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 
39 odd, 17, 20, 21,
24, 25, 26, 40 2abc, 3cd, 10, 21, 33, 34 
Feb 1 
2.5 Congruences 2.6 Congruence classes 
115 odd, 27, 28 1abcd, 2ab, 3abd, 4abc, 5abg, 6ac, 7ac, 8bde, 16, 18, 2023 

Feb 8 
1.6 Matrices 1.4 Binary operations 
3, 912, 14, 16, 30, 31 1abcd, 2abcd, 36, 78,
1213 

Feb 15 
No class : Mon, Feb 15 
3.1 Groups 3.2 Properties 
17, 1115, 17, 20, 21,
23, 25, 28, 29 16, 1115, 17, 1920 
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 
Mar 1 

3.5 Isomorphisms 3.6 Homomorphisms 
14, 7, 8, 10, 12, 15, 24, 26 15, 8, 9, 11, 1518 
Mar 8 
4.1 Permutation groups 4.4 Cosets 
110abc, 14 3, 7, 8, 12, 19, 2022, 24 

Mar 15 
Test # 2: Thursday 
4.5 Normal subgroups 4.6 Quotient groups 
1c, 32, 2, 4, 6, 22, 25,
2930, 33 3, 7, 1819, 21, 30, 34, 37 
Mar 2228 
Spring Break 
Spring Break 
Spring Break 
Mar 29 
Last day to drop: Mar 29 
4.7 Direct sums 5.1 Rings 
1, 3, 7, 1617, 19 1ab, 2abcdf, 7, 8, 10, 14ac, 16, 2325, 27, 30, 39, 4748 
Apr 5 

5.2 Integral domains, fields 6.1 Ideals and quotient rings 
1abeg, 2, 8, 11, 1516, 18, 21, 23 1, 34, 68, 1115, 19acd, 2021, 2627, 31 
Apr 12 

6.2 Ring homomorphisms 6.3 Characteristic 
1, 3, 6, 7, 10, 12, 14, 2122, 24, 25a 14, 8, 9, 10, 14, 16, 18, 20 
Apr 19 
Test #3: Tuesday 
6.4 Maximal ideals 8.1 Polynomials over a
ring 
15, 911, 1315, 19, 2125,
2728 3, 5 7, 1012, 14, 1618 
Apr 26 

8.2 Polynomial
Divisibility 8.3 Factorization in F[x] 
14, 21, 3334 1, 2, 5, 6 
May 2 
Last day – May 3 

