A Computational Introduction to Number Theory and Algebra

Abstract

Chapter 1: Basic properties of the integers. Chapter 2: Congruences. Chapter 3: Computing with large integers. Chapter 4: Euclid’s algorithm. Chapter 5: The distribution of primes. Chapter 6: Abelian groups. Chapter 7: Rings. Chapter 8: Finite and discrete probability distributions. Chapter 9: Probabilistic algorithms. Chapter 10: Probabilistic primality testing. Chapter 11: Finding generators and discrete logarithms in Z∗p. Chapter 12: Quadratic reciprocity and computing modular square roots. Chapter 13: Modules and vector spaces. Chapter 14: Matrices. Chapter 15: Subexponential-time discrete logarithms and factoring. Chapter 16: More rings. Chapter 17: Polynomial arithmetic and applications. Chapter 18: Finite Fields. Chapter 19: Linearly generated sequences and applications. Chapter 20: Algorithms for finite fields. Chapter 21: Deterministic primality testing.