This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon — the functional equation of the associated zeta-function. It starts from the basics be
This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka’s paper is a continuation of his earlier paper published in the
"Preface This book is a result of my teaching a Masters-level course with the same name for five years in the Indian Institute of Technology Kharagpur. The course was attended mostly by MTech and fina
Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps
Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate student
This introductory book, which grew out of lectures given at the Mathematics Institute of Wurzburg University, proposes a combination of coding theory and number theory. Chapter I gives a standard cour
This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be id
Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, e
This second edition is a solid introduction to classical and modern number theory and its applications in computer science. It introduces basic concepts, results and methods, and discusses their appli
Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first
Dependence with complete connections is a more general type of stochastic process than the well-known Markovian dependence, accounting for a complete history of a stochastic evolution. This book is an authoritative survey of knowledge of the subject, dealing with the basic theoretical understanding and also with applications. These arise in a variety of situations as diverse as stochastic models of learning, branching processes in random environments, continued fractions and dynamical systems. Thus the book will appeal to mathematicians working in probability theory, ergodic theory and number theory, as well as applied mathematicians, engineers, biologists and social scientists interested in applications of stochastic methods.
This unified account of various aspects of a powerful classical method, easy to understand in its simplest forms, is illustrated by applications in several areas of number theory. As well as including diophantine approximation and transcendence, which were mainly responsible for its invention, the author places the method in a broader context by exploring its application in other areas, such as exponential sums and counting problems in both finite fields and the field of rationals. Throughout the book, the method is explained in a 'molecular' fashion, where key ideas are introduced independently. Each application is the most elementary significant example of its kind and appears with detailed references to subsequent developments, making it accessible to advanced undergraduates as well as postgraduate students in number theory or related areas. It provides over 700 exercises both guiding and challenging, while the broad array of applications should interest professionals in fields from
A revised and updated translation of a work originally published in Portuguese in 1997. It introduces the algorithmic aspects of number theory and its applications to the study of codes, and of code-b
Number theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptogr
Explicit Brauer Induction is an important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this 1994 book it is derived algebraically, following a method of R. Boltje - thereby making the technique, previously topological, accessible to algebraists. Once developed, the technique is used, by way of illustration, to re-prove some important known results in new ways and to settle some outstanding problems. As with Brauer's original result, the canonical formula can be expected to have numerous applications and this book is designed to introduce research algebraists to its possibilities. For example, the technique gives an improved construction of the Oliver–Taylor group-ring logarithm, which enables the author to study more effectively algebraic and number-theoretic questions connected with class-groups of rings.
