Number theory

Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level.

Ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) are widely used to model control systems in engineering, natural sciences, and economy.

This is the unique book on cross-fertilisations between stream ciphers and number theory.

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 aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud.

Like the intriguing Fibonacci and Lucas numbers, Catalan numbers are also ubiquitous.

Philosophen und Theologen haben über das Unendliche nachgedacht.

In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry.

This book is dedicated to the common theory creation problems of recognition systems.

Through three editions, Cryptography: Theory and Practice, has been embraced by instructors and students alike.

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry.

Many of the best researchers and writers in discrete mathematics come together in a volume inspired by Ron Graham.

The first contribution covers the theory of finite groups of Lie type, which is an important field of current mathematical research.

This text is intended as an introduction to mathematical proofs for students.

A central problem in differential geometry is to relate algebraic properties of the Riemann curvature tensor to the underlying geometry of the manifold.

The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program.

This book is a concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists.

A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.

This is a modern introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function.

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

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.

Because traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples.

In this book, the author pays tribute to Bernhard Riemann (1826-1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc.

The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great- est common divisor at least three centuries B.

With this translation, the classic monograph Uber die Klassenzahl abelscher Zahlkorper by Helmut Hasse is now available in English for the first time.

The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics.

Timely collection of articles bringing together topics at the forefront of the theory, including the local Langlands programme and automorphic forms.

This volume presents a comprehensive collection of Wang Yuan's original important papers which are not available elsewhere, since the majority of the papers were published in China.

This unique volume presents a fruitful and beautiful mathematical world hidden in Caianiello's neuronic equations, which describe the instantaneous behavior of a model of a brain or thinking machine.

A large number of comprehensive publications has been devoted to the Antarctic, to its plant and animal life.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup.

The book discusses major topics in complex analysis with applications to number theory.

P-adic Analytic Functions describes the definition and properties of p-adic analytic and meromorphic functions in a complete algebraically closed ultrametric field.

Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science.

This book provides a detailed description of a most important unsolved mathematical problem - the Goldbach conjecture.

Approach your problems from the right end It isn't that they can't see the solution.

This book constitutes the refereed post-conference proceedings of the 4th International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2024, held in Szczecin, Poland, during June 24–26, 2024.

A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.

Building on the tradition of an outstanding series of conferences at the University of Illinois at Urbana-Champaign, the organizers attracted an international group of scholars to open the new Millennium with a conference that reviewed the current state of number theory research and pointed to future directions in the field.

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering.

Eine kombinierte Einführung in die Algebra bis zur Galoistheorie und ihren klassischen Anwendungen sowie in die Zahlentheorie: Dabei profitiert die Algebra von den Motivationen und dem reichen Beispielmaterial der Zahlentheorie; letztere gewinnt an Klarheit und Kürze durch Strukturen und Sätze der Algebra.