Number theory

The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916.

This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra.

A fascinating journey into the mind-bending world of prime numbersCicadas of the genus Magicicada appear once every 7, 13, or 17 years.

Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications.

Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications.

The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras.

The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject.

The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject.

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover.

Pell's Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years.

This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations.

Number Theory is more than a comprehensive treatment of the subject.

This is a textbook on Galois theory.

Several years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Hecke operators, and related zeta functions.

Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics.

The Primality Testing Problem (PTP) has now proved to be solvable in deterministic polynomial-time (P) by the AKS (Agrawal-Kayal-Saxena) algorithm, whereas the Integer Factorization Problem (IFP) still remains unsolvable in (P).

ThecreationofpublickeycryptographybyDi?

Over the past two decades, the once small local Colorado Springs Mathematics Olympiad, founded by the author himself, has now become an annual state-wide competition, hosting over one-thousand high school contenders each year.

Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory.

From Math Reviews: This is Volume II of a two-volume introductory text in classical algebra.

A book on any mathematical subject above textbook level is not of much value unless it contains new ideas and new perspectives.

This book is a collection of about 500 problems in analytic number theory with the singular purpose of training the beginning graduate student in some of its significant techniques.

Collecting papers never before published in book form, this volume presents an analysis of the Riemann Hypothesis as well as connected problems.

Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability.

This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory.

This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area.

The central theme of this book is the solution of Diophantine equations, i.

This book deals with several aspects of what is now called "e;explicit number theory.

RSA is the first workable and practicable public-key cryptographic system, based on the use of large prime numbers.

The world is continuous, but the mind is discrete.

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.

The square root of 2 is a fascinating number - if a little less famous than such mathematical stars as pi, the number e, the golden ratio, or the square root of -1.

In introducing his essays on the study and understanding of nature and e- lution, biologist Stephen J.

Undergraduate courses in mathematics are colnmonly of two types.

Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory.

Prime numbers beckon to the beginner, the basic notion of primality being accessible to a child.

It is often said that mathematics and music go together, and that people with a special aptitude for mathematics often have similar gifts in music.

Intended for graduate courses or for independent study, this book presents the basic theory of fields.

Asking how one does mathematical research is like asking how a composer creates a masterpiece.

This is a small book on algebra where the stress is laid on the structure of ?

Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied.

This book introduces the theory of modular forms with an eye toward the Modularity Theorem:All rational elliptic curves arise from modular forms.

He [Kronecker] was, in fact, attempting to describe and to initiate a new branch of mathematics, which would contain both number theory and alge- braic geometry as special cases.

This volume contains papers by invited speakers of the symposium "e;Zeta Functions, Topology and Quantum Physics"e; held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003.

Sphere Packings is one of the most attractive and challenging subjects in mathematics.

Dear Friends of Numbers: This little book is for you.

Analytic Number Theory presents some of the central topics in number theory in a simple and concise fashion.

Elementary Methods in Number Theory begins with "e;a first course in number theory"e; for students with no previous knowledge of the subject.

Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields.

This book grew out of a set of notes for a series of lectures I orginally gave at the Center for Communications Research and then at Princeton University.