Algebraic Structures

Math 210B, Spring 2010

Table of Contents

3.4 Greatest Common Divisors
            Lecture Notes 1/25/10
                        HW #1, Rotman 3.4 #33, Cor 3.34, Handout #3 - 8
                        Hand in #2, 6, 8

3.5 Homomorphisms
            Lecture Notes 1/25/10
            Lecture Notes 1/27/10
                        HW #2, Rotman 3.6 #58(ii), 60, 61, 64           
                        Hand in #3.64
            Lecture Notes 2/1/10

6.1 Prime Ideals and Maximal Ideals
            Lecture Notes 2/1/10
                        HW #3, Rotman 6.1 #1, 3, 4, 5, 7, 16(ii), Handout #2, 3
                        Hand in #6.3, 6.15
            Lecture Notes 2/3/10
            Lecture Notes 2/10/10

6.2 Unique Factorization Domains
            Lecture Notes 2/10/10
                        HW #4, Rotman 6.2 #17, 18, 23, 25, 26, 27, 29
                        Hand in #6.27
            Lecture Notes 2/17/10
            Lecture Notes 2/22/10
Exam 1

Exam 1 solutions, 2/24/10           
            Lecture Notes 3/1/10

3.7 Vector Spaces (Handout)
            Lecture Notes 3/3/10
                        HW #5 Handout #1 - 13
                        Hand in #7, 8, 13

3.8 Quotient Rings and Finite Fields
            (Extensions Fields - Part I, Handout)
            Lecture Notes 3/8/10
                        HW #6a, Handout (Ext Flds Part I) #1 - 11
                        HW #6b, Handout (Ext Flds Part I) #12 - 21
                        Hand in #11, 12
                        Hand in #18, 19
            Lecture Notes 3/10/10
            Lecture Notes 3/15/10
            Lecture Notes 3/17/10
            (Extension Fields - Part II, Handout)
            Lecture Notes 3/22/10
                        HW #7a, Handout (Fld Ext Part II) #1 - 3
                        HW #7b, Handout (Fld Ext Part II) #4 - 7
                        Hand in #2, 7
            Lecture Notes 3/24/10
            (Extension Field - Part III, Handout)
                        HW #8, Handout (Ext Flds Part III) #1 - 4

4.1 Insolvability of the Quintic
            (Galois Theory I Handout)
            Lecture Notes 4/5/10
                        HW #9, (Galois Theory I HW) Handout #1 - 4
                        Hand in #3, 4

4.2 Fundamental Theorem of Galois Theory
            Lecture Notes 4/7/10
            Lecture Notes 4/12/10
                        HW #10, (Galois Theory II HW) Handout #1, 2
                        Hand in #1, 2
Exam 2, 4/14/10           
            Lecture Notes 4/19/10
            Lecture Notes 4/21/10
                        HW #11, (Galois Theory III HW) Handout #1 - 5
                        Hand in #5
            Lecture Notes 4/26/10
            Lecture Notes 4/28/10
                        HW #12, (Galois Theory IV HW) Handout #1
                        HW #12, (Galois Theory IV HW) Handout #2 – 6
                        HW #12, (Galois Theory IV HW) Handout #7 – 9
                        Hand in #2, 6
            Lecture Notes 5/3/10
            Lecture Notes 5/5/10
            Lecture Notes 5/10/10
Final Exam