Number Theory in Science and Communication

Author: Manfred Schroeder
Publisher: Springer Science & Business Media
ISBN: 3540852972
Format: PDF, ePub
Download Now
"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudo primes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvelous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner

Number Theory and Its History

Author: Oystein Ore
Publisher: Courier Corporation
ISBN: 9780486656205
Format: PDF, Kindle
Download Now
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

Computational Number Theory and Modern Cryptography

Author: Song Y. Yan
Publisher: John Wiley & Sons
ISBN: 1118188616
Format: PDF, ePub
Download Now
The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.

Elementary Number Theory Primes Congruences and Secrets

Author: William Stein
Publisher: Springer Science & Business Media
ISBN: 0387855254
Format: PDF, ePub, Mobi
Download Now
This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.

Number Theory and the Periodicity of Matter

Author: Jan C. A. Boeyens
Publisher: Springer Science & Business Media
ISBN: 9781402066603
Format: PDF, ePub, Mobi
Download Now
This book presents a fully scientific account of the use of the golden ratio. It explores the observation that stable nucleides obey a number theory based general law. The discovery described in this book could be of seminal significance, also in other fields where the golden ratio is known to be of fundamental importance.

A Course in Number Theory

Author: H. E. Rose
Publisher: Oxford University Press
ISBN: 9780198523765
Format: PDF, Docs
Download Now
The second edition of this undergraduate textbook is now available in paperback. Covering up-to-date as well as established material, it is the only textbook which deals with all the main areas of number theory, taught in the third year of a mathematics course. Each chapter ends with acollection of problems, and hints and sketch solutions are provided at the end of the book, together with useful tables.

Science Communication in Theory and Practice

Author: S.M. Stocklmayer
Publisher: Springer Science & Business Media
ISBN: 9401006202
Format: PDF, Mobi
Download Now
This book provides an overview of the theory and practice of science communication. It deals with modes of informal communication such as science centres, television programs, and journalism and the research that informs practitioners about the effectiveness of their programs. It aims to meet the needs of those studying science communication and will form a readily accessible source of expertise for communicators.

The Unreasonable Effectiveness of Number Theory

Author: Stefan Andrus Burr
Publisher: American Mathematical Soc.
ISBN: 9780821855010
Format: PDF, ePub, Mobi
Download Now
This book is based on the AMS Short Course, The Unreasonable Effectiveness of Number Theory, held in Orono, Maine, in August 1991. This Short Course provided some views into the great breadth of applications of number theory outside cryptology and highlighted the power and applicability of number-theoretic ideas. Because number theory is one of the most accessible areas of mathematics, this book will appeal to a general mathematical audience as well as to researchers in other areas of science and engineering who wish to learn how number theory is being applied outside of mathematics. All of the chapters are written by leading specialists in number theory and provides excellent introduction to various applications.

A Survey of Scientific Communication Theory

Author: Charles Pavitt
Publisher: Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften
ISBN: 9781433133770
Format: PDF, Mobi
Download Now
This detailed survey of present-day scientific communication theory rejects the outmoded «levels» organizational scheme in favor of a system based on the underlying model and fundamental explanatory principle each theory presupposes. In doing so it shows the fundamental similarities among all communication-relevant contexts. Most theories included in the book are causal in nature, derived from one of three underlying models: message production, message reception, or interactive. A few theories take on a functional form, sometimes in dialectic or systemic versions. An introductory chapter describes what is meant by scientific explanation, how that concept is instantiated in scientific communication theory, and delineates the three causal models prevalent in these theories. A useful resource for scholars, this book is suitable for graduate and advanced undergraduate courses in communication theory.