 50 (for grads), 56 (for grads).

• Chapter 16 - Polynomial rings: 1, 2, 3, 6, 7, 8, 9, 10, 11, 12, 14, 15, 27, 28, 32, 33, 34.

• Chapter 17 - Factorization of polynomials: 3, 4, 5, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 25, 29.