Combinatorics: Ancient & Modern

Author: John J. Watkins,Ronald Graham

Publisher: Oxford University Press

ISBN: 0199656592

Category: Mathematics

Page: 381

View: 7503

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Combinatorics is the branch of discrete mathematics that studies (and counts) permutations, combinations, and arrangements of sets of elements. This book constitutes the first book-length survey of the history of combinatorics and uniquely assembles research in the area that would otherwise be inaccessible to the general reader.
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Unsolved!

The History and Mystery of the World's Greatest Ciphers from Ancient Egypt to Online Secret Societies

Author: Craig P. Bauer

Publisher: Princeton University Press

ISBN: 1400884799

Category: Computers

Page: 624

View: 9551

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Watch Craig Bauer discuss the Zodiac Killer’s cipher on HISTORY’s new miniseries The Hunt for the Zodiac Killer In 1953, a man was found dead from cyanide poisoning near the Philadelphia airport with a picture of a Nazi aircraft in his wallet. Taped to his abdomen was an enciphered message. In 1912, a book dealer named Wilfrid Voynich came into possession of an illuminated cipher manuscript once belonging to Emperor Rudolf II, who was obsessed with alchemy and the occult. Wartime codebreakers tried—and failed—to unlock the book's secrets, and it remains an enigma to this day. In this lively and entertaining book, Craig Bauer examines these and other vexing ciphers yet to be cracked. Some may reveal the identity of a spy or serial killer, provide the location of buried treasure, or expose a secret society—while others may be elaborate hoaxes. Unsolved! begins by explaining the basics of cryptology, and then explores the history behind an array of unsolved ciphers. It looks at ancient ciphers, ciphers created by artists and composers, ciphers left by killers and victims, Cold War ciphers, and many others. Some are infamous, like the ciphers in the Zodiac letters, while others were created purely as intellectual challenges by figures such as Nobel Prize–winning physicist Richard P. Feynman. Bauer lays out the evidence surrounding each cipher, describes the efforts of geniuses and eccentrics—in some cases both—to decipher it, and invites readers to try their hand at puzzles that have stymied so many others. Unsolved! takes readers from the ancient world to the digital age, providing an amazing tour of many of history's greatest unsolved ciphers.
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Latin Squares and Their Applications

Author: A. Donald Keedwell,József Dénes

Publisher: Elsevier

ISBN: 0444635580

Category: Mathematics

Page: 455

View: 1477

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Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the beginnings of the subject to the frontiers of research’. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties. Retains the organization and updated foundational material from the original edition Explores current and emerging research topics Includes the original 73 ‘Unsolved Problems’ with the current state of knowledge regarding them, as well as new Unsolved Problems for further study
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Number Theory

A Historical Approach

Author: John J. Watkins

Publisher: Princeton University Press

ISBN: 1400848741

Category: Mathematics

Page: 592

View: 574

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The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors)
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Topics in Chromatic Graph Theory

Author: Lowell W. Beineke,Robin J. Wilson

Publisher: Cambridge University Press

ISBN: 1316239853

Category: Mathematics

Page: N.A

View: 9127

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Chromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks, where colouring algorithms form an important feature. While other books cover portions of the material, no other title has such a wide scope as this one, in which acknowledged international experts in the field provide a broad survey of the subject. All fifteen chapters have been carefully edited, with uniform notation and terminology applied throughout. Bjarne Toft (Odense, Denmark), widely recognized for his substantial contributions to the area, acted as academic consultant. The book serves as a valuable reference for researchers and graduate students in graph theory and combinatorics and as a useful introduction to the topic for mathematicians in related fields.
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Mathematical thought from ancient to modern times

Author: Morris Kline

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 1238

View: 8799

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A journey into the realm of mathematics that focuses on the major concepts and developments that have emerged throughout the centuries. Bibliogs
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The Turing Guide

Author: Jack Copeland,Jonathan Bowen,Mark Sprevak,Robin Wilson

Publisher: Oxford University Press

ISBN: 0191065005

Category: Science

Page: 400

View: 4500

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Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work. This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.
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The Art of the Conductor

The Definitive Guide to Music Conducting Skills, Terms, and Techniques

Author: John J. Watkins

Publisher: N.A

ISBN: 9780595433964

Category: Music

Page: 77

View: 6263

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"John Watkins has used his years of experience on both sides of the baton to create a charming introduction to the art of conducting. There are not many reference books that deal with the 'how to' of directing a group of musicians. This practical guide to conducting wisely stays away from musical theory and concentrates on how to communicate with musicians from base amateur to seasoned professional This is a must for a newly aspiring conductor, and an experienced conductor could very well use this as a refresher." -John Tozer, music director, Scarborough, Ontario An invaluable reference guide for musicians of all types, The Art of the Conductor contains clear and detailed descriptions of universally accepted techniques used by the world's best and most successful music conductors. Classically trained musician and conductor John J. Watkins discusses the evolution of conducting technique and how it relates to various forms of music, and he outlines the wide array of skills conductors need today. He also explains the finer points of technique and control, including beat patterns and signals, tempo changes, and using the left hand, to make the conducting experience as rewarding as possible. The Art of the Conductor will help conductors, choristers, and instrumentalists build their skills and confidence for more relaxed, enjoyable, and polished performances that audiences will love.
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Codes

The Guide to Secrecy From Ancient to Modern Times

Author: Richard A. Mollin

Publisher: CRC Press

ISBN: 9781420035087

Category: Computers

Page: 704

View: 3181

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From the Rosetta Stone to public-key cryptography, the art and science of cryptology has been used to unlock the vivid history of ancient cultures, to turn the tide of warfare, and to thwart potential hackers from attacking computer systems. Codes: The Guide to Secrecy from Ancient to Modern Times explores the depth and breadth of the field, remaining accessible to the uninitiated while retaining enough rigor for the seasoned cryptologist. The book begins by tracing the development of cryptology from that of an arcane practice used, for example, to conceal alchemic recipes, to the modern scientific method that is studied and employed today. The remainder of the book explores the modern aspects and applications of cryptography, covering symmetric- and public-key cryptography, cryptographic protocols, key management, message authentication, e-mail and Internet security, and advanced applications such as wireless security, smart cards, biometrics, and quantum cryptography. The author also includes non-cryptographic security issues and a chapter devoted to information theory and coding. Nearly 200 diagrams, examples, figures, and tables along with abundant references and exercises complement the discussion. Written by leading authority and best-selling author on the subject Richard A. Mollin, Codes: The Guide to Secrecy from Ancient to Modern Times is the essential reference for anyone interested in this exciting and fascinating field, from novice to veteran practitioner.
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