Algebraic Structures

Math 210A, Fall 2009

 

Chronological list of lecture notes and homework by date        

 

Topic(s)

Homework

Monday 8/31/09

1.1 Number Theory, 2.2 Permutations

HW #1, Rotman 2.2 #2, 7, 9, 11, 15, +Proof of Theorem

Wednesday 9/2/09

2.2 Permutations

 

Monday 9/7/09

Labor Day

 

Wednesday 9/9/09

1.2 Roots of Unity, 2.3 Groups

HW #2, Rotman 2.3  #18, 21 - 28

Monday 9/14/09

2.4 Lagrange's Theorem

HW #3, Rotman 2.4 #29, 31 - 35, 37

Wednesday 9/16/09

2.4 Lagrange's Theorem

 

Monday 9/21/09

2.5 Homomorphisms, 2.6 Quotient Groups

HW #4, Rotman 2.5 #42, 47, 51, 52, 53, 64

Wednesday 9/23/09

3.5 Homomorphisms

HW #5, Rotman 2.6 #67, 68, 69, 71, 76

Monday 9/28/09

2.6 Quotient Groups

 

Wednesday 9/30/09

Exam 1

Exam 1 Solutions

 

Monday 10/5/09

2.6 Quotient Groups

HW #6, Direct Products Homework Handout #1 - 4

Wednesday 10/7/09

2.7 Group Action

HW #7, Rotman 2.7 #81, 83, 84, 85, 89, 90, 94, 98, 99

Monday 10/12/09

2.7 Group Action

 

Wednesday 10/14/09

2.7 Group Action

 

Monday 10/19/09

5.1 Finite Abelian Groups

HW #8, Finite Abelian Groups Handout #1 - 16

Wednesday 10/21/09

5.1 Finite Abelian Groups

 

Monday 10/26/09

5.2  The Sylow Theorems

HW #9, Rotman 5.2 #23, 27, 28, 29, 30, 31; Sylow Theorems Handout #1 - 16

Wednesday 10/28/09

5.2  The Sylow Theorems

 

Monday 11/2/09

5.2  The Sylow Theorems

 

Wednesday 11/4/09

5.2  The Sylow Theorems

 

Monday 11/9/09

3.2  First Properties (Rings)
Received handout

HW #10, Rotman, 3.2 #3, 5, 6, 7, 8, 10, 12, 13 + Handout #3 - 8

Wednesday 11/11/09

Exam 2

 

Monday 11/16/09

3.3  Polynomials

 

Wednesday 11/18/09

3.3  Polynomials

 

Monday 11/23/09

3.5 Homomorphisms,
3.8 Quotient Rings

HW #11, Rotman, 3.5 #40, 41, 42, 44, 45, 49, 50(i), (ii), 51, + Handout #2 - 4

Wednesday 11/25/09

Furlough Day

 

Monday 11/30/09

3.8 Quotient Rings

HW #12, Rotman 3.8 #81, 82, 83 + Handout (based on 3.5) #2, 3, 4

Wednesday 12/2/09

3.2 First Properties (Rings),
3.4 Greatest Common Divisors

 

Monday 12/7/09

3.2 First Properties (Rings),
3.4 Greatest Common Divisors,
3.5 Homomorphisms

HW #13, Rotman 3.2 #17, 3.4 #29, 3.5 #46, 47, 48(i)

Monday 12/14/09

Final Exam  

Table of Contents
Chapter 1  Things Past
1.1 Some Number Theory
            Lecture Notes 8/31/09
1.2 Roots of Unity
            Lecture Notes 9/9/09
1.3 Some Set Theory
Chapter 2 Groups I
2.1 Introduction
2.2 Permutations
            Lecture Notes 8/31/09
                        HW #1, Rotman 2.2 #2, 7, 9, 11, 15, +Proof of Theorem
            Lecture Notes 9/2/09
2.3 Groups
            Lecture Notes 9/9/09
                        HW #2, Rotman 2.3  #18, 21 - 28
                        Hand in 22(ii) and (vi), 24
2.4 Lagrange's Theorem
            Lecture Notes 9/14/09
                        HW #3, Rotman 2.4 #29, 31 - 35, 37
                        Hand in #35
            Lecture Notes 9/16/09
2.5 Homomorphisms
            Lecture Notes 9/21/09
                        HW #4, Rotman 2.5 #42, 47, 51, 52, 53, 64
            Lecture Notes 9/23/09
                        HW #5, Rotman 2.6 #67, 68, 69, 71, 76
2.6 Quotient Groups
            Lecture Notes 9/21/09
            Lecture Notes 9/28/09
Exam 1, 9/30/09
            Lecture Notes 10/5/09
                        HW #6, Direct Products Homework Handout #1 - 4
                        Hand in #4a
2.7 Group Action
            Lecture Notes 10/7/09
                        HW #7, Rotman 2.7 #81, 83, 84, 85, 89, 90, 94, 98, 99
                        Hand in #83, 89, 89(ii), 94
            Lecture Notes 10/12/09
            Lecture Notes 10/14/09
Chapter 3 Commutative Rings I
3.1 Introduction
3.2 First Properties
            Handout 11/9/09 (no lecture notes)
                        HW #10 Rotman, 3.2 #3, 5, 6, 7, 8, 10, 12, 13 + Handout #3 - 8
                        Hand in #3.12
            Lecture Notes 12/2/09
            Lecture Notes 12/7/09
                        HW #13 Rotman 3.2 #17, 3.4 #29, 3.5 #46, 47, 48(i)
3.3  Polynomials
            Lecture Notes 11/16/09
            Lecture Notes 11/18/09
3.4 Greatest Common Divisors
            Lecture Notes 11/30/09
                        HW #11 Rotman, 3.4 #41, 42, 44, 45, 49, 50(i), (ii), 51,
                        + Handout #2 - 4
            Lecture Notes 12/2/09
3.5 Homomorphisms
            Lecture Notes 11/18/09
            Lecture Notes 11/23/09
3.8 Quotient Rings
            Lecture Notes 11/23/09
                        HW #12 Rotman 3.8 #81, 82, 83 + Handout #2, 3, 4
            Lecture Notes 11/30/09
Chapter 5  Groups II
5.1 Finite Abelian Groups
            Lecture Notes 10/19/09 (See also Finite Abelian Groups Handout)
                        HW #8, Finite Abelian Groups Handout #1 - 16
            Lecture Notes 10/21/09
5.2  The Sylow Theorems
            Lecture Notes 10/26/09
                        HW #9, Rotman 5.2 #23, 27, 28, 29, 30, 31;
                        Sylow Theorems Handout #1 - 16
            Lecture Notes 10/28/09
            Lecture Notes 11/2/09
            Lecture Notes 11/4/09
Exam 2  11/11/09