Detailed Schedule -- Abstract Algebra I

Fall 2007, Prof. Little

This is a tentative, evolving schedule. As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.

Date Class Topic Reading (Hungerford)
8/29 Course Introduction 3.1
8/31 Rings 3.1
9/3 Additional examples of rings 3.1
9/5 Basic properties of rings 3.2
9/7 Isomorphisms and homomorphisms of rings; Problem Set 1 due 3.3
9/10 Polynomials in one variable, division algorithm 4.1
9/12 Divisibility in F[x] 4.2
9/14 Irreducibles and unique factorization in F[x]; Problem Set 2 due 4.3
9/17 Roots of polynomials 4.4
9/19 Irreducibles in Q[x] 4.5
9/21 Irreducibles in Irreducibles in R[x] and in C[x]; Problem Set 3 due 4.6
9/24 Congruence in F[x] 5.1
9/26 F[x]/(p(x)) as a ring 5.2
9/28 F[x]/(p(x)) is a field if p(x) is irreducible over F; Problem Set 4 due 5.3
10/1 Review for Exam 1; Exam 1 given in evening Chapters 3,4, sections 5.1,5.2
10/3 Ideals and quotient rings 6.1
10/5 Quotient rings and homomorphisms 6.2
10/8 Columbus Day Break -- no class 6.2
10/10 More on quotient rings and homomorphisms (First Isomorphism Theorem) 6.2
10/12 R/I when I is prime or maximal; Problem Set 5 due 6.3
10/15 Groups revisited 7.1
10/17 Basic properties of groups 7.2
10/19 Subgroups; Problem Set 6 due 7.3
10/22 Isomorphisms and homomorphisms of groups 7.4
10/24 Congruences and Lagrange's Theorem 7.5
10/26 Normal subgroups; Problem Set 7 due 7.6
10/29 Spare day 7.6
10/31 Quotient groups 7.7
11/2 Quotients and homomorphisms; Problem Set 8 due 7.8
11/5 Symmetric and alternating groups 7.9
11/7 More on the symmetric and alternating groups 7.9
11/9 Direct products of groups; Problem Set 9 due 8.1
11/12 Structure theorem for finite abelian groups 8.2
11/14 Review for Exam 2; Exam 2 given in evening Chapters 6,7, section 8.1
11/16 More on the structure theorem for finite abelian groups 8.2
11/19 The Sylow theorems 8.3
11/21,23 Thanksgiving Break -- no class 8.4
11/26 Proofs of Sylow theorems 8.4
11/28 Applications to structure of finite groups 8.5
11/30 More applications to structure of finite groups 8.5
12/3 Course wrap-up
The final exam for this course will be given at 8:30 am on Wednesday, December 12, 2007.

Last modified: August 15, 2007