Table of contents
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2
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4
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Chapter 1. Arithmetic
- Divisors and multiples
- Euclid's algorithm
- Linear diophantine equations
- Prime numbers
- Factorization
- Exercises
- Summary of Chapter 1
Chapter 2. Modular arithmetic
- Arithmetic modulo n
- Linear congruences
- The a-ary number system
- The RSA cryptosystem
- Radar detection
- Exercises
- Summary of Chapter 2
Chapter 3. Polynomials
- The notion of a polynomial
- Polynomial division
- Leading term and degree
- Division with remainder
- Gcd and lcm
- Euclid's algorithm
- Characterization of the gcd
- Polynomial functions
- Factorization
- Shift registers
- Exercises
- Summary of Chapter 3
Chapter 4. Arithmetic modulo polynomials
- Congruence modulo a polynomial
- The residue class ring
- Construction
- Arithmetical rules
- Constants modulo a polynomial
- Class rings as vector spaces
- Projection onto the residue class ring
- Two special cases
- Inverses and fields
- Finite fields
- Error-correcting codes
- Exercises
- Summary of Chapter 4
Chapter 6. Monoids and groups
- Binary operations
- Monoids
- Invertibility in monoids
- Groups
- Subgroups
- Subgroups generated by subsets
- Intersections
- Some special subgroups
- Morphisms
- Kernel and image
- Cyclic groups
- Cosets
- Exercises
- Summary of Chapter 6
Chapter 7. Rings and fields
- The structure ring
- Constructions with rings
- Domains and fields
- Fields
- Ideals
- Residue class rings
- Finite fields
- Exercises
- Summary of Chapter 7