Number theory

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, "e;down-to-earth"e; manner.

This book combines rigorous proofs with commentary on the underlying ideas to provide a rich insight into these mathematical landmarks.

Now the most used texbook for introductory cryptography courses in both mathematics and computer science, the Third Edition builds upon previous editions by offering several new sections, topics, and exercises.

This book arose from a course of lectures given by the first author during the winter term 1977/1978 at the University of Munster (West Germany).

'The book is mainly addressed to the non-expert reader, in that it assumes only a little background in complex analysis and algebraic geometry, but no previous knowledge in transcendental number theory is required.

One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.

This book presents a printed testimony for the fact that George Andrews, one of the world's leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80.

Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras.

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history.

The Journey Ahead At the heart of transcendental number theory lies an intriguing paradox: While essen- tially all numbers are transcendental, establishing the transcendence of a particular number is a monumental task.

Simplified Independence Proofs

A systematic exposition of the basics of period domains.

Forming the basis of a second course in algebraic geometry, this book explains key ideas, each illustrated with abundant examples.

Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

This book comprises five parts.

Applied Dimensional Analysis and Modeling provides the full mathematical background and step-by-step procedures for employing dimensional analyses, along with a wide range of applications to problems in engineering and applied science, such as fluid dynamics, heat flow, electromagnetics, astronomy and economics.

State-of-the-art analytic number theory proceedings.

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures.

The continuation of an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

This book is devoted to algebraic models and their applications.

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics.

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

A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, with exercises and open problems.

Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians.

Curvature and Homology

Covers extensions of Buchberger''s Theory and Algorithm, and promising recent alternatives to Gröbner bases.

Critical Point Theory in Global Analysis and Differential Topology

Praise for the First Edition beautiful and well worth the reading with many exercises and a good bibliography, this book will fascinate both students and teachers.

This textbook is a practical yet in depth guide to cryptography and its principles and practices.

This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including ?

This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics.

This book is an outgrowth of the special term "e;Harmonic Analysis, Representation Theory, and Integral Geometry,"e; held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects.

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed.

The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?

Chord Transformations in Higher-Dimensional Networks proposes an in-depth formal framework for generalized Tonnetze.

Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A.

This book can be seen as a continuation of Equations and Inequalities: El- ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series.

Decompositions of Manifolds

Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals.

An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.

Positive Operators

Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing.

Nolan Wallach's mathematical research is remarkable in both its breadth and depth.

Kernel Functions and Differential Equations