Spring 25 Math 312GT Abstract Algebra Groups



01/29/25 Wed - Day 1:
- 1.1. Symmetries of a Square
- hw 1
sec 1.1: 1,3,4,5,6 {2}
sec 1.2: 1,4,5 {2}
- Reading
page 4 : the entire page
page 5 : the entire page
01/31/25 Fri - Day 2:
- 1.1. Symmetries of a Square
- Reading
page 9: Definition 1.9
page 10: Definition 1.12
page 12: Definition 1.17
02/03/25 Mon - Day 3:
- 1.2. 1-1 and Onto Functions
- Reading
page 20: Definition 1.34
page 35: Definition 1.35
02/05/25 Wed - Day 4:
# Class Canceled
02/07/25 Fri - Day 5:
- hw 1 due; include sections {1.1,1.2}
- journal 1 due; include worksheets {1.1,1.2}
02/10/25 Mon - Day 6:
- 1.3. Integers mod n and Elementary Properties of Integers
- Reading
page 26: Theorem 1.50 and its proof
02/12/25 Wed - Day 7:
- 1.3. Integers mod n and Elementary Properties of Integers
- hw 2
sec 1.3: 1a,1b,1c,2,3,4,9,10,13a,15a {6,7}
sec 1.4: 1,2,4,6,11 {8}
- Reading
page 29: Definition 1.60
02/14/25 Fri - Day 8:
02/17/25 Mon - Day 9:
- 1.4. Invertible Matrices & 2.1. Definitions and Examples
- Reading
page 38: Definition 2.5
page 43: Definition 2.23
page 43: Theorem 2.24 and its proof
02/19/25 Wed - Day 10:
- 2.2. Cancellation Properties
- hw 3
sec 2.1: 1,3,5a {5b}
sec 2.2: 1,3,4 {2}
sec 2.3: 2,6,7,11,16 {1,3}
- Reading
page 45: Definition 2.27
page 45: Example 2.28
02/21/25 Fri - Day 11:
- hw 2 due; include sections {1.3,1.4}
- journal 2 due; include worksheets {1.3,1.4}
02/24/25 Mon - Day 12:
- 2.3. Cyclic Groups
- Reading
page 48: Definition 2.39
page 49: Example 2.41
02/26/25 Wed - Day 13:
- 2.3. Cyclic Groups and the Order of an Element
- hw 4
sec 2.4: 1,2,3,4,8,12,13,14 {5,9,15}
sec 2.5: 2,4,7,14 {1,15}
- Reading
page 55: Definition 2.51
page 56: Lemma 2.52 and its proof
02/28/25 Fri - Day 14:
# Exam Review
- hw 3 due; include sections {2.1,2.2,2.3}
- journal 3 due; include worksheets {2.1,2.2,2.3}
03/03/25 Mon - Day 15:
# No Class
03/05/25 Wed - Day 16:
# Exam
03/07/25 Fri - Day 17:
- 2.4. Isomorphisms
- Reading
page 59: Definition 2.55
page 59: Lemma 2.56 and its proof
03/10/25 Mon - Day 18:
- 2.5. Direct Products (New Groups from Old Groups)
- Reading
page 61: Definition 2.60
page 62: Lemma 2.63 and its proof
03/12/25 Wed - Day 19:
- 2.6. Subgroups
- hw 5
sec 2.6p1: 1,2,4,8 {3,7}
sec 2.6p2: 5,9,11,19,27a,27c,31b,32 {6,18}
- Reading
page 69: Definition 2.79
03/14/25 Fri - Day 20:
- hw 4 due; include sections {2.4,2.5}
- journal 4 due; include worksheets {2.4,2.5}
03/17/25 Mon - Day 21:
# No Class
03/19/25 Wed - Day 22:
# No Class
03/21/25 Fri - Day 23:
# No Class
03/24/25 Mon - Day 24:
- 2.6. Subgroups
- Reading
page 75: Definition 3.1
03/26/25 Wed - Day 25:
- 3.1. Permutations, Cycles, and Transpositions
- hw 6
sec 3.1: 2,4,9a,10,11,13 {1}
sec 3.2: 2,4,5,10 {1,7}
- Reading
page 78: Definition 3.5
03/28/25 Fri - Day 26:
- hw 5 due; include sections {2.6p1,2.6p2}
- journal 5 due; include worksheets {2.6p1,2.6p2}
03/31/25 Mon - Day 27:
- 3.2. Even and Odd Permutations and An
- Reading
page 86: Definition 4.1
04/02/25 Wed - Day 28:
- 4.1. Definitions and Examples
- hw 7
sec 4.1p1: 1,2,3,5,7 {1}
sec 4.1p2: 4,6 {1}
- Reading
page 88: Definition 4.9
page 88: Definition 4.10
04/04/25 Fri - Day 29:
- hw 6 due; include sections {3.1,3.2}
- journal 6 due; include worksheets {3.1,3.2}
04/07/25 Mon - Day 30:
- 4.1. Definitions and Examples
04/09/25 Wed - Day 31:
- 4.2. The Cayley Graph of a Group Action
04/11/25 Fri - Day 32:
- hw 7 due; include sections {4.1p1,4.1p2}
- journal 7 due; include worksheets {4.1p1,4.1p2}