Class Schedule and HW Assignments

Practice problems are from Pinter's A Book of Abstract Algebra

Week Date Topics Ch. Practice Problems
(don't turn in)

1 6/21 Course Introduction; What is Algebra?;
Symmetries of a Triangle
1

2 6/24 Binary Operations; Definition of a Group 2,3 Ch. 2: A2,3,6; B2,4
Ch. 3: A3, D
6/25(x) Set Theory and Proofs Suggested: Proofs
Tips
Proofs practice
6/26 Properties of Groups; Orders of Group Elements 4,10 Ch. 4: B1,2,3; C1,2,5; D7,8
Ch. 10: A(all); C3,5; D3,4
6/28 Subgroups; Cyclic Groups;
Direct Products
5,11 Ch. 5: A4,5; C2,3,6; D1,8
Ch. 11: A1,3; B4
Ch. 4: G3,4
Problem Set 1: Due Wednesday, July 3

3 7/1 Proofs II; Functions;
Permutations
6,7,8 Ch 6: A1,2,3,5; B4,5,6; F2,3,4; G1,2,3
Ch 7. A(all), B1,2,4; D1,2,3
7/3 Permutations II 7,8 Ch 8: A1,2,3,4; B1,4; C1,3,4; F1,2
7/5 Group Homomorphisms and Isomorphisms; Cayley's Theorem 14,9 Ch 14: A3; B3,4,5; C1,3,4,8,9; G1,2,3,4,5
Ch 9: A1,2,3; E2,4; H1,3
Problem Set 2: Due Wednesday, July 10

4 7/8 Permutation Representations; Normal Subgroups 9,14 Ch 9: J
Ch 14: D4,5,6; E2,3
7/10 Partitions and Equivalence Relations; Midterm Review 12 Ch 12: A1,2,5; B2,8,9; D1,2,3,4
7/12 Counting Cosets; Lagrange's Theorem; Survey of Small Groups 13 Ch. 13: A3,5; B1,2,7; C1,2,6; D1,2,3,6; E1,3,5; H(hard)
Problem Set 3: Due Wednesday, July 17

5 7/15 Dihedral Groups; Quotient Groups 15 Ch. 15: A, B
7/17 Quotient Groups II, Fundamental Homomorphism Theorem 15,16 Ch. 15: C1,2,3,4; F
Ch. 16: A1,5; C; E
7/19 Using the FHT; Decomposition of Finite Abelian Groups 16
Problem Set 4: Due Wednesday, July 24

6 7/22 Class Cancelled
7/23(x) Introduction to Rings 17 Ch. 17: A1,2,3,4; E1,2,3,4; H1,2,5,6,7; I1,2,3,7
7/24 Types of Rings; Subrings and Ideals 17,18 Ch. 17: G, J1,2,3,6
Ch. 18: A1,2,3,6; B1,2,9; C1,2,4,8; D3,6
7/26 Ring Homomorphisms and Quotient Rings 18,19 Ch. 18: C3; D2; F1,2,4,5; G, H3,4; J1,2,3,4
Ch. 19: B1,2; D1,2; E2
Problem Set 5 (TeX): Due Wednesday, July 31

7 7/29 Integral Domains 20 Ch. 19: F
Ch. 20: A1,2,3; B1,2; C2,3
7/31 Finite Fields; Midterm Review 20 Ch. 20: B4,5; E1,2,3,5,7
8/2 Factorization; Intro to Number Theory 22,23 Ch. 22: A1,7,8; B7; D5,6; E
Ch. 23: E2,3,5
Problem Set 6 (TeX): Due Wednesday, August 7

8 8/5 Euler's Theorem; Polynomial Rings 23,24 Ch. 23: F1,2,3,6,7
Ch. 24: A1,2,4; B1,2,3,5; C2,4,8; D1,2,3; E1,2,3,4; G1,2,3,4,5;
8/7 Factoring Polynomials 25 Ch. 25: A1,2,3; C1,2; B1,2,3,4; F
8/9 Polynomial Roots and Irreducibility 26 Ch. 26: A2,3,4; B3,4,5; C1,2,4,5,8
Problem Set 7 (TeX): Due Wednesday, August 14

9 8/12 Irreducibility over the Integers and Rationals 26 Ch. 26: C6; D3; E3; I1,2,3
8/14 Field Extensions 27 Ch. 27: A1def,2; B1acef,3,4ac;D2,3,6; G3,4
8/16 Vector Spaces 28 Ch. 28: A1,4; B1,2,6; C3,5; D1,2,5,6
Problem Set 8 (TeX): Due Wednesday, August 21

10 8/19 Field Extensions as Vector Spaces 28,29 Ch. 28: E3; F1,2,3
A1,2,6,7; B; C2,5; D1,2,3
8/20(x) The Field of Constructible Numbers 30
8/21 Final Exam Review

Important Dates

Date Event
Friday, June 21: First lecture
Thursday, July 11: Midterm Exam 1 (6-8 pm, Kemeny 004)
Thursday, August 1: Midterm Exam 2 (6-8 pm, Kemeny 004)
Wednesday, August 7: Final day to withdraw from the course
Wednesday, August 21: Final lecture
Saturday, August 24: Final Exam (3-6 pm, Location TBD)

C. Coscia
Last updated August 20, 2019