Jeffrey Shallit's Books

Automatic Sequences

Theory, Applications, Generalizations

By: Jean-Paul Allouche,Jeffrey Shallit

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Automatic Sequences

Theory, Applications, Generalizations

By: Jean-Paul Allouche,Jeffrey Shallit

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.

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Page Count

592

Publisher

Cambridge University Press

Published Date

ISBN 10

0521823323

ISBN 13

9780521823326

Neverending Fractions

An Introduction to Continued Fractions

By: Jonathan Borwein,Alf van der Poorten,Jeffrey Shallit,Wadim Zudilin

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Neverending Fractions

An Introduction to Continued Fractions

By: Jonathan Borwein,Alf van der Poorten,Jeffrey Shallit,Wadim Zudilin

Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results together, offering fresh perspectives on a mature subject. Beginning with a standard introduction to continued fractions, the book covers a diverse range of topics, from elementary and metric properties, to quadratic irrationals, to more exotic topics such as folded continued fractions and Somos sequences. Along the way, the authors reveal some amazing applications of the theory to seemingly unrelated problems in number theory. Previously scattered throughout the literature, these applications are brought together in this volume for the first time. A wide variety of exercises guide readers through the material, which will be especially helpful to readers using the book for self-study, and the authors also provide many pointers to the literature.

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Page Count

223

Publisher

Cambridge University Press

Published Date

ISBN 10

1139991396

ISBN 13

9781139991391

The Logical Approach to Automatic Sequences

Exploring Combinatorics on Words with Walnut

By: Jeffrey Shallit

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The Logical Approach to Automatic Sequences

Exploring Combinatorics on Words with Walnut

By: Jeffrey Shallit

Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.

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Page Count

376

Publisher

Cambridge University Press

Published Date

ISBN 10

1108786979

ISBN 13

9781108786973

Algorithmic Number Theory: Efficient algorithms

By: Eric Bach,Jeffrey Outlaw Shallit

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Algorithmic Number Theory: Efficient algorithms

By: Eric Bach,Jeffrey Outlaw Shallit

Volume 1.

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Page Count

536

Publisher

MIT Press

Published Date

ISBN 10

0262024055

ISBN 13

9780262024051

An Introduction to Mathematical Cryptography

By: Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman

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An Introduction to Mathematical Cryptography

By: Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

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Page Count

549

Publisher

Springer

Published Date

ISBN 10

1493917110

ISBN 13

9781493917112

Scrambled Feet

By: John Driver,Jeffrey Haddow

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Scrambled Feet

By: John Driver,Jeffrey Haddow

This intimate musical revue is a zany, hilarious spoof dedicated to satirizing every conceivable aspect of show business. Among the many skits are a pointed parody of theatre party ladies, a wrestling match between the "Elephant Man" and the paraplegic hero of Whose Life Is It Anyway?, the traumas of a suburban couple getting to and going from the theater, a madrigal on the popularity of British plays and performers, and takeoffs on critics and Joseph Papp and his Public Theatre. It's a perfect show for anyone involved with the theatre.

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Publisher

Samuel French, Inc.

Published Date

ISBN 10

0573681201

ISBN 13

9780573681202

Algorithmic Number Theory: Efficient algorithms

By: Eric Bach,Jeffrey Outlaw Shallit

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Algorithmic Number Theory: Efficient algorithms

By: Eric Bach,Jeffrey Outlaw Shallit

Volume 1.

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Solve jigsaw puzzle

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Page Count

536

Publisher

MIT Press

Published Date

ISBN 10

0262024055

ISBN 13

9780262024051

Automatic Sequences

Theory, Applications, Generalizations

By: Jean-Paul Allouche,Jeffrey Shallit

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Automatic Sequences

Theory, Applications, Generalizations

By: Jean-Paul Allouche,Jeffrey Shallit

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Solve jigsaw puzzle

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Page Count

592

Publisher

Cambridge University Press

Published Date

ISBN 10

0521823323

ISBN 13

9780521823326

Book's by Jeffrey Shallit

Automatic Sequences

Automatic Sequences

Neverending Fractions

Neverending Fractions

The Logical Approach to Automatic Sequences

The Logical Approach to Automatic Sequences

Algorithmic Number Theory: Efficient algorithms

Algorithmic Number Theory: Efficient algorithms

An Introduction to Mathematical Cryptography

An Introduction to Mathematical Cryptography

Scrambled Feet

Scrambled Feet

Algorithmic Number Theory: Efficient algorithms

Algorithmic Number Theory: Efficient algorithms

Automatic Sequences

Automatic Sequences

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