## 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