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A Handbook of Integer Sequences

Author: N.J.A. Sloane

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 221

ISBN-13: 148326467X

A Handbook of Integer Sequences contains a main table of 2300 sequences of integers that are collected from all branches of mathematics and science. This handbook describes how to use the main table and provides methods for analyzing and describing unknown and important sequences. This compilation also serves as an index to the literature for locating references on a particular problem and quickly finds numbers such as 712, number of partitions of 30, 18th Catalan number, or expansion of ? to 60 decimal places. Other topics include the method of differences, self-generating sequences, polyominoes, permutations, and puzzle sequences. This publication is a good source for students and researchers who are confronted with strange and important sequences.

Towards Mechanized Mathematical Assistants

Author: Manuel Kauers

Publisher: Springer Science & Business Media

Published: 2007-06-19

Total Pages: 418

ISBN-13: 3540730834

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This book constitutes the refereed proceedings of the 6th International Conference on Mathematical Knowledge Management, MKM 2007, and the 14th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2006, held in Hagenberg, Austria in June 2007 as events of the RISC Summer 2007, organized by the Research Institute for Symbolic Computation.

Homage to a Pied Puzzler

Author: Alan Schoen

Publisher: CRC Press

Published: 2009-02-26

Total Pages: 320

ISBN-13: 1439865000

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The tradition of honoring Martin Gardner continues with this edited collection of articles by those who have been inspired by Gardner to enter mathematics, to enter magic, to bring magic into their mathematics, or to bring mathematics into their magic. Contributing authors include world-leading puzzle designers, puzzle collectors, mathematicians, a

Unsolved Problems in Number Theory

Author: Richard Guy

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 176

ISBN-13: 1475717385

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Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.

The Encyclopedia of Integer Sequences

Author: N. J.A. Sloane

Publisher: Academic Press

Published: 1995-03-28

Total Pages: 622

ISBN-13:

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The Encyclopedia of Integer Sequences contains more than 5000 integer sequences, arranged for easy reference, with more than half never before catalogued. In addition to having more than double the material of Sloane's A Handbook of Integer Sequences (Academic Press, 1973), this encyclopedia gives the name, mathematical description, and citations to the literature for each sequence. It includes essays on origins, uses, and connections, with interesting diagrams or illustrations. More than a table, this is an introduction to the field, showing readers how to identify and work with sequences. It includes an extensive bibliography of current and classic references. An index to all the sequences in the book is also available separately in Macintosh and IBM formats.

Mathematics by Experiment

Author: Jonathan Borwein

Publisher: CRC Press

Published: 2008-10-27

Total Pages: 393

ISBN-13: 1439865361

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This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational P

The Penguin Dictionary of Curious and Interesting Numbers

Author: David Wells

Publisher: Penguin

Published: 1997-09-04

Total Pages: 260

ISBN-13: 9780140261493

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Provides information on numbers and what makes particular ones noteworthy

Fibonacci and Lucas Numbers with Applications

Author: Thomas Koshy

Publisher: John Wiley & Sons

Published: 2011-10-24

Total Pages: 676

ISBN-13: 1118031318

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The first comprehensive survey of mathematics' most fascinatingnumber sequences Fibonacci and Lucas numbers have intrigued amateur and professionalmathematicians for centuries. This volume represents the firstattempt to compile a definitive history and authoritative analysisof these famous integer sequences, complete with a wealth ofexciting applications, enlightening examples, and fun exercisesthat offer numerous opportunities for exploration andexperimentation. The author has assembled a myriad of fascinating properties of bothFibonacci and Lucas numbers-as developed by a wide range ofsources-and catalogued their applications in a multitude of widelyvaried disciplines such as art, stock market investing,engineering, and neurophysiology. Most of the engaging anddelightful material here is easily accessible to college and evenhigh school students, though advanced material is included tochallenge more sophisticated Fibonacci enthusiasts. A historicalsurvey of the development of Fibonacci and Lucas numbers,biographical sketches of intriguing personalities involved indeveloping the subject, and illustrative examples round out thisthorough and amusing survey. Most chapters conclude with numericand theoretical exercises that do not rely on long and tediousproofs of theorems. Highlights include: * Balanced blend of theory and real-world applications * Excellent reference material for student reports andprojects * User-friendly, informal, and entertaining writing style * Historical interjections and short biographies that add a richerperspective to the topic * Reference sections providing important symbols, problemsolutions, and fundamental properties from the theory of numbersand matrices Fibonacci and Lucas Numbers with Applications providesmathematicians with a wealth of reference material in oneconvenient volume and presents an in-depth and entertainingresource for enthusiasts at every level and from any background.

Automatic Sequences

Author: Jean-Paul Allouche

Publisher: Cambridge University Press

Published: 2003-07-21

Total Pages: 592

ISBN-13: 9780521823326

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Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.

The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics

Author: James Haglund

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 178

ISBN-13: 0821844113

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This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.