MTH 316 (Abstract Algebra) Spring 2009

Instructor: R. A. Beauregard

Office/Hours: Lippitt 202K, Tues, Wed, Thurs 11:30-12:30

 

 

Text: Elements of Modern Algebra, 6th 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 19

Classes start:  Wed Jan 21

2.3 Divisibility 

3-9 odd, 17, 20-24                  

Jan 26

 

2.4 Primes, GCDs 

2.5 Congruences 

2abc, 3cdk, 7, 26, 27

1-15 odd

Feb 2

 

 

 

2.6 Congruence classes

1.6 Matrices

1abcd, 2ab, 3abd, 4abc, 5abg, 6ac, 8ac, 16, 22-23

3, 8, 9-12, 14, 16, 25,  26

Feb 9

  

 

1.4 Binary operations

3.1 Groups

1abcd, 2abcde, 3-6, 9, 10

1-7, 11-13, 21, 23, 25, 28, 29, 33, 42-44, 48, 49, 52

Feb 16

No Mon classes, Mon classes meet Wed.

   Test # 1: Tuesday
 

3.2 Subgroups

3.3 Cyclic groups

2, 3, 5-9, 12-14, 17, 18a, 35

5, 7ab, 8ab, 9ac, 10ac, 11ac, 12, 14-15, 19-21, 23-24

Feb 23

 

 

3.4 Isomorphisms

3.5 Homomorphisms 

1-4, 7, 10, 13, 16, 23

1, 2, 3, 7, 11, 12-14

Mar 2

 

 

4.1 Permutation groups

4.4 Normal subgroups

1-10abc

5-8, 32, 41, 42, 45, 46, 48

Mar 9

 

    Test # 2:  Thursday

4.5 Quotient groups

4.6 Direct sums 

3, 4, 11, 19, 30

6, 8, 9-12, 16

Mar 16

Spring Break 

Spring Break

Spring Break

Mar 23

 

 

  Last day to drop:

      Mar 24

 

5.1 Rings

5.2 Integral domains and fields  

1, 2, 7, 8, 10, 14ac, 15, 20, 21, 24, 31, 38
1, 2, 6, 9-10, 16, 18

Mar 30

 

 

6.1 Ideals and quotient rings

6.2 Ring homomorphisms

 

3, 5-10, 13-15, 23

1, 2, 4, 6, 15, 17

 

Apr 6

 

 

6.3 Characteristic

6.4 Maximal ideals

 

1-3, 8, 9,  10, 13

1, 5, 9-11, 13, 19, 21-23

 

Apr 13

 

      Test #3: Tuesday

8.1 Polynomials over a ring

8.2 Polynomial Divisibility
 

3, 5, 6, 7, 8, 9, 11

1-4, 21

 

Apr 20

 

 

8.3 Factorization in F[x]

8.6 Algebraic extensions

1, 2, 4, 6

2ab, 3, 5, 10, 11ab

Apr 27 

Last day :Apr 29