Math 307
Abstract Algebra

Progression and homework

Presentation: written work should be done on one side only of 8.5''x11'' paper with smooth edges. Each problem should begin a new page.

Deadlines: papers should be turned in by 2pm on the due date. Extensions may (and usually will) be granted if requested at least twenty-four hours before the due date. Late homework will not be accepted.

	Date	Reading	Topic	Assignments
1	8/29		Introduction
	8/31	Chap. 2	Composition laws
2	9/03	Chap. 3 & 4	Groups
	9/05	Chap. 5	Subgroups	Homework 1 and a solution.
	9/07	Chap. 5	Operations on subgroups
3	9/10	Chap. 3 & 11	Euclidean division, $\mathbb{Z}_n$ as a group
	9/12		No class
	9/14		No class
4	9/17	Chap 3. & 9	Tables, isomorphisms
	9/19	Chap. 14	Homomorphisms	Homework 2 and a solution.
	9/21	Chap. 14	Kernels
5	9/24	Chap 8	Symmetric groups: cycle decomposition
	9/26	Chap. 8	Symmetric groups: the signature morphism
	9/28	Chap. 8	Symmetric groups: the signature morphism
6	10/01	Chap. 13	Lagrange's Theorem
	10/03		Midterm 1	Midterm 1 and a solution
	10/05	Chap. 13	Index of subgroups	Homework 3 and a solution.
7	10/08	Chap. 11	Cyclic groups
	10/10	Chap. 11 Chap. 15	Classification of cyclic groups Normal subgroups
	10/12	Chap. 15	Quotient groups
8	10/15		Fall Break	Homework 4 and a solution.
	10/17	Chap. 16	The First Isomorphism Theorem
	10/19		Group actions
9	10/22		Orbits and stabilizers
	10/24		Semi-direct products: inner case
	10/26		Semi-direct products: general case	Homework 5 and a solution.
10	10/29	Chap. 7	Dihedral groups
	10/31		Group theory wrap-up
	11/02	Chap. 17	Rings
11	11/05		$\mathbb{Z}_n$ as a ring, zero divisors
	11/07		Division rings, fields	Homework 6 and a solution.
	11/09	Chap. 18	Morphisms and ideals
12	11/12	Chap. 22	Ideals in $\mathbb{Z}$
	11/14	Chap. 19	Quotient rings
	11/16		Midterm 2	Midterm 2 and a solution.
13	11/19	Chap. 19	First Isomorphism Theorem for rings
	11/21		Thanksgiving Break
	11/23		Thanksgiving Break
14	11/26	Chap. 24	Rings of polynomials
	11/28		Ideals in polynomial rings	Homework 7 and a solution.
	11/29		More on quotient rings
15	12/03	Prime ideals, maximal ideals
	12/05		Properties of PIDs
	12/07	Fields of fractions, Grothendieck groups