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 |
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| 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 |
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| 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 |
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| 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 |
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| 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) |