Preface

  1. Arithmetic

    1. Divisors and multiples
    2. Euclid's algorithm
    3. Linear diophantine equations
    4. Prime numbers
    5. Factorization
    6. Exercises
    7. Summary of Chapter 1


  2. Modular arithmetic

    1. Arithmetic modulo n
    2. Linear congruences
    3. The a-ary number system
    4. The RSA cryptosystem
    5. Radar detection
    6. Exercises
    7. Summary of Chapter 2


  3. Polynomials

    1. The notion of a polynomial
    2. Division of polynomials
    3. Polynomial functions
    4. Factorization
    5. Shift registers
    6. Exercises
    7. Summary of Chapter 3


  4. Modular arithmetic for polynomials

    1. Congruence modulo a polynomial
    2. The residue class ring
    3. Two special cases
    4. Inverses and fields
    5. Finite fields
    6. Error correcting codes
    7. Exercises
    8. Summary of Chapter 4


  5. Permutations

    1. Symmetric groups
    2. Cycles
    3. Alternernating groups
    4. Exercises
    5. Summary of Chapter 5


  6. Monoids and groups

    1. Binary operations
    2. Monoids
    3. Invertibility in monoids
    4. Groups
    5. Cyclic groups
    6. Cosets
    7. Exercises
    8. Summary of Chapter 6


  7. Rings and fields

    1. The structure ring
    2. Constructions with rings
    3. Domains and fields
    4. Fields
    5. Ideals
    6. Quotient rings
    7. Finite fields
    8. Exercises
    9. Summary of Chapter 7


  8. Permutation groups

    1. Permutation groups
    2. Orbits
    3. Order
    4. Automorphisms
    5. Quotient groups
    6. Small groups
    7. Exercises
    8. Summary of Chapter 8