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Elsevier

Books in Number theory

  • Handbook of Mathematics

    • 1st Edition
    • L. Kuipers + 1 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examples), Rolle's theorem, and the logarithmic function. The book also discusses extensively the functions of two variables in partial differentiation and multiple integrals. The book then describes the theory of functions, ordinary differential functions, special functions and the topic of sequences and series. The book explains vector analysis (which includes dyads and tensors), the use of numerical analysis, probability statistics, and the Laplace transform theory. Physicists, engineers, chemists, biologists, and statisticians will find this book useful.

  • A Selection of Problems in the Theory of Numbers

    Popular Lectures in Mathematics
    • 1st Edition
    • Waclaw Sierpinski
    • I. N. Sneddon + 1 more
    • English
    A Selection of Problems in the Theory of Numbers focuses on mathematical problems within the boundaries of geometry and arithmetic, including an introduction to prime numbers. This book discusses the conjecture of Goldbach; hypothesis of Gilbreath; decomposition of a natural number into prime factors; simple theorem of Fermat; and Lagrange's theorem. The decomposition of a prime number into the sum of two squares; quadratic residues; Mersenne numbers; solution of equations in prime numbers; and magic squares formed from prime numbers are also elaborated in this text. This publication is a good reference for students majoring in mathematics, specifically on arithmetic and geometry.

  • Enzyme mathematics

    • 1st Edition
    • Volume 10
    • English

  • The geometry of geodesics

    • 1st Edition
    • Volume 6
    • English

  • Fourier analysis and approximation

    • 1st Edition
    • Volume 40
    • English

  • Linear lie groups

    • 1st Edition
    • Volume 35
    • English

  • Entire functions

    • 1st Edition
    • Volume 5
    • English

  • Linear differential equations and function spaces

    • 1st Edition
    • Volume 21
    • English

  • Curvature and homology

    • 1st Edition
    • Volume 11
    • English

  • Geometry of manifolds

    • 1st Edition
    • Volume 15
    • English

  • Projective geometry and projective metrics

    • 1st Edition
    • Volume 3
    • English

  • An Introduction to Nonassociative Algebras

    • 1st Edition
    • Volume 22
    • English

  • Simplified independence proofs

    Boolean valued models of set theory
    • 1st Edition
    • Volume 31
    • English

  • A theory of sets

    • 1st Edition
    • Volume 18
    • English

  • The four-color problem

    • 1st Edition
    • Volume 27
    • English

  • Markov processes and potential theory

    • 1st Edition
    • Volume 29
    • English

  • Kernel functions and differential equations

    • 1st Edition
    • Volume 4
    • English

  • Differential forms in mathematical physics

    • 1st Edition
    • Volume 3
    • English

  • Theory of extremal problems

    • 1st Edition
    • Volume 6
    • English

  • Fundamentals of the theory of operator algebras. V4

    Special topics--advanced theory, an exercise approach
    • 1st Edition
    • Volume 100D
    • English

  • Stream Ciphers and Number Theory

    • 1st Edition
    • Volume 66
    • Thomas W. Cusick + 2 more
    • English
    This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields.

  • Quantum Mechanics in Hilbert Space

    • 1st Edition
    • Volume 41
    • English

  • Elementary Number Theory with Applications, Student Solutions Manual

    • 1st Edition
    • Thomas Koshy
    • English
    This is a student solutions manual for Elementary Number Theory with Applications 1st edition by Thomas Koshy (2002). Note that the textbook itself is not included in this purchase. From the back cover of the textbook: Modern technology has brought a new dimension to the power of number theory: constant practical use. Once considered the purest of pure mathematics, number theory has become an essential tool in the rapid development of technology in a number of areas, including art, coding theory, cryptology, and computer science. The range of fascinating applications confirms the boundlessness of human ingenuity and creativity. Elementary Number Theory captures the author's fascination for the subject: its beauty, elegance, and historical development, and the opportunities number theory provides for experimentation, exploration, and, of course, its marvelous applications.

  • Codes on Euclidean Spheres

    • 1st Edition
    • Volume 63
    • T. Ericson + 1 more
    • English
    Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to number theory, geometry, combinatorial theory, and - of course - to algebraic coding theory. The connections to physics occur within areas like crystallography and nuclear physics. In engineering spherical codes are of central importance in connection with error-control in communication systems. In that context the use of spherical codes is often referred to as "coded modulation." The book offers a first complete treatment of the mathematical theory of codes on Euclidean spheres. Many new results are published here for the first time. Engineering applications are emphasized throughout the text. The theory is illustrated by many examples. The book also contains an extensive table of best known spherical codes in dimensions 3-24, including exact constructions.

  • Stream Ciphers and Number Theory

    • 1st Edition
    • Volume 55
    • T.W. Cusick + 2 more
    • English
    This book is almost entirely concerned with stream ciphers, concentrating on a particular mathematical model for such ciphers which are called additive natural stream ciphers. These ciphers use a natural sequence generator to produce a periodic keystream. Full definitions of these concepts are given in Chapter 2.This book focuses on keystream sequences which can be analysed using number theory. It turns out that a great deal of information can be deducted about the cryptographic properties of many classes of sequences by applying the terminology and theorems of number theory. These connections can be explicitly made by describing three kinds of bridges between stream ciphering problems and number theory problems. A detailed summary of these ideas is given in the introductory Chapter 1.Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

  • Numbers, Sequences and Series

    • 1st Edition
    • Keith Hirst
    • English
    Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite processes involving sequences and series of numbers, including power series. The book also has worked examples throughout and includes some suggestions for self-study projects. In addition there are tutorial problems aimed at stimulating group work and discussion.

  • Algebraic Groups and Number Theory

    • 1st Edition
    • Volume 139
    • Vladimir Platonov + 2 more
    • English
    This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.

  • Real Reductive Groups II

    • 1st Edition
    • Volume 132II
    • English

  • A First Course in Rational Continuum Mechanics V1

    • 2nd Edition
    • Volume 71I
    • English

  • Large Deviations

    • 1st Edition
    • Volume 137
    • English
    The first four chapters of this volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).

  • Initial-Boundary Value Problems and the Navier-Stokes Equations

    • 1st Edition
    • Volume 136
    • English

  • Infinite Crossed Products

    • 1st Edition
    • Volume 135
    • English

  • General Theory of Markov Processes

    • 1st Edition
    • Volume 133
    • English

  • Ring Theory V2

    • 1st Edition
    • Volume 127II
    • English

  • Ring Theory V1

    • 1st Edition
    • Volume 127I
    • English

  • Elementary Theory of Numbers

    Second English Edition (edited by A. Schinzel)
    • 1st Edition
    • Volume 31
    • W. Sierpinski
    • English
    Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian integers.

  • Geometry of Numbers

    • 2nd Edition
    • Volume 37
    • C.G. Lekkerkerker + 1 more
    • English
    This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definite advantage of showing clearly where recent progress has taken place and in what areas interesting results may be expected in the future.

  • Leonardo Pisano (Fibonacci)

    The Book of Squares
    • 1st Edition
    • L. E. Sigler
    • English
    The Book of Squares by Fibonacci is a gem in the mathematical literature and one of the most important mathematical treatises written in the Middle Ages. It is a collection of theorems on indeterminate analysis and equations of second degree which yield, among other results, a solution to a problem proposed by Master John of Palermo to Leonardo at the Court of Frederick II. The book was dedicated and presented to the Emperor at Pisa in 1225. Dating back to the 13th century the book exhibits the early and continued fascination of men with our number system and the relationship among numbers with special properties such as prime numbers, squares, and odd numbers. The faithful translation into modern English and the commentary by the translator make this book accessible to professional mathematicians and amateurs who have always been intrigued by the lure of our number system.

  • Decompositions of Manifolds

    • 1st Edition
    • Volume 124
    • English

  • Real-variable Methods in Harmonic Analysis

    • 1st Edition
    • Volume 123
    • English

  • Nonstandard Methods in Stochastic Analysis and Mathematical Physics

    • 1st Edition
    • Volume 122
    • English

  • Fundamentals of the Theory of Operator Algebras. V2

    Advanced Theory
    • 1st Edition
    • Volume 100II
    • English

  • A Theory of Sets

    • 2nd Edition
    • Volume 108
    • English
    This book provides graduate students and professional mathematicians with a formal unified treatment of logic and set theory. The formalization can be used without change to build just about any mathematical structure on some suitable foundation of definitions and axioms. In addition to most of the topics considered standard fare for set theory several special ones are treated. This book will be found useful as a text for a substantial one-semester course in set theory and that the student will find continuing use for the formal and highly flexible language

  • Number Theory

    • 1st Edition
    • Volume 20
    • English
    This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.

  • Complex Cobordism and Stable Homotopy Groups of Spheres

    • 1st Edition
    • Volume 121
    • English

  • An Introduction to Differentiable Manifolds and Riemannian Geometry

    • 2nd Edition
    • Volume 120
    • English

  • Positive Operators

    • 1st Edition
    • Volume 119
    • English

  • Theory of Codes

    • 1st Edition
    • Volume 117
    • English

  • Differential Manifolds and Theoretical Physics

    • 1st Edition
    • Volume 116
    • English

  • Differential Algebraic Groups

    • 1st Edition
    • Volume 114
    • English