Weeks | Topics | Sections |
1 | Binary operations | 1.4, 1.5 |
2 | Integers, divisibility, prime factors, greatest common divisor | 2.1-2.4 |
3 | Congruence of integers, congruence classes | 2.5, 2.6 |
4 | Groups, subgroups | 3.1, 3.2 |
5 | Subgroups, cyclic groups | 3.2, 3.3 |
6 | Cyclic groups, isomorphisms | 3.3, 3.4 |
7 | Permutation groups | 4.1. |
8 | Normal subgroups, quotient groups | 4.4*, 4.5** |
9 | Rings | 5.1. |
10 | Ring isomorphisms, integral domains | 5.2, 6.2*** |
11 | Fields, the fields of real and complex numbers | 5.2, 7.1, 7.2 |
12 | Polynomials, divisibility | 8.1, 8.2 |
13 | GCD, factorization | 8.2, 8.3 |
14 | Zeros of a polynomial | 8.4**** |
(*) (4.8), 4.9, 4.17, 4.19 and 4.20 will be skipped.
(**) Only 4.21 and 4.22.
(***) We will cover 6.7 and 6.8 (only in the context of
isomorphisms).
(****) 8.30 - 8.33
will not be covered.
Suggested Problems:
Section 1.4: 1, 2a, 2f, 3, 4, 5, 6, 8, 9, 10e, 10k, 13
Section 1.5: 2a, 2b, 3d, 3e, 3i, 20, 22, 23, 24, 26
Section 2.1: This seciton is optional.
Section 2.3: 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 29
Section 2.4: 2a, 3c, 3j, 4a, 5, 7, 9, 10, 11, 13, 14, 15, 16, 19, 27
Section 2.5: 5, 6,16, 19, 20, 21, 22, 23a, 25, 26, , 27, 28
Section 2.6: 5a, 6e, 8c, 8f, 9, 10c, 16, 18, 22
Section 3.1: 1, 2, 4,5, 6, 7, 11, 15, 17, 23, 28, 31, 33, 45
Section 3.2: 2b, 2c, 3, 5a,6a, 10, 11, 13a, 14b, 17, 23, 24, 28, 35
Section 3.3: 7, 8, 9 a, 9b, 10a, 10b, 12, 14, 15, 18, 23, 24
Section 3.4: 1, 3, 6, 10, 11, 16, 17, 18, 20(a, b), 26, 28.
Section 4.1: 1(a, e, h), 2(a, b, f), 3, 4, 5, 6, 7, 8, 13, 14.
Section 4.4: 5, 6, 7, 8, 25, 26, 27, 30, 32, 35.
Section 4.5: 2, 4, 10, 15, 16.
Section 5.1: 1(a, b), 2(b, c), 5, 7(a, b, e, f), 8(c, d), 9, 10, 12, 16, 19, 21, 22, 24.
Section 5.2: 1(a, b), 2, 3, 5, 6, 8, 9, 10, 11, 12, 15(a, c), 18, 19.
Section 6.2: 1, 2, 3, 7, 8, 10, 12, 15 (Replace "homomorphism" with "isomorphism".), 19.
Section 7.1: 15, 16, 17, 18, 19, 20.
Section 7.2: 1, 4, 7, 11, 12, 13b, 14d, 16, 17, 18, 19, 20.
Section 8.1: 3e, 5, 7, 8, 9, 15 (replace epimorphism with isomorphism).
Section 8.2: 3, 6, 10, 14, 15, 16, 21.
Section 8.3: 1, 2, 3a, 5, 6, 7, 11 (Assume problem 9 to solve 11.).
Section 8.4: 1 (c,e), 2 (a,c), 4, 7, 15, 17a, 18, 19, 20, 21, 23, 24.
Last updated on
15 March 2007.