MTH 316 Calendar and Syllabus  Spring 2007

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 22

Classes start Mon

 

1.1 Sets
1.2 Mappings

1.5 Permutations and inverses
1.7 Relations 

1-3, 4ace, 5acegi, 9a, 13, 33
1ab, 2, 3bc, 4abcde, 6, 11, 13, 15ab
(1-2)abcdef, 3, 6-10
1, 2abcd, 3, 4, 10, 23

Jan 29

 

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 5

 

2.5 Congruences  
2.6 Congruence classes 
 

1-15 odd
1abcd, 2ab, 3abd, 4abc, 5abg, 6ac, 8ac, 16, 22-23

Feb 12

  

1.6 Matrices

1.4 Binary operations
3.1 Groups

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 19

Monday no class
 

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 26

 

3.4 Isomorphisms
3.5 Homomorphisms 
4.1 Permutation groups 

1-4, 7, 10, 13, 23
1, 2, 3, 7, 11, 12-14, 17
(1-11)abc

Mar 5

 

4.4 Normal subgroups
4.5 Quotient groups 
4.6 Direct sums 

3-6, 32, 41, 42, 46
3, 4, 19, 30
9-12

Mar 12

  

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 19

Spring Break 

Spring Break

Spring Break

Mar 26

 

5.3 Field of quotients
6.1 Ideals and quotient rings

1, 7, 8, 16
3, 5-10, 13-15, 23

Apr 2

 

6.2 Ring homomorphisms
6.3 Characteristic

1, 2, 4, 6, 15, 17
1-3, 8, 9, 13

Apr 9

 

6.4 Maximal ideals
8.1 Polynomials over a ring

1-3, 5, 9-10, 17, 21-23
3, 5, 6, 13, 14

Apr 16

 

8.2 Polynomial Divisibility 
8.3 Factorization in F[x}

1-4, 21
1, 2, 4, 6

Apr 23

 

8.6 Algebraic extensions

2ab, 3, 5, 10, 11ab

Apr 30

Last day of class Mon