Math 30710 Assignments, Fall 2009


Reading should be completed before class on the given date.

Be careful to justify your solution when a homework problem calls for it.

Date Section/Topic Reading (page numbers) Problems Due
8/26/09 0. Sets and relations 1–8 §0: #3, 5, 7, 11, 12, 13, 15, 16, 17, 25, 28, 31, 32 9/2/09
8/28/09,
8/31/09 		1. Introduction 11–18 §1: #3, 7, 11, 13, 19, 23, 29, 33, 35, 37, 39, 40 9/2/09
9/2/09 2. Binary operations 20–25 §2: #2–8, 12, 14–18, 23, 24 9/9/09
9/4/09 3. Isomorphisms 28–34 §3: #1, 2–4, 6–7, 17, 20–23, 26–29 9/9/09
9/7/09 4. Groups 36–43 §4: #1–3, 7, 10, 11–13, 19, 22, 23, 25 9/16/09
9/9/09 4/5. Groups/subgroups 43–45, 49–52 §4: #26–28, 31–33;
§5: 1, 2, 5, 11–12, 14 		9/16/09
9/11/09 5. Subgroups 53–55 §5: #20, 22, 23, 26, 36, 39, 42, 44, 53, 54 9/16/09
9/14/09,
9/16/09
9/18/09 		6. Cyclic groups 59–65 §6: #1, 5, 11, 14, 15, 17, 20, 21, 22, 25, 30, 31, 32 9/23/09
9/21/09 7. Generators and Cayley digraphs 68–72 §6: #36, 37, 38, 42, 44, 49;
§7: #1, 6, 7, 10, 16, 17, 18, 19 		FRIDAY
10/2/09
9/23/09
9/25/09 		8. Permutation groups 75–81 §8: #1, 5, 6, 8, 10, 11, 17, 18, 23, 24 FRIDAY
10/2/09
9/25/09
9/28/09
8–9 Cayley's theorem, orbits, cycles 81–83, 87–90 §8: #30, 31, 35, 39, 41, 43, 47;
§9: 1, 6, 7, 10 		FRIDAY
10/2/09
9/28/09
9/30/09
10/2/09
9. Even and odd permutations, alternating groups 90–93 §9: #13, 14, 15, 19–23, 29, 34 Not
collected
10/5/09 Review for Exam 1
10/7/09 Exam 1 – covers §§1–9
10/9/09 10. Cosets 96–100 §10: #1–4, 6–7, 12, 13, 15, 19, 20–24 FRIDAY
10/16/09
10/12/09 10 Cosets/Lagrange's Theorem 100–101 §10: #27, 30–34, 37, 41, 43 FRIDAY
10/16/09
10/14/09 11. Products 104–110 get started on §11 HW 10/28/09
10/16/09 11. Finite abelian groups 104–110 §11: #1, 2, 7, 8, 9, 13, 14, 18, 20, 24, 32, 36, 46, 47 10/28/09
Fall Break
10/26/09 13. Homomorphisms 125–129 §13: #1–5, 9, 10, 16, 17, 22, 24, 25, 28, 29 11/4/09
10/28/09
10/30/09 		13. Homomorphisms 129–133 §13: #32, 33, 34, 39, 42, 47, 48, 49, 52 11/4/09
10/30/09 14. Factor groups 135–139 §14: #1–2, 7, 9–10 FRIDAY
11/13/09
11/2/09
11/4/09
11/6/09 		14. Factor groups 139–141 §14: #17, 18, 20, 23a-d, 24, 30 FRIDAY
11/13/09
11/6/09
11/9/09 		15. Factor group computations 144–148 §15: #1–5, 19, 28 FRIDAY
11/13/09
11/9/09 18. Rings and Fields 167–170 §18: #3, 5, 7, 9, 11, 14, 15, 16, 17, 19 FRIDAY
11/13/09
11/11/09 18. Rings and Fields 171–174 §18: #20, 22, 23, 24, 25, 27, 28, 33, 37, 38 Not collected
but is on exam
11/13/09 18 Rings and Fields 177–179, 224–226 No additional HW
11/16/09 Review for Exam 2
11/18/09 Exam 2 – covers §§10, 11, 13, 14, 15, 18
11/20/09
11/23/09 		19. Domains 177–182 §19: #1–4, 5, 7, 9, 11, 12, 14, 15–18, 23, 29 12/4/09
11/30/09
12/2/09 		20. Fermat's and Eulers theorem 184–189 §20: #1–10 12/4/09
12/2/09 22. Polynomials 198–207 §22: #1, 2, 6, 7, 9, 13, 17, 22, 23, 25 Not collected
but is on exam
12/4/09 22. Polynomials (ctd)      
12/07/09 Overview of field theory  
12/9/09 Go over practice final    
GOOD LUCK ON FINALS!!!!