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Chapter B Hints and Solutions to Selected Exercises

Chapter 1 Preliminaries

Section 1.3 Exercises

Chapter 2 The Integers

Section 2.3 Exercises

2.3.17 Fibonacci Numbers

Chapter 3 Groups

Section 3.4 Exercises

Chapter 4 Cyclic Groups

Section 4.4 Exercises

Chapter 5 Permutation Groups

Section 5.3 Exercises

Chapter 6 Cosets and Lagrange's Theorem

Section 6.4 Exercises

Chapter 7 Introduction to Cryptography

Section 7.3 Exercises

Chapter 8 Algebraic Coding Theory

Section 8.5 Exercises

Chapter 9 Isomorphisms

Section 9.3 Exercises

Chapter 10 Normal Subgroups and Factor Groups

Section 10.3 Exercises

Chapter 11 Homomorphisms

Section 11.3 Exercises

Chapter 12 Matrix Groups and Symmetry

Section 12.3 Exercises

Chapter 13 The Structure of Groups

Section 13.3 Exercises

Chapter 14 Group Actions

Section 14.4 Exercises

Chapter 15 The Sylow Theorems

Section 15.3 Exercises

Chapter 16 Rings

Section 16.6 Exercises

Chapter 17 Polynomials

Section 17.4 Exercises

17.4.20 Cyclotomic Polynomials

Chapter 18 Integral Domains

Section 18.3 Exercises

Chapter 19 Lattices and Boolean Algebras

Section 19.4 Exercises

Chapter 20 Vector Spaces

Section 20.4 Exercises

20.4.15 Linear Transformations
20.4.17 Direct Sums

Chapter 21 Fields

Section 21.4 Exercises

Chapter 22 Finite Fields

Section 22.3 Exercises

22.3.24 Wilson's Theorem

Chapter 23 Galois Theory

Section 23.4 Exercises