Math 251: Abstract Algebra I
Fall 2011
Course Info:
- Lectures: Monday, Wednesday, Friday, 11:45 a.m. - 12:35 p.m.
- Dates: 29 August 2011 - 8 December 2011
- Room: Lafayette L210
- Course Record Number (CRN): 90878
- Instructor: John Voight
- Office: 16 Colchester Ave, Room 207C
- Phone: (802) 656-2271
- E-mail: jvoight@gmail.com
- Office hours: Mondays, 2:30 - 4:30 p.m.; Wednesdays, 9:00 - 10:00 a.m.; or just make an appointment!
- Course Web Page: http://www.cems.uvm.edu/~voight/251/
- Instructor's Web Page: http://www.cems.uvm.edu/~voight/
- Prerequisites: Math 52, 124 or permission.
- Required Text: David Dummit and Richard Foote, Abstract Algebra, third edition, 2004.
- Grading: Homework will count for 40% of the grade. Class participation and preparedness will count for 10% of the grade. There will be two 50-minute exams that will each count for 10% of the grade and one comprehensive final exam that will count for 30% of the grade.
Syllabus:
[PDF] Syllabus
Homework:
[PDF] Homework Submission Guidelines
Homework is due on the same day as the row in which it appears. Problem 3.5.2 means in section 3.5, exercise 2.
Chapter 0: Basics | ||||
1 | 29 Aug | (M) | Hurricane Irene | |
2 | 31 Aug | (W) | Introduction, 0.1: Basics | |
3 | 2 Sep | (F) | 0.2: Properties of the Integers | 0.1.5, 0.1.7 |
5 Sep | (M) | No class, Labor Day | ||
4 | 7 Sep | (W) | 0.3: The Integers modulo n | 0.2.1(b), 0.2.2, 0.2.11 |
Chapter 1: Introduction to Groups | ||||
5 | 9 Sep | (F) | No class | |
6 | 12 Sep | (M) | 1.1: Basic Axioms and Examples | 0.3.9, 0.3.12, 0.3.15(a) |
7 | 14 Sep | (W) | 1.2: Dihedral Groups | 1.1.1(a), 1.1.5, 1.1.8(a), 1.1.12, 1.1.20 |
8 | 16 Sep | (F) | 1.3: Symmetric Groups | 1.2.1(a), 1.2.2, 1.2.3, 1.2.10 |
9 | 19 Sep | (M) | 1.4: Matrix Groups, 1.5: The Quaternion Group | 1.3.1, 1.3.7, 1.1.24, 1.3.15 |
10 | 21 Sep | (W) | 1.6: Homomorphisms and Isomorphisms | 1.4.2, 1.4.3, 1.5.1, 1.5.2 |
11 | 23 Sep | (F) | 1.7: Group Actions | 1.6.1(a), 1.6.2, 1.6.4, 1.6.8, 1.6.17 |
12 | 26 Sep | (M) | 2.1: Definitions and Examples | 1.7.3, 1.7.21 |
13 | 28 Sep | (W) | Chapter 1 Review | 1.1.9, 1.1.25, 1.3.9, 1.4.10, 1.6.3 |
14 | 30 Sep | (F) | Exam 1, covering 0.1-1.6 | |
Chapter 2: Subgroups | ||||
15 | 3 Oct | (M) | 2.2: Centralizers, Normalizers, Stabilizers, and Kernels | 2.1.1(b), 2.1.2(a), 2.1.9 |
16 | 5 Oct | (W) | 2.3: Cyclic Groups and Cyclic Subgroups | 2.2.4, 2.2.6 |
17 | 7 Oct | (F) | 2.4: Subgroups Generated by Subsets | 2.3.1, 2.3.10, 2.3.11, 2.3.16 |
18 | 10 Oct | (M) | 2.5: The Lattice of Subgroups | 2.3.20, 2.3.21, 2.4.5, 2.4.10 |
Chapter 3: Quotient Groups and Homomorphisms | ||||
19 | 12 Oct | (W) | 3.1: Definitions and Examples | 2.5.9(c), 2.5.11 |
20 | 14 Oct | (F) | 3.1 | 3.1.1, 3.1.3, 3.1.5, 3.1.7, 3.1.8 |
21 | 17 Oct | (M) | 3.2: More on Cosets and Lagrange's Theorem | 3.1.22(a), 3.1.24, 3.1.25(a), 3.1.32 |
22 | 19 Oct | (W) | 3.3: The Isomorphism Theorems | 3.2.5, 3.2.7, 3.2.8, 3.2.16 |
23 | 21 Oct | (F) | 3.4: Composition Series and the Holder Program | 3.3.1, 3.3.5 |
24 | 24 Oct | (M) | 3.5: Transpositions and the Alternating Group | 3.4.1, 3.4.2 |
25 | 26 Oct | (W) | 4.1: Group Actions and Permutation Representations | 3.5.1 (from 1.3.1), 3.5.3, 3.5.9 |
26 | 28 Oct | (F) | Chapters 2-3 Review | 2.2.14, 2.5.10, 3.1.11(a), 3.2.4, 3.2.6, 3.5.7, 3.5.8 |
27 | 31 Oct | (M) | 4.2: Groups Acting on Themselves | |
28 | 2 Nov | (W) | Exam 2, covering 2.1-3.5 | |
Chapters 4 and 5: Group Actions, Direct Products, and Abelian Groups | ||||
29 | 4 Nov | (F) | 4.4: Automorphisms | 4.1.4, 4.2.6 |
30 | 7 Nov | (M) | 4.5: Sylow's Theorem | |
31 | 9 Nov | (W) | 4.5 | 4.4.1, 4.4.3, 4.4.5 |
32 | 11 Nov | (F) | 5.1: Direct Products | 4.5.8, 4.5.13, 4.5.30 |
Chapter 7: Introduction to Rings | ||||
33 | 14 Nov | (M) | 5.2: Finitely Generated Abelian Groups | 5.1.1, 5.1.5 |
34 | 16 Nov | (W) | 7.1: Basic Definitions and Examples | 5.2.2(a)(b)(c), 5.2.3(a)(b)(c) |
35 | 18 Nov | (F) | 7.2: Polynomial Rings, Matrix Rings, and Group Rings | 7.1.1, 7.1.2, 7.1.7, 7.1.15 |
21-25 Nov | (M-F) | No class, Thanksgiving Recess | ||
36 | 28 Nov | (M) | 7.3: Ring Homomorphisms and Quotient Rings | |
37 | 30 Nov | (W) | 7.3 | 7.3.2, 7.3.11, 7.3.18(a), 7.3.20, 7.3.21 |
38 | 2 Dec | (F) | 7.4: Properties of Ideals | 7.3.29, 7.3.31, 7.3.34 |
39 | 5 Dec | (M) | 7.4 | 7.4.6, 7.4.9, 7.4.15 |
40 | 7 Dec | (W) | Chapters 4,5,7 Review | 4.2.10, 4.3.2, 4.4.17(e), 4.5.15, 5.2.9, 7.1.12, 7.3.4, 7.4.11 |
16 Dec | (F) | Comprehensive Final Exam, 7:30 a.m.-10:15 a.m. |
Exams:
There will be two midterm exams and a comprehensive final exam.
[PDF] Exam #1 ... [PDF] Solutions
[PDF] Review #2
[PDF] Exam #2 ... [PDF] Solutions
[PDF] Final Exam ... [PDF] Solutions
Links:
There are additional resources on the 251 Fall 2007 website.