Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
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
598Pages
This book contains below topics, A First Course in Modular Forms, Springer GUNNING, Introduction to Elliptic Curves and Modular Forms, Elliptic Curves, Booksurge Available on my website MIYAKE, Cours dArithmetique, Presses Univ de France The last.
Author(s): J.S. Milne
134Pages
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
296Pages
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
108Pages
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
191Pages
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
172Pages
This note explains the following topics, Divisibility, Multiplicative functions, Modular arithmetic, Primitive roots, Quadratic residues, Diophantine equations, Quadratic number fields, Chebyshevs theorem.
Author(s): Vahagn Aslanyan
69Pages
This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in the context of cryptography, computation, and deep open research problems. The second part is about elliptic curves, their applications to algorithmic problems, and their connections with problems in number theory.
Author(s): William Stein
NAPages
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
88Pages
