Number theory

Focusing Your Attention The purpose of this book is Cat least) twofold.

Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory.

This book is an outgrowth of the Workshop on "e;Regulators in Analysis, Geom- etry and Number Theory"e; held at the Edmund Landau Center for Research in Mathematical Analysis of The Hebrew University of Jerusalem in 1996.

This book is intended as a text for a problem-solving course at the first- or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training.

This is an introduction to diophantine geometry at the advanced graduate level.

The present book is rare, even unique of its kind, at least among mathematics texts published in Russian.

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems.

Neal Koblitz was a student of Nicholas M.

Srinivasa Ramanujan is, arguably, the greatest mathematicianthat India has produced.

Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others.

This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory.

The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e.

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "e;the theory of elliptic curves is rich, varied, and amazingly vast,"e; and as a consequence, "e;many important topics had to be omitted.

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes.

In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem.

A book about numbers sounds rather dull.

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years.

This modem introduction to the foundations of logic, mathematics, and computer science answers frequent questions that mysteriously remain mostly unanswered in other texts: * Why is the truth table for the logical implication so unintuitive?

Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties.

Quantum mechanics and quantum field theory are highly successful physical theo- ries that have numerous practical applications.

This book delves into the mathematical theory of causal functions over discrete time, offering a fresh perspective on causality beyond its philosophical roots.

This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory.

Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success.

This book, which is based on Polya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics.

This volume marks the 20th anniversary of the New York Number Theory Sem- inar (NYNTS).

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The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years.

The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations.

This books gives an introduction to discrete mathematics for beginning undergraduates.

Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques.

Cryptography is a key technology in electronic key systems.

Alladi Ramakrishnan (1923-2008) was an eminent scientist who had a wide range of research interests in theoretical and mathematical physics.

From the reviews of the second edition:"e;This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations.

This book can be divided into two parts.

The book provides a self-contained introduction to classical Number Theory.

Let N be the set of nonnegative integers.

From Zero to Infinity is a combination of number lore, number history, and sparkling descriptions of the simply stated but exceedingly difficult problems posed by the most ordinary numbers that first appeared in 1955 and has been kept in print continuously ever since.

Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields.

New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them.

This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem.

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem.

This volume comprises an imaginative collection of pieces created in tribute to Martin Gardner.

Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory.

The concept of factorization, familiar in the ordinary system of whole numbers that can be written as a unique product of prime numbers, plays a central role in modern mathematics and its applications.

This book is based on a course given by the author at Harvard University in the fall semester of 1988.

This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries.

This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.

Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis.

Join the Cryptokids as they apply basic mathematics to make and break secret codes.