Policy: homework should be submitted no later than 5pm on the due date. Let your instructor know in advance if you feel that you need extra time.
In order to be well-prepared for the examinations, it is strongly suggested that you treat all the problems listed here.

wk	date	reading	topic	homework / comments
1	09/16	§0.1 - §0.3	Equivalence relations, integers modulo n	§0.1: 1, 4, 7 §0.2: 1, 2, 3, 7, 10, 11 §0.3: 4, 6, 10, 11, 12, 13, 14
	09/17 (x)	§1.1	Groups: definitions and first examples	§1.1: 1, 2, 5, 6, 8, 9, 11, 13, 14, 17, 20, 22, 23, 24, 25, 29, 30, 34
	09/18	§1.4, §1.5	Examples of groups	§1.4: 1, 2, 4, 5, 8, 10, 11 §1.5: 2
2	09/21	§ 1.2	Dihedral groups	§1.2: 1(a,b), 2, 3, 7, 9, 10, 14, 15, 17, 18
	09/23	§ 1.3, §1.6	Symmetric groups, group homomorphisms	§1.3: 1, 4(a), 5, 6, 9(a), 11, 13 §1.6: 1 - 4, 8, 9, 13, 16, 17, 19, 20, 25
	09/24 (x)		Problem session	Homework #1, due Tuesday 09/29 and solution.
	09/25	§2.1	Subgroups	§2.1: 1 to 17
3	09/28	§2.3	Cyclic groups	§2.3: 1 - 3, 9, 12, 13, 16, 18, 20, 21, 26
	09/30	§2.4	Subgroups generated by subsets	§2.4: 1 - 6, 13, 14, 18, 20, 21, 26
	10/01 (x)		Problem session	Homework #2, due Tuesday 10/06 and solution.
	10/02	§3.1	Quotients, First Isomorphism Theorem	§3.1: 1 - 3, 5, 7, 9, 10, 11, 12, 13, 14, 16, 22, 28, 29, 35, 36, 37, 38, 40, 41 §3.2: 1, 4, 5, 6, 7, 8, 9, 11, 12, 15, 16, 18, 19, 22 §3.3: 1, 3, 4, 8, 9
4	10/05		Problem session
	10/07	§3.2	Lagrange's Theorem
	10/08		Midterm 1 and solution	Homework #3, due 10/16 and solution.
	10/09	§3.5	Transpositions and the Alternating Group	§3.5: 1 - 4, 6, 9, 14
5	10/12	§1.7, §4.1	Group actions	§1.7: 1 - 4, 6, 8, 13, 16, 17, 19, 21 §4.1: 1 - 3, 6, 7, 8, 10
	10/14	§4.2	Group actions	§4.2: 8, 10, 14
	10/16	§4.3	Group acting by conjugation	§4.3: 4, 5, 8, 23, 24, 25
6	10/19	§3.4, §4.5	Composition series and the Hölder Program, Sylow's Theorems	§3.4: 1, 4, 5, 7 §4.5: 2, 3, 10, 17, 27, 32
	10/21	§5.2, § 5.4	The Fundamental Theorem of Finitely Generated Abelian groups, Direct Products	§5.2: 1, 5, 6, 7, 11, 14 §5.4: 1 - 5, 15, 16, 20
	10/22 (x)	§5.5	Semi-direct products	§5.5: 1, 2, 3, 18, 23
	10/23	§7.1, § 7.2	Rings: polynomial, matrix and group rings	§7.1: 1 - 7, 11, 12, 13, 23, 25, 26, 27 §7.2: 1, 3, 5, 6, 7, 8, 9, 12
7	10/26	§7.3	Ring homomorphisms	§7.3: 1 - 4, 6, 7, 8, 10, 11, 12, 13, 16, 17, 23, 24, 25, 26, 28, 29, 34
	10/28	§7.4	Ideals	§7.4: 1 - 6, 10, 11, 14, 18, 19, 29, 30, 31, 33, 38
	10/29		Midterm 2 and solution Take-home and solution	Homework #4, due Friday 11/06 and solution.
	10/30	§8.1, §9.1	Euclidean domains, polynomial rings	§8.1: 1 - 5, 7, 8, 10 §9.1: 1 - 9, 13, 15, 16, 17, 18
8	11/02	§8.2, §9.2	Principal ideal domains	§8.2: 1 - 8 §9.2: 1 - 12
	11/04	§8.3	Unique factorization domains	§8.3: 1 - 9, 11
	11/05 (x)		Problem session	Homework #5, due Monday 11/16 and solution.
	11/06	§8.3	Unique factorization domains
9	11/09	§9.3	Gauss Lemma and consequences	§9.3: 1 - 5
	11/11	§9.3	Transfer theorem for UFDs
	11/12 (x)		Problem session
	11/13	§13.1	Extension fields
10	11/16	Further topics	Introduction to representation theory	Final examination, due 11/24 at 8am and solution.

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