Math 4281: Class Outlines, Spring 2011

o 5/6/11: Midterm Exam III. [Sections 2.6-7, 3.1, 3.3 (3.6 in the on-line edition), 5.1, 5.2 (omitting 5.2.5), 6.1-3]

o 5/4/11: Homework due and discussed. Sample exam discussed. [Sections 2.6-7, 3.1, 3.3 (3.6 in the on-line edition), 5.1, 5.2 (omitting 5.2.5), 6.1-3]

o 5/2/11: Quotient Rings. [Section 6.3]

o 4/29/11: Ring homomorphisms and ideals. [Section 6.2]

o 4/27/11: Homework due and discussed. Ring homomorphisms. [Sections 5.1, 5.2, 6.1, and 6.2 through 6.2.7]

o 4/25/11: Counting orbits: Burnside's lemma. Rings revisited (left for self-study). [Sections 5.2 (skip Example 5.2.5) and 6.1]

o 4/22/11: Group actions on sets. [Section 5.1]

o 4/20/11: Homework due and discussed. [Sections 3.1 and 3.3 (Edition 2) or 3.6 (Edition 2.5)]

o 4/18/11: Finite abelian groups. [Section 3.3 (It corresponds to Section 3.6 in the on-line edition, but Section 3.3 in the printed edition is less general and significantly easier to understand.]

o 4/15/11: Direct products. [Section 3.1]

o 4/13/11: Homework due and discussed. [Sections 2.6-7]

o 4/11/11: Homomorphism theorems. [Section 2.7 through the end]

o 4/8/11: Quotient groups. [Section 2.7 before Homomorphism Theorems]

o 4/6/11: Equivalence relations and set partitions. [Section 2.6]

o 4/4/11: Solutions to Exam II. [Sections 1.5, 1.10-11, 2.1-5]

o 4/1/11: Midterm Exam II. [Sections 1.5, 1.10-11, 2.1-5]

o 3/30/11: Homework is due and discussed. Discussion of Sample Exam II. [Sections 1.5, 1.10-11, 2.1-5]

o 3/28/11: Cosets and Lagrange's Theorem. [Section 2.5]

o 3/25/11: More on the last homework: Exercise 2.2.11 and 2.2.15. Homomorphisms (through the end). [Section 2.4]

o 3/23/11: Homework due and discussed: Exercises 2.2.14-15. [Sections 2.2-3]

o 3/21/11: Homomorphisms (before the kernel). [Section 2.4 before the Kernel]

o 3/14-18/11: No classes: Spring Break. Have a great break and come back refreshed!

o 3/11/11: The dihedral groups. [Section 2.3]

o 3/9/11: Cyclic groups and their subgroups. [Section 2.2]

o 3/7/11: Homework due and discussed. Subgroups. [Section 2.2 before Cyclic Groups and Subgroups]

o 3/4/11: First results on groups. [Section 2.1]

o 3/2/11: Rings and Fields. [Section 1.11]

o 2/28/11: Homework due and discussed. Groups. [Sections 1.5 and 1.10]

o 2/25/11: Permutations. [Section 1.5]

o 2/23/11: Solutions to Exam 1. [Sections 1.1-4 and 1.6-9]

o 2/21/11: Classes canceled: snow day.

o 2/18/11: Midterm Exam I. [Sections 1.1-4 and 1.6-9]

o 2/16/11: Discussion of Sample Exam I. [Sections 1.1-4 and 1.6-9]

o 2/14/11: Symmetry and matrices. [Section 1.4]

o 2/11/11: Symmetry and multiplication tables. [Sections 1.1-1.3]

o 2/9/11: Discussion of homework Exercise 1.8.16 and related topics, such as Proposition 1.8.23 and irreducibility in R[x] and C[x], as opposed to that in Q[x]. [Section 1.8]

o 2/7/11: Counting, III: Euler's function and theorem. [Section 1.9, skipping derangements: 1.9.13-14]

o 2/4/11 (Professor Webb substituting): Counting, II. [Section 1.9 through 1.9.16, skipping derangements: 1.9.13-14, but not 1.9.15 yet]

o 2/2/11 (Professor Webb substituting): Counting, I. [Section 1.9 through 1.9.8]

o 1/31/11: Polynomials (continued). [Section 1.8 through the end]

o 1/28/11: Polynomials (beginning). [Section 1.8 through Proposition 1.8.16]

o 1/26/11: Modular arithmetic (continued). [Section 1.7]

o 1/24/11: Modular arithmetic. [Section 1.7 through 1.7.8]

o 1/21/11: Division with remainder. The greatest common divisor. The Euclid algorithm for finding the greatest common divisor. Uniqueness of prime factorization. [Section 1.6 through the end]

o 1/19/11: Basic Number Theory. Divisibility in the integers. Primes. The fundamental theorem of Arithmetics (prime factorization). [Section 1.6 through Theorem 1.6.6]


Last modified: Wed Jan 19 11:46:09 CDT 2011