MTH 316 Calendar and Syllabus  Spring 2008

Text: Elements of Modern Algebra, 6th edition by Gilbert & Gilbert.

The following calendar gives a timetable for the course. You should work out all of the problems given below.

Attendance at each class is expected.

Week

Events

Sections

Problems

Jan 21

Classes start Wed Jan 23

1.5 Permutations and inverses

1.7 Relations 

(1-2)abcdefgk, 3, 6-10

1, 2abcd, 3, 4, 10, 23

Jan 28

 

 

2.2 Induction 
2.3 Divisibility 
2.4 Primes, GCDs 

1-10 odd, 27-29
3-9 odd, 17, 31
2abc, 3cd, 7, 26

Feb 4

 

 

2.5 Congruences 

2.6 Congruence classes

1-15 odd

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

Feb 11

  

 

1.6 Matrices

1.4 Binary operations

3.1 Group

1ad, 3, 8, 9-12, 14, 16, 25,  26

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

1-7, 11-13, 21, 23, 25, 28, 29, 33, 42-44, 48, 49, 51

Feb 18


 

3.2 Subgroups

3.3 Cyclic groups

2, 3, 5-9, 12, 17, 18ac, 35


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

Feb 25

 

 

3.4 Isomorphisms

3.5 Homomorphisms 

1-4, 7, 10, 13, 23

1, 2, 3, 7, 11, 12-14, 17

Mar 3

 

 

4.1 Permutation groups

 
4.4 Normal subgroups

1-10 abc

3-6,32,41,42,46

Mar 10

 

  

4.5 Quotient groups

4.6 Direct sums 

3, 4, 19, 30

9-12

Mar 17

Spring Break 

Spring Break

Spring Break

Mar 24

 

 

Last day to drop:

Mar 24

 

5.1 Rings

5.2 Integral domains and fields  
6.1 Ideals and quotient rings

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

3, 5-10, 13-15, 23

Mar 31

 

 

6.2 Ring homomorphisms

6.3 Characteristic

1, 2, 4, 6, 15, 17

1-3, 8, 9, 13

Apr 7

 

 

6.4 Maximal ideals

8.1 Polynomials over a ring

1-3, 5, 9-10, 17, 21-23

3, 5, 6, 13, 14

Apr 14

 

 

8.2 Polynomial Divisibility
 
8.3 Factorization in F[x]

1-4, 21

1, 2, 4, 6

Apr 21

 

 

8.6 Algebraic extensions

2ab, 3, 5, 10, 11ab

Apr 28 

Last day :Apr 29