Math 31
Topics in Algebra
Fall 2013

General Info | Day-to-day

Syllabus and homework assignments

 wk date reading topic homework 1 6/20 Ch 1.2, 1.3 Intro; Sets 1.2: 8, 12a, 21a; 1.3: 1, 2. 6/21 Ch 1.5, 1.6 Integers 1.5: 4, 17; 1.6: 1, 8, 12. HW #1: Due Wed 6/25 2 6/23 Ch 2.1 Groups 2.1: 1abde, 8, 9. 6/25 Ch 2.2, 1.4 Permutations 2.2: 1; 1.4: 9acf, 15, 34 6/27 Ch 2.3 Subgroups 2.3: 1, 3, 8 HW #2: Due Wed 7/2 3 6/30 Ch 2.4 Equivalence Relns 2.4: 1a, 2, 4 7/2 Ch 2.4 Lagranges Thm 2.4: 5, 9, 31 HW #3: Due Friday 7/11 4 7/9 Ch 2.5 Isomorphisms 2.4: 25; 2.5: 1bcde, 2 7/10 Ch 2.5 Homomorphisms 2.5: 3, 4, 5 7/11 Ch 2.6 Factor Groups 2.5: 15; 2.6: 3, 4, 5. HW #4: Due Wed 7/16 5 7/14 Ch 2.7 Homomorphism Thms 2.7: 2, 3, 6. 7/16 Ch 2.7 (continued) 2.7: 4abc 7/18 Ch 2.8 Cauchys Thm 2.8: 2, 6, 7, 8 HW #5: Due Wed 7/23 6 7/21 2.9 Direct Products 2.9: 2 7/23 2.10 Finite Abelian Groups - 7/25 3 Symmetric Group 3.2: 2ab; 3.3: 1ab 7 7/28 4.1 Rings 4.1: 10a, 31, 32, 33a 7/30 4.2 Quaternions 4.2: 2 8/1 4.3 Homomorphisms 4.3: 4, 15 HW #6: Due Friday 8/8 8 8/4 4.4 Maximal Ideals 4.4: 10, 11, 12, 13 8/6 4.3 Correspondence Thm - 8/8 4.5 Polynomial rings 4.5: 1, 2 HW #7: Due Wed 8/13 9 8/11 4.5 PIDs - 8/13 4.5 Unique factorization - 8/14 4.5 Polynomial equations - 8/15 4.5 Field Extensions - 10 8/18 Chinese Remainder Thm 8/20 No class