MTH 316 (Abstract Algebra) Spring 2010

Instructor: R. A. Beauregard

Office/Hours: Lippitt 202K, Tues, Wed, Thurs 12:30-1:30

Text: Elements of Modern Algebra, 7th edition by Gilbert & Gilbert.

Attendance at each class is expected.

The following calendar gives a timetable for the course.

You should work out all of the problems given below.

 

Week

Events

Sections

Problems

Jan 25

Class starts: Mon Jan 25

2.3 Divisibility 

2.4 Primes, GCDs 

3-9 odd, 17, 20, 21, 24, 25, 26, 40

2abc, 3cd, 10, 21, 33, 34

Feb 1

2.5 Congruences 

2.6 Congruence classes

1-15 odd, 27, 28

1abcd, 2ab, 3abd, 4abc, 5abg, 6ac, 7ac, 8bde, 16, 18, 20-23

Feb 8

1.6 Matrices

1.4 Binary operations

3, 9-12, 14, 16, 30, 31

1abcd, 2abcd, 3-6, 7-8, 12-13

Feb 15  

 No class : Mon, Feb 15

3.1 Groups

3.2 Properties

1-7, 11-15, 17, 20, 21, 23, 25, 28, 29

1-6, 11-15, 17, 19-20

Feb 22

Test # 1: Tuesday

3.3 Subgroups

3.4 Cyclic groups

2, 3, 6a, 7a, 8, 13ac, 14ab, 17, 18a, 29, 30, 33, 40, 41

2, 5, 7, 8, 9ac, 10c, 11ac, 12a, 16, 18c, 23ab, 25, 27-28

Mar 1

 

3.5 Isomorphisms

3.6 Homomorphisms 

1-4, 7, 8, 10, 12, 15, 24, 26

1-5, 8, 9, 11, 15-18

Mar 8

4.1 Permutation groups

4.4 Cosets

1-10abc, 14

3, 7, 8, 12, 19, 20-22, 24

Mar 15

   Test # 2: Thursday

4.5 Normal subgroups

4.6 Quotient groups

1c, 32, 2, 4, 6, 22, 25, 29-30, 33

3, 7, 18-19, 21, 30, 34, 37

Mar 22-28

Spring Break 

Spring Break

Spring Break

Mar 29

Last day to drop:

Mar 29

4.7 Direct sums 

5.1 Rings

1, 3, 7, 16-17, 19

1ab, 2abcdf, 7, 8, 10, 14ac, 16, 23-25, 27, 30, 39, 47-48

Apr 5

 

5.2 Integral domains, fields  

6.1 Ideals and quotient rings

1abeg, 2, 8, 11, 15-16, 18, 21, 23

1, 3-4, 6-8, 11-15, 19acd, 20-21, 26-27, 31

Apr 12

 

6.2 Ring homomorphisms

6.3 Characteristic

1, 3, 6, 7, 10, 12, 14, 21-22, 24, 25a

1-4, 8, 9, 10, 14, 16, 18, 20

Apr 19

  Test #3: Tuesday

6.4 Maximal ideals

8.1 Polynomials over a ring

1-5, 9-11, 13-15, 19, 21-25, 27-28

3, 5- 7, 10-12, 14, 16-18

Apr 26

 

8.2 Polynomial Divisibility

8.3 Factorization in F[x]

1-4, 21, 33-34

1, 2, 5, 6

May 2 

Last day  May 3