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Books in Number theory

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Handbook of Mathematics

  • 1st Edition
  • July 10, 2014
  • L. Kuipers + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 4 9 2 4 - 0
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

  • 1st Edition
  • May 16, 2014
  • Waclaw Sierpinski
  • I. N. Sneddon + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 5 1 4 6 - 5
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
  • October 10, 2011
  • Jean Pierre Kernevez
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 5 3 1 - 6

Theory of extremal problems

  • 1st Edition
  • Volume 6
  • June 15, 2009
  • A.D. Ioffe + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 5 2 7 - 9

Stream Ciphers and Number Theory

  • 1st Edition
  • Volume 66
  • February 17, 2004
  • Thomas W. Cusick + 2 more
  • English
  • Hardback
    9 7 8 - 0 - 4 4 4 - 5 1 6 3 1 - 2
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 4 1 8 3 - 9
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.

Codes on Euclidean Spheres

  • 1st Edition
  • Volume 63
  • April 27, 2001
  • T. Ericson + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 0 2 1 6 - 8
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
  • April 20, 1998
  • T.W. Cusick + 2 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 4 1 8 4 - 6
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
  • December 8, 1994
  • Keith Hirst
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 2 8 5 8 - 6
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.