Number Theory in Science and Communication

Author: Manfred R. Schroeder
Publisher: Springer Science & Business Media
ISBN: 3662023954
Format: PDF, Mobi
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"Beauty is the first test: there is no permanent place in the world for ugly mathematics. " - G. H. Hardy N umber theory has been considered since time immemorial to be the very paradigm of pure (some would say useless) mathematics. In fact, the Chinese characters for mathematics are Number Science. "Mathematics is the queen of sciences - and number theory is the queen of mathematics," according to Carl Friedrich Gauss, the lifelong Wunderkind, who hirnself enjoyed the epithet "Princeps Mathematicorum. " What could be more beautiful than a deep, satisfying relation between whole numbers. {One is almost tempted to call them wholesome numbersJ In fact, it is hard to come up with a more appropriate designation than their learned name: the integers - meaning the "untouched ones". How high they rank, in the realms of pure thought and aesthetics, above their lesser brethren: the real and complex number- whose first names virtually exude unsavory involvement with the complex realities of everyday life! Yet, as we shall see in this book, the theory of integers can provide totally unexpected answers to real-world problems. In fact, discrete mathematics is ta king on an ever more important role. If nothing else, the advent of the digital computer and digital communication has seen to that. But even earlier, in physics the emergence of quantum mechanics and discrete elementary particles put a premium on the methods and, indeed, the spirit of discrete mathematics.

The Philosophy of Science and Communication Theory

Author: Charles Pavitt
Publisher: Nova Science Pub Incorporated
ISBN: 9781560728757
Format: PDF, Kindle
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The is not an attempt to provide an overview of theories in communication. Nor is it an attempt to provide a complete picture of approaches to communication theory. The book is an attempt to defend a very general empiricist approach to the scientific study of communication. The author is referring to the most general notion of empiricism, that we can come to some knowledge about the world through the use of our perceptions. Empiricism in these senses has taken quite a critical beating over the centuries, but in the sense in which he uses this term here it remains alive and well and prepared to serve as the foundation for the scientific study of communication, as it has for several decades. Secondly, the book is an attempt to defend a 'conventional' view of scientific theory. Thirdly, the book is an attempt to introduce into the mainstream of communication scholarship an approach to the philosophy of science known as 'scientific realism'. Fourthly, the book is a small part of the attempt to close some of the gaps between different sub-areas within communication science.

Computational Number Theory and Modern Cryptography

Author: Song Y. Yan
Publisher: John Wiley & Sons
ISBN: 1118188616
Format: PDF
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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.

Science Communication in Theory and Practice

Author: S.M. Stocklmayer
Publisher: Springer Science & Business Media
ISBN: 9401006202
Format: PDF, Mobi
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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.

Communication Science Theory and Research

Author: Marina Krcmar
Publisher: Routledge
ISBN: 1136288996
Format: PDF
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This volume provides a graduate-level introduction to communication science, including theory and scholarship for masters and PhD students as well as practicing scholars. The work defines communication, reviews its history, and provides a broad look at how communication research is conducted. It also includes chapters reviewing the most frequently addressed topics in communication science. This book presents an overview of theory in general and of communication theory in particular, while offering a broad look at topics in communication that promote understanding of the key issues in communication science for students and scholars new to communication research. The book takes a predominantly "communication science" approach but also situates this approach in the broader field of communication, and addresses how communication science is related to and different from such approaches as critical and cultural studies and rhetoric. As an overview of communication science that will serve as a reference work for scholars as well as a text for the introduction to communication graduate studies course, this volume is an essential resource for understanding and conducting scholarship in the communication discipline.

Elementary Number Theory Primes Congruences and Secrets

Author: William Stein
Publisher: Springer Science & Business Media
ISBN: 0387855254
Format: PDF, Docs
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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 Its History

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

Number Theory and the Periodicity of Matter

Author: Jan C. A. Boeyens
Publisher: Springer Science & Business Media
ISBN: 9781402066603
Format: PDF, Mobi
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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.

Creative Research Communication

Author: Clare Wilkinson
Publisher: Oxford University Press
ISBN: 1784997382
Format: PDF, ePub
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Considering how to communicate your research or engage others with the latest science, social science or humanities research? This book explores new and emerging approaches to engaging people with research, placing these in the wider context of research communication. Split into three sections, Creative research communication explores the historical routes and current drivers for public engagement, before moving on to explore practical approaches and finally discussing ethical issues and the ways in which research communication can contribute to research impact. Starting from the premise that researchers can and ought to participate in the public sphere, this book provides practical guidance and advice on contributing to political discourse and policymaking, as well as engaging the public where they are (whether that is at the theatre, at a music festival or on social media). By considering the plurality of publics and their diverse needs and interests, it is quite possible to find a communications niche that neither offers up bite-sized chunks of research, nor conceptualises the public as lacking the capacity to consider the myriad of issues raised by research, but explains and considers thoughtfully the value of research endeavours and their potential benefits to society. It's time for researchers to move away from one-size fits all, and embrace opportunities for creative approaches to research communication. This book argues for a move away from metrics and tick box approaches and towards approaches that work for you, as an individual researcher, in the context of your own discipline and interests.