Emerging Applications Of Number Theory PDF Download
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| Author | : Dennis A. Hejhal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 693 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461215447 |
Download Emerging Applications of Number Theory Book in PDF, ePub and Kindle
Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.
| Author | : Richard A. Mollin |
| Publisher | : CRC Press |
| Total Pages | : 382 |
| Release | : 2008-02-21 |
| Genre | : Mathematics |
| ISBN | : 1420066617 |
Download Fundamental Number Theory with Applications Book in PDF, ePub and Kindle
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.
| Author | : Jordi Guàrdia |
| Publisher | : Springer Nature |
| Total Pages | : 457 |
| Release | : |
| Genre | : |
| ISBN | : 3031519590 |
Download New Frontiers in Number Theory and Applications Book in PDF, ePub and Kindle
| Author | : Amir Akbary |
| Publisher | : Springer |
| Total Pages | : 528 |
| Release | : 2018-09-18 |
| Genre | : Mathematics |
| ISBN | : 3319973797 |
Download Geometry, Algebra, Number Theory, and Their Information Technology Applications Book in PDF, ePub and Kindle
This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The theory of automorphic forms and their associated L-functions Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties The emerging applications of number theory in information technology Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.
| Author | : Steven J. Miller |
| Publisher | : Princeton University Press |
| Total Pages | : |
| Release | : 2020-08-04 |
| Genre | : Mathematics |
| ISBN | : 0691215979 |
Download An Invitation to Modern Number Theory Book in PDF, ePub and Kindle
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
| Author | : Hailong Li |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 288 |
| Release | : 2017-11-29 |
| Genre | : Technology & Engineering |
| ISBN | : 9813231610 |
Download Number Theory and Its Applications II Book in PDF, ePub and Kindle
The aim of the book is to give a smooth analytic continuation from basic subjects including linear algebra, group theory, Hilbert space theory, etc. to number theory. With plenty of practical examples and worked-out exercises, and the scope ranging from these basic subjects made applicable to number-theoretic settings to advanced number theory, this book can then be read without tears. It will be of immense help to the reader to acquire basic sound skills in number theory and its applications. Number theory used to be described as the queen of mathematics, that is, there is no practical use. However, with the development of computers and the security of internet communications, the importance of number theory has been exponentially increasing daily. The raison d'être of the present book in this situation is that it is extremely reader-friendly while keeping the rigor of serious mathematics and in-depth analysis of practical applications to various subjects including control theory and pseudo-random number generation. The use of operators is prevailing rather abundantly in anticipation of applications to electrical engineering, allowing the reader to master these skills without much difficulty. It also delivers a very smooth bridging between elementary subjects including linear algebra and group theory (and algebraic number theory) for the reader to be well-versed in an efficient and effortless way. One of the main features of the book is that it gives several different approaches to the same topic, helping the reader to gain deeper insight and comprehension. Even just browsing through the materials would be beneficial to the reader.
| Author | : David Chudnovsky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 284 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780387406558 |
Download Number Theory Book in PDF, ePub and Kindle
This volume marks the 20th anniversary of the New York Number Theory Seminar (NYNTS). Beginning in 1982, the NYNTS has tried to present a broad spectrum of research in number theory and related fields of mathematics, from physics to geometry to combinatorics and computer science. The list of seminar speakers includes not only Fields Medallists and other established researchers, but also many other younger and less well known mathematicians whose theorems are significant and whose work may become the next big thing in number theory.
| Author | : G. Everest |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2007-05-21 |
| Genre | : Mathematics |
| ISBN | : 1852339179 |
Download An Introduction to Number Theory Book in PDF, ePub and Kindle
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
| Author | : Shigeru Kanemitsu |
| Publisher | : World Scientific |
| Total Pages | : 212 |
| Release | : 2015-02-10 |
| Genre | : Mathematics |
| ISBN | : 9814644943 |
Download Number Theory: Plowing And Starring Through High Wave Forms - Proceedings Of The 7th China-japan Seminar Book in PDF, ePub and Kindle
Based on the successful 7th China-Japan seminar on number theory conducted in Kyushu University, this volume is a compilation of survey and semi-survey type of papers by the participants of the seminar. The topics covered range from traditional analytic number theory to elliptic curves and universality. This volume contains new developments in the field of number theory from recent years and it provides suitable problems for possible new research at a level which is not unattainable. Timely surveys will be beneficial to a new generation of researchers as a source of information and these provide a glimpse at the state-of-the-art affairs in the fields of their research interests.
| Author | : Marty Lewinter |
| Publisher | : John Wiley & Sons |
| Total Pages | : 240 |
| Release | : 2015-06-02 |
| Genre | : Mathematics |
| ISBN | : 1119062764 |
Download Elementary Number Theory with Programming Book in PDF, ePub and Kindle
A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area. Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes: Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas Select solutions to the chapter exercises in an appendix Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set A related website with links to select exercises An Instructor’s Solutions Manual available on a companion website Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.
