Number theory

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.

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.

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.

Children's Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods.

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

Let N be the set of nonnegative integers.

Designed for mathematics majors and other students who intend to teach mathematics at the secondary school level, College Geometry: A Unified Development unifies the three classical geometries within an axiomatic framework.

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.

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 carefully prepared manuscript presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings.

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.

Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.

Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation.

First developed in the early 1980s by Lenstra, Lenstra, and Lovasz, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients.

Master the tools of MATLAB through hands-on examplesShows How to Solve Math Problems Using MATLABThe mathematical software MATLAB integrates computation, visualization, and programming to produce a powerful tool for a number of different tasks in mathematics.

The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature.

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory.

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications.