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Number Theory A Contemporary Introduction
This note describes the following topics: Pythagorean Triples, Quadratic Rings, Quadratic Reciprocity, The Mordell Equation, The Pell Equation, Arithmetic Functions, Asymptotics of Arithmetic Functions, The Primes: Infinitude, Density and Substance, The Prime Number Theorem and the Riemann Hypothesis, The Gauss Circle Problem and the Lattice Point Enumerator, Minkowski’s Convex Body Theorem, The Chevalley-Warning Theorem, Dirichlet’s Theorem on Primes in Arithmetic Progressions, Rational Quadratic Forms and the Local-Global Principle.
Author(s): Pete L. Clark
272 Pages 
A Computational Introduction to Number Theory and Algebra
This note contains below topics, Title, Preliminaries, Basic properties of the integers, Congruences, Computing with large integers, Euclid s algorithm, The distribution of primes, Abelian groups, Rings, Finite and discrete probability distributions, Probabilistic algorithms, Probabilistic primality testing, Finding generators and discrete logarithms in Zp, Quadratic reciprocity and computing modular square roots, Modules and vector spaces, Matrices, Subexponentialtime discrete logarithms and factoring, More rings.
Author(s): Victor Shoup
598 Pages
This book contains below topics, Local Class Field Theory LubinTate Theory, The Cohomology of Groups, III Local Class Field Theory Cohomology, Brauer Groups, V Global Class Field Theory Statements, VI LSeries and the Density of Primes, VII Global Class Field Theory Proofs, VIII Complements, A Exercises, B Solutions to Exercises, C Sources for the history of class field theory.
Author(s): J.S. Milne
296 Pages
This note contains below topics, Analytic Theory, The Arithmetic Theory, III CMMotives, Applications, A Additional Notes Solutions to the Exercises, B Summary, Index of definitions.
Author(s): J.S. Milne
108 Pages
Lectures notes on number theory for computer science
This brief collects notes on elementary and medium level number theory, mainly for computer science students. It can support a discrete mathematics course, a foundations course, or a cryptography course. The opening chapters cover divisibility, primes, modular arithmetic, and Eulers totient function.
Author(s): Alexandros V. Gerbessiotis
191 Pages
Elementary Number Theory Primes Congruences and Secrets
This book contains below topics, Prime Numbers, The Ring of Integers Modulo n, Public key Cryptography, Quadratic Reciprocity, Continued Fractions, Elliptic Curves.
Author(s): William Stein
172 Pages
Robert Daniel Carmichael March 1, 1879 May 2, 1967 was a leading American mathematician.The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows, The five chapters are devoted to the development of those elements which are essential to any study of the subject. The sixth and last chapter is intended to give the reader some indication of the direction of further study with a brief account of the nature of the material in each of the topics suggested.
Author(s): R. D. Carmichael
88 Pages