AATA Hints and Answers to Selected Exercises
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Solutions B Hints and Answers to Selected Exercises
Section 1.2 Sets and Functions
Exercises 1.2.4 Practice Problems
1.2.4.1.
1.2.4.2.
1.2.4.3.
1.2.4.4.
1.2.4.5.
Exercises 1.2.5 Collected Homework
1.2.5.2.
Section 1.3 Equivalence Relations and Partitions
Exercises Practice Problems
1.3.1.
1.3.2.
1.3.3.
Exercises 1.5 Additional Exercises
1.5.1.
1.5.5.
1.5.9.
1.5.13.
1.5.16.
1.5.17.
1.5.19.
1.5.21.
1.5.22.
1.5.24.
1.5.26.
1.5.28.
1.5.33.
1.5.36.
1.5.40. Fibonacci Numbers.
Section 2.2 Definitions and Examples
Exercises 2.2.3 Practice Problems
2.2.3.1.
2.2.3.2.
2.2.3.3.
2.2.3.6.
2.2.3.x1.
2.2.3.x4.
Exercises 2.2.4 Collected Homework
2.2.4.7.
Section 2.3 Basic Properties of Groups
Exercises Collected Homework
2.3.1.
2.3.2.
Exercises 2.4.4 Practice Problems
2.4.4.1.
2.4.4.2.
2.4.4.3.
2.4.4.5.
2.4.4.6.
Exercises 2.4.5 Collected Homework
2.4.5.C2.
Section 2.6 Permutation Groups
Exercises 2.6.7 Practice Problems
2.6.7.1.
2.6.7.2.
2.6.7.3.
2.6.7.5.
2.6.7.6.
2.6.7.7.
2.6.7.8.
2.6.7.9.
2.6.7.10.
Exercises 2.7 Additional Exercises
2.7.2.
2.7.9.
2.7.10.
2.7.11.
2.7.12.
2.7.19.
2.7.25.
2.7.29.
2.7.35.
2.7.40.
2.7.43.
2.7.49.
2.7.50.
2.7.51.
2.7.52.
2.7.58.
2.7.59.
2.7.66.
2.7.71.
2.7.75.
2.7.81.
2.7.91.
2.7.92.
2.7.98.
2.7.106.
2.7.111.
Chapter 3 Cosets and Factor Groups
Exercises Practice Problems
3.1.5.
3.1.12.
Exercises Collected Homework
3.1.1.
Section 3.2 Factor Groups and Normal Subgroups
Exercises 3.2.4 Practice Problems
3.2.4.4.
Exercises 3.2.5 Collected Homework
3.2.5.C2.
Exercises 3.3 Exercises
3.3.1.
3.3.2.
3.3.4.
3.3.13.
3.3.16.
3.3.18.
3.3.25.
3.3.28.
3.3.29.
3.3.31.
Chapter 4 Isomorphisms and Homomorphisms
Section 4.1 Definition and Examples
Exercises 4.1.4 Practice Problems
4.1.4.4.
4.1.4.5.
Exercises 4.1.5 Collected Homework
4.1.5.C1.
4.1.5.C2.
Section 4.2 Group Homomorphisms
Exercises Collected Homework
4.2.C1.
Section 4.3 The Isomorphism Theorems
Exercises Practice Problems
4.3.1.
4.3.3.
Exercises 4.4 Additional Exercises
4.4.1.
4.4.2.
4.4.3.
4.4.6.
4.4.8.
4.4.11.
4.4.16.
4.4.19.
4.4.20.
4.4.25.
4.4.27.
4.4.38.
4.4.45.
4.4.57.
4.4.59.
4.4.60.
4.4.64.
4.4.72.
Exercises Practice Problems
5.1.2.
Section 5.2 Integral Domains and Fields
Exercises Collected Homework
5.2.C2.
Section 5.3 Ring Homomorphisms and Ideals
Exercises Practice Problems
5.3.4.
5.3.5.
Exercises Collected Homework
5.3.C1.
Exercises 5.6 Additional Exercises
5.6.1.
5.6.3.
5.6.4.
5.6.7.
5.6.8.
5.6.13.
5.6.16.
5.6.18.
5.6.26.
5.6.28.
5.6.33.
5.6.37.
Exercises 6.1.5 Exercises
6.1.5.4.
6.1.5.8.
6.1.5.12.
6.1.5.14.
Section 6.3 The Division Algorithm
Exercises Practice Problems
6.3.4.
6.3.9.
Section 6.4 Irreducible Polynomials
Exercises 6.4.5 Collected Homework
6.4.5.2.
Section 6.5 Factoring over \(\C\) and \(\R\)
Exercises 6.5.3 Practice Problems
6.5.3.1.
6.5.3.2.
6.5.3.3.
6.5.3.4.
Exercises 6.5.4 Collected Homework
6.5.4.1.
Exercises 6.6 Additional Exercises
6.6.2.
6.6.3.
6.6.5.
6.6.7.
6.6.8.
6.6.10.
6.6.13.
6.6.14.
6.6.16.
6.6.20. Cyclotomic Polynomials.
6.6.26.
Chapter 7 Integral Domains
Exercises 7.4 Exercises
7.4.1.
7.4.2.
7.4.4.
7.4.9.
7.4.15.
7.4.16.
Section 8.1 Geometric Constructions
Exercises 8.1.4 Collected Homework
8.1.4.1.
Section 8.3 Extension Fields
Exercises 8.3.3 Collected Homework
8.3.3.1.
(a)
Section 8.4 Algebraic Elements
Exercises Collected Homework
8.4.1.
(b)
Section 8.7 What's Not Constructible
Exercises 8.7.4 Collected Homework
8.7.4.2.
Section 9.1 Splitting Fields
Exercises 9.1.2 Collected Homework
9.1.2.1.
(a)
(c)
Section 9.2 Field Automorphisms
Exercises Collected Homework
9.2.1.
(a)
Part III More Group Theory
Chapter 10 Some of the Structure of Groups
Section 10.1 Isomorphisms and Cayley's Theorem
Exercises 10.1.4 Collected Homework
10.1.4.1.
Section 10.2 Permutation Groups
Exercises 10.2.6 Practice Problems
10.2.6.1.
10.2.6.2.
10.2.6.3.
10.2.6.5.
10.2.6.6.
10.2.6.7.
10.2.6.8.
10.2.6.9.
10.2.6.10.
Chapter 11 More of the Structure of Groups
Section 11.1 Cyclic Groups and Orders of Elements
Exercises 11.1.5 Collected Homework
11.1.5.1.
(b)
Chapter 12 Introduction to Cryptography
Exercises 12.5 Exercises
12.5.1.
12.5.3.
12.5.4.
12.5.7.
12.5.9.
12.5.10.
Section 13.3 Burnside's Counting Theorem
Exercises 13.3.3 Collected Homework
13.3.3.2.
Exercises 13.4 Exercises
13.4.1.
13.4.2.
13.4.3.
13.4.6.
13.4.8.
13.4.11.
13.4.15.
13.4.17.
13.4.22.
Chapter 14 The Sylow Theorems
Exercises 14.4 Exercises
14.4.1.
14.4.2.
14.4.5.
14.4.8.
14.4.10.
14.4.17.
14.4.23.
14.4.26.
Part IV Additional Topics
Chapter 15 Matrix Groups and Symmetry
Exercises 15.4 Exercises
15.4.1.
15.4.3.
15.4.5.
15.4.7.
15.4.10.
15.4.13.
15.4.17.
Chapter 16 Algebraic Coding Theory
Exercises 16.6 Exercises
16.6.2.
16.6.3.
16.6.4.
16.6.6.
16.6.7.
16.6.9.
16.6.11.
16.6.12.
16.6.15.
16.6.19.
16.6.23.
Exercises 17.4 Exercises
17.4.1.
17.4.4.
17.4.5.
17.4.7.
17.4.8.
17.4.11.
17.4.12.
17.4.17.
17.4.18.
17.4.24. Wilson's Theorem.
Chapter 18 Lattices and Boolean Algebras
Exercises 18.5 Exercises
18.5.2.
18.5.4.
18.5.5.
18.5.6.
18.5.8.
18.5.10.
18.5.14.
18.5.18.
18.5.20.
