Number theory

"e;About binomial theorems I'm teeming with a lot of news, With many cheerful facts about the square on the hypotenuse.

The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae.

During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs.

The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere.

Problem-solving competitions for mathematically talented sec- ondary school students have burgeoned in recent years.

On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory.

Journey through the world of numbers with the foremost authorities and writers in the field.

On May 16 -20, 1995, approximately 150 mathematicians gathered at the Conference Center of the University of Illinois at Allerton Park for an Inter- national Conference on Analytic Number Theory.

This book of tables includes a reduced representative of each class of.

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

This volume is dedicated to Harvey Cohn, Distinguished Professor Emeritus of Mathematics at City College (CUNY).

Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.

This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University.

A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed.

Most people tend to view number theory as the very paradigm of pure mathematics.

For many years Serge Lang has given talks to undergraduates on selected items in mathematics which could be extracted at a level understandable by students who have had calculus.

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.

NUMBERS AND GEOMETRY is a beautiful and relatively elementary account of a part of mathematics where three main fields--algebra, analysis and geometry--meet.

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.

During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India.

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?

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.

Number theory was once famously labeled the queen of mathematics by Gauss.

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.