Mathematics 5331  Abstract Algebra Schedule/Homework

 Date Section/Topic Homework Tuesday 4/18 § 3.1 Rings Prove Propositions 1-5 given in class. Study the proof of Theorem 1.9 Problem # 6 on page 120. Thursday 4/20 § 3.2 Ideals. The Isomorphism Theorems HW # 9. Due Thursday 4/27        Page 120 # 3, 6, 7, 15 Tuesday 4/25 § 3.2 Prime and maximal ideals Page 133 # 3, 4, 7a Thursday 4/27 §3.3 Factorization in commutative rings HW # 10. Due Thursday 5/4       Page 133 # 3, 4, 7a, 10, 20 Tuesday 5/2 § 3.3 Unique factorization domains Thursday 5/4 § 3.3 and Review Tuesday 5/9 Final Examination 11:00 a.m.-1:30 p.m.

 Date Section/Topic Homework Thursday 3/2 § 2.1 Free abelian groups Tuesday 3/7 § 2.1 Basis of free abelian groups Classwork handout Thursday 3/9 § 2.1 Rank of free abelian groups MARCH 13-17 SPRING BREAK Tuesday 3/21 § 2.2 Finitely generated abelian groups Handout # 3- Problems in Group Theory-Problems # 1-3 HW # 6. Due Tuesday 3/28   Prove the two corollaries of  the Fundamental Theorem.   Problem # 12 on page 82. Thursday 3/23 § 2.4 Group actions 1. Prove the equivalent version of the class equation. 2.Complete the table of orbits and stabilizers.3. Problems # 3, 9, 14 on page 92. Tuesday 3/28 § 2.4 Cayley's theorem HW # 7. Due Thursday 4/6      Proposition 4.8 and Corollary 4.10 Thursday 3/30 § 2.5 Sylow's Theorems Problems # 1, 10, 11, 13 on page 96 Tuesday 4/4 § 2.5 Sylow's Theorems 1. Show that a group of order 36 is not simple. 2. Handout # 4- Problems on Group Theory-Problems # 1- 10 3. HW # 8. Due Tuesday 4/11     Problems # 1, 10, 11, 13 on page 96 Thursday 4/6 § 2.6 Finite groups Study the proof of Proposition 6.3 and Proposition 6.4 See link below for a listing of groups of small order. http://www.math.usf.edu/~eclark/algctlg/small_groups.html Tuesday 4/11 Review Test # 2 Thursday 4/13 Test # 2

 Date Section/Topic Homework Tuesday 1/17 §1.1 Semigroups, monoids and groups Prove Proposition 1.3 on page 25. Problem 4, p.29. Give the Cayley table for the group of symmetries of the square. Prove Sn is non-abelian for n greater than 2. Problem 5, p.29. Prove the order of Sn is n! Problem 6 on page 29. Thursday 1/19 § 1.1 Groups § 1.2 Homomorphisms Prove Proposition 1.4 on page 25. Problem 15 on page 30. Tuesday 1/24 § 1.2 Homomorphisms and subgroups Pages 33-34 Problems # 1, 2, 6, 7, 9, 10, 11, 13, 17 HW # 1: Turn-in Problem # 6 on Tuesday January 31st. Thursday 1/26 § 1.3 Cyclic groups Pages 36-37 Problems # 1, 3, 4, 5, 6, 8, 9 HW # 2: Turn-in Problem # 3 on Tuesday February 7. Tuesday 1/31 § 1.4 Cosets Page 40 # 2, 3, 5 Thursday 2/2 § 1.4 Counting § 1.5 Normality Page 40 # 6 Page 45 # 1, 2, 6, 7 Tuesday 2/7 § 1.5 Quotient groups and Isomorphism Theorems Page 45 # 5, 9a, 10, 11, 16 HW # 3: Turn-in Problems: # 6 page 40; # 1, 7, 11, 16 pages 45-46  on Thursday 2/16. Thursday 2/9 § 1.5 Isomorphism Theorems Problems in group theory (Handouts I and II)  HW # 4: Turn-in Problems # 4, 6, 7, 9, 10 from Handout II on  Tuesday 2/21. Tuesday 2/14 NO CLASS Thursday 2/16 § 1.6 Symmetric group Study the proof of Corollary 6.4. Tuesday 2/21 § 1.6 Alternating groups; Cayley's Theorem Page 51 # 2, 3, 4, 5, 7, 8, 10 HW # 5: Turn-in Problems # 3, 10 on Tuesday February 28. Thursday 2/23 Review Test # 1 Tuesday 2/28 Test # 1