Computational Excursions in Analysis and Number Theory
Computational Excursions in Analysis and Number Theory

Author: Peter Borwein

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 220

ISBN-13: 0387216529

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This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.

An Introduction to Number Theory
An Introduction to Number Theory

Author: G. Everest

Publisher: Springer Science & Business Media

Published: 2007-05-21

Total Pages: 296

ISBN-13: 1852339179

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Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight

Number Theory and Polynomials
Number Theory and Polynomials

Author: James Fraser McKee

Publisher: Cambridge University Press

Published: 2008-05-08

Total Pages: 350

ISBN-13: 0521714672

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Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.

Algorithmic Number Theory
Algorithmic Number Theory

Author: Duncan Buell

Publisher: Springer Science & Business Media

Published: 2004-06

Total Pages: 461

ISBN-13: 3540221565

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This book constitutes the refereed proceedings of the 6th International Algorithmic Number Theory Symposium, ANTS 2004, held in Burlington, VT, USA, in June 2004. The 30 revised full papers presented together with 3 invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are zeta functions, elliptic curves, hyperelliptic curves, GCD algorithms, number field computations, complexity, primality testing, Weil and Tate pairings, cryptographic algorithms, function field sieve, algebraic function field mapping, quartic fields, cubic number fields, lattices, discrete logarithms, and public key cryptosystems.

Multiplicative Number Theory I
Multiplicative Number Theory I

Author: Hugh L. Montgomery

Publisher: Cambridge University Press

Published: 2007

Total Pages: 574

ISBN-13: 9780521849036

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A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.

Geometry of Continued Fractions
Geometry of Continued Fractions

Author: Oleg Karpenkov

Publisher: Springer Science & Business Media

Published: 2013-08-15

Total Pages: 409

ISBN-13: 3642393683

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Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Sequential Experiments with Primes
Sequential Experiments with Primes

Author: Mihai Caragiu

Publisher: Springer

Published: 2017-06-22

Total Pages: 281

ISBN-13: 3319567624

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With a specific focus on the mathematical life in small undergraduate colleges, this book presents a variety of elementary number theory insights involving sequences largely built from prime numbers and contingent number-theoretic functions. Chapters include new mathematical ideas and open problems, some of which are proved in the text. Vector valued MGPF sequences, extensions of Conway’s Subprime Fibonacci sequences, and linear complexity of bit streams derived from GPF sequences are among the topics covered in this book. This book is perfect for the pure-mathematics-minded educator in a small undergraduate college as well as graduate students and advanced undergraduate students looking for a significant high-impact learning experience in mathematics.

Advances in Cryptology – EUROCRYPT 2021
Advances in Cryptology – EUROCRYPT 2021

Author: Anne Canteaut

Publisher: Springer Nature

Published: 2021-06-16

Total Pages: 849

ISBN-13: 3030778703

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The 3-volume-set LNCS 12696 – 12698 constitutes the refereed proceedings of the 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2021, which was held in Zagreb, Croatia, during October 17-21, 2021. The 78 full papers included in these proceedings were accepted from a total of 400 submissions. They were organized in topical sections as follows: Part I: Best papers; public-key cryptography; isogenies; post-quantum cryptography; lattices; homomorphic encryption; symmetric cryptanalysis; Part II: Symmetric designs; real-world cryptanalysis; implementation issues; masking and secret-sharing; leakage, faults and tampering; quantum constructions and proofs; multiparty computation; Part III: Garbled circuits; indistinguishability obfuscation; non-malleable commitments; zero-knowledge proofs; property-preserving hash functions and ORAM; blockchain; privacy and law enforcement.

Recent Advances in Computational Optimization
Recent Advances in Computational Optimization

Author: Stefka Fidanova

Publisher: Springer Nature

Published: 2022-09-16

Total Pages: 388

ISBN-13: 3031068394

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This book presents recent advances in computational optimization. The book includes important real problems like modeling of physical processes, parameter settings for controlling different processes, transportation problems, machine scheduling, air pollution modeling, solving multiple integrals and systems of differential and integral equations which describe real processes, solving engineering and financial problems. It shows how to develop algorithms for them based on new intelligent methods like evolutionary computations, ant colony optimization, constrain programming Monte Carlo method and others. This research demonstrates how some real-world problems arising in engineering, economics and other domains can be formulated as optimization problems.

Computational Excursions in Analysis and Number Theory
Computational Excursions in Analysis and Number Theory

Author: Peter Borwein

Publisher: Springer Science & Business Media

Published: 2002-07-12

Total Pages: 236

ISBN-13: 9780387954448

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This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.