## Course Webpage - Fall 2016

### Fall 2016

This course is an introduction to abstract algebraic systems, including groups, rings and fields.

Prerequisites: CALC3, Linear Algebra (Math 250) and Math 300

Text: Abstract Algebra (3rd ed.), by Thomas Hungerford, Brooks/Cole (Cengage since 2015), 2014

### Tentative Course Syllabus (Fall 2016)

WeekLecture DatesSectionsTopics
1 9/7 1.1-1.3 The integers and factorization
2 9/12, 14 1.3, 2.1-2.3, 3.1-3.3 congruences and Z/n, Rings
3 9/19, 21 3.3, 6.1-6.2 properties of rings and homomorphisms
4 9/26, 28 4.1-4.4 Polynomial rings F[x] and factorization
5 10/3, 5 5.1-5.3, 6.3 R/I, F[x]/I and F[x]/P
6 10/10, 12 4.5-4.6 Irreducibility for F=Q,R,C; review
7 10/17, 19 chapters 1-6, 14 Exam 1, Chinese Remainder Theorem
8 10/24, 26 7.1-7.3 Groups and subgroups
9 10/31, 11/2 7.4, 8.1 Group homomorphisms, Lagrange's Theorem
11 11/7, 9 8.2-8.4 Normal subgroups and quotient groups
12 11/14, 16 7.5 Symmetric groups, review
13 11/21 (not 23rd) chapters 7, 8 Exam 2, Thanksgiving break
14 11/28, 30 9.1-9.2 Finite abelian groups
15 12/5, 7 10.1-10.2, 10.4 Domains, fractions and factorization
16 12/12, 14 10.2, 10.3 UFD's, PID's, review
17 December 23 (Friday) 12-3 PM Final Exam (cumulative)

### Homework for Math 351(Fall 2016)

DueProblems
9/14 1.1 #8 ;  1.2 #8,13,15b ;  1.3 #21
9/21 2.1 #4a,12,21b; 2.2 #2,12; 3.1 #13, 15a; 3.2 #7
9/28 3.3 #9,19,38; 4.1 #5(b,d),10,15; 4.2 #5(b,d),8
10/5 4.3 #4,12,14 ;  4.4 #2(c,d), 6a, 8(a,b,c), 24
10/12 5.1 #4,8,10;   5.2 #6,14; 5.3 #1,5b,9
10/31 7.1 #4,5,16;   7.2 #2,5,7(b,c),13,25
11/7 7.3 #28,52; 7.4 #12,39,45; 7.5 #13,16,21
11/14 8.1 #5,9,11,39;   8.2 #1,14,18;   8.3 #2,7,22;   8.4 #2,13,19
12/7 9.1 #2,18;   9.2 #1,2,7(a,b,c), 12,22
12/14 10.2 #9,13,14,20;   10.4 #6,11,12

Course Grades will be determined by counting the Final Exam as double the weight of the HW, and two hour exams.