Number Theory With Computations
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Number Theory With Computations
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Author : Peter Shiu
language : en
Publisher: Springer Nature
Release Date : 2024-09-02
Number Theory With Computations written by Peter Shiu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-02 with Mathematics categories.
This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. The book emphasises computational aspects, including algorithms and their implementation in Python. The book is divided into two parts. The first part, on elementary number theory, deals with concepts such as induction, divisibility, congruences, primitive roots, cryptography, and continued fractions. The second part is devoted to analytic number theory and includes chapters on Dirichlet’s theorem on primes in arithmetic progressions, the prime number theorem, smooth numbers, and the famous circle method of Hardy and Littlewood. The book contains many topics not often found in introductory textbooks, such as Aubry’s theorem, the Tonelli–Shanks algorithm, factorisation methods, continued fraction representations of e, and the irrationality of ζ(3). Each chapter concludes with a summary and notes, as well as numerous exercises. Assuming only basic calculus for the first part of the book, the second part assumes some knowledge of complex analysis. Familiarity with basic coding syntax will be helpful for the computational exercises.
Arithmetic Geometry Number Theory And Computation
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Author : Jennifer S. Balakrishnan
language : en
Publisher: Springer Nature
Release Date : 2022-03-15
Arithmetic Geometry Number Theory And Computation written by Jennifer S. Balakrishnan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-15 with Mathematics categories.
This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Number Theory With Computations
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Author : Peter Shiu
language : en
Publisher: Springer
Release Date : 2024-11-11
Number Theory With Computations written by Peter Shiu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-11 with Mathematics categories.
This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. The book emphasises computational aspects, including algorithms and their implementation in Python. The book is divided into two parts. The first part, on elementary number theory, deals with concepts such as induction, divisibility, congruences, primitive roots, cryptography, and continued fractions. The second part is devoted to analytic number theory and includes chapters on Dirichlet’s theorem on primes in arithmetic progressions, the prime number theorem, smooth numbers, and the famous circle method of Hardy and Littlewood. The book contains many topics not often found in introductory textbooks, such as Aubry’s theorem, the Tonelli–Shanks algorithm, factorisation methods, continued fraction representations of e, and the irrationality of ζ(3). Each chapter concludes with a summary and notes, as well as numerous exercises. Assuming only basic calculus for the first part of the book, the second part assumes some knowledge of complex analysis. Familiarity with basic coding syntax will be helpful for the computational exercises.
Computational Number Theory And Modern Cryptography
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Author : Song Y. Yan
language : en
Publisher: John Wiley & Sons
Release Date : 2013-01-29
Computational Number Theory And Modern Cryptography written by Song Y. Yan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-29 with Computers categories.
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.
Computational Perspectives On Number Theory
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Author : Duncan A. Buell
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Computational Perspectives On Number Theory written by Duncan A. Buell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This volume contains papers presented at the conference "Computational Prespectives on Number Theory" held at the University of Illinois at Chicago in honor of the retirement of A. O. L. Atkin. In keeping with Atkin's interests and work, the papers cover a range of topics, including algebraic number theory, p-adic modular forms and modular curves. Many of the paers reflect Atkin's particular interest in computational and algorithmic questions.
Lucant Lmfdb Computation And Number Theory
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Author : John Cremona
language : en
Publisher: American Mathematical Soc.
Release Date : 2024-03-22
Lucant Lmfdb Computation And Number Theory written by John Cremona and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-22 with Mathematics categories.
This book will be published Open Access with a Creative Commons Attribution 4.0 International License (CC BY 4.0). The eBook can be downloaded electronically for free. This volume contains the proceedings of the LuCaNT (LMFDB, Computation, and Number Theory) conference held from July 10–14, 2023, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island and affiliated with Brown University. This conference provided an opportunity for researchers, scholars, and practitioners to exchange ideas, share advances, and collaborate in the fields of computation, mathematical databases, number theory, and arithmetic geometry. The papers that appear in this volume record recent advances in these areas, with special focus on the LMFDB (the L-Functions and Modular Forms Database), an online resource for mathematical objects arising in the Langlands program and the connections between them.
A Course In Computational Algebraic Number Theory
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Author : Henri Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Course In Computational Algebraic Number Theory written by Henri Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
With the advent of powerful computing tools and numerous advances in math ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.
Computational Number Theory
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Author : Attila Pethoe
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-01
Computational Number Theory written by Attila Pethoe and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Mathematics categories.
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Computational Number Theory And Cryptography
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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-04-03
Computational Number Theory And Cryptography written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-03 with Mathematics categories.
EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.
Cryptology And Computational Number Theory
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Author : Carl Pomerance
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Cryptology And Computational Number Theory written by Carl Pomerance and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Computers categories.
In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.