# Math 71: Algebra

Fall 2013

Week 1 Section(s) Description Assigned Reading Assigned Problems
9/16 0.2,0.3 Definition of Z/nZ, Division Alg 0.1-0.3 Do problems 1,2 of Homework#1
9/18 0.1 Equivalence Relations and Partitions 1.1 Do problems 3,4 of Homework#1
9/20 1.1 Definition of groups; examples; begin Dihedral group 1.2-1.3 Do problems 5-8 of Homework#1

Week 2 Section(s) Description Assigned Reading Assigned Problems
9/23 1.2,1.3 Dihedral and Symmetric groups 1.4-1.5 Do problems 1-3 of Homework#2
9/25 1.4,1.5 Symmetric Group, Matrix groups, Quaternions 1.6 Do problems 4-7 of Homework#2
9/27 1.6,2.1 Homomorphisms 2.1 Do problems 8-11 of Homework#2

Week 3 Section(s) Description Assigned Reading Assigned Problems
9/30 2.1 Subgroups 2.3 Do problems 1-4 of Homework#3
10/2 2.3 Cyclic Groups 2.4 Do problems 5-8 of Homework#3
10/4 2.4 Cyclic Groups, Subgroups generated by a set 3.1,3.2 Continue working on Homework#3

Week 4 Section(s) Description Assigned Reading Assigned Problems
10/7 3.1,3.2 Cosets and Homomorphisms 3.2 Do problems 1-4 of Homework#4
10/9 3.2 More on cosets and Lagrange's Theorem 3.3 Do problems 4-8 of Homework#4
10/10 Midterm #1 in-class portion; take-home due Friday at beginning of class Midterm 1 Solutions
10/11 3.3 Isomorphism Theorems 3.3,3.4 Continue working on Homework#4

Week 5 Section(s) Description Assigned Reading Assigned Problems
10/14 3.3,3.4 Isomorphism and the Holder Program 3.5,1.7,4.1 Do problems 1-5 of Homework#5
10/16 3.5,1.7,4.1 Alternating Group, Group Actions, Cayley's Theorem 4.2,4.3 Do problems 6-8 of Homework#5
10/18 4.2,4.3 Group Actions, Class Equation 4.5,5.2,5.4 Do problems 10-12 of Homework#5

Week 6 Section(s) Description Assigned Reading Assigned Problems
10/21 4.5,5.2,5.4 Sylow Theorems, Recognizing Direct Products, Fundamental Theorem 5.2,7.1 Do problems 1-3 of Homework#6
10/23 5.2 Fundamental Theorem 7.1,7.2 Do problems 4,5 of Homework#6
10/25 7.1,7.2 Rings, Polynomial Rings 7.3 Do problems 6-9 of Homework#6

Week 7 Section(s) Description Assigned Reading Assigned Problems
10/28 7.3 Homomorphisms, Quotient Rings 7.4 Do problems 1,3,4 of Homework#7
10/30 7.4 Quotient Rings and Properties of Ideals 7.4,8.1 Do problems 2,5,6 of Homework#7
10/31 Midterm #2 in-class portion; take-home due Saturday at 10:00am
11/1 7.4 Maximal Ideals 8.1,9.1 Do problems 7,8 of Homework#7

Week 8 Section(s) Description Assigned Reading Assigned Problems
11/4 8.1,9.1 Euclidean Domains, Polynomial Rings 8.2,9.2
11/6 8.2,9.2 PIDs 8.3 Do problems 1-4 of Homework#8
11/8 8.3 gcds, irreducibles, primes 8.3 Do problems 5,6,7 of Homework#8

Week 9 Section(s) Description Assigned Reading Assigned Problems
11/11 8.3 UFDs 9.3 Start looking at Homework#9
11/13 9.3 Gauss' Lemma and Consequences 9.4 Continue working on Homework#9
11/15 9.4 Irreducibility Criteria 9.4 Continue working on Homework#9

Week 10 Section(s) Description Assigned Reading Assigned Problems
11/18 9.4 Extension Fields