From Great Discoveries In Number Theory To Applications

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From Great Discoveries in Number Theory to Applications

Michal Křížek,Lawrence Somer,Alena Šolcová
From Great Discoveries in Number Theory to Applications Book PDF

Author : Michal Křížek,Lawrence Somer,Alena Šolcová
Publisher : Springer Nature
Page : 342 pages
File Size : 50,9 Mb
Release : 2021-09-21
Category : Mathematics
ISBN : 9783030838997

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From Great Discoveries in Number Theory to Applications by Michal Křížek,Lawrence Somer,Alena Šolcová Pdf

This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.

From Great Discoveries in Number Theory to Applications

Michal Křížek,Lawrence Somer,Alena Šolcová
From Great Discoveries in Number Theory to Applications Book PDF

Author : Michal Křížek,Lawrence Somer,Alena Šolcová
Publisher : Unknown
Page : 0 pages
File Size : 42,8 Mb
Release : 2021
Category : Electronic
ISBN : 3030839001

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From Great Discoveries in Number Theory to Applications by Michal Křížek,Lawrence Somer,Alena Šolcová Pdf

This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague's astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.

Fundamental Number Theory with Applications, Second Edition

Richard A. Mollin
Fundamental Number Theory with Applications Second Edition Book PDF

Author : Richard A. Mollin
Publisher : CRC Press
Page : 384 pages
File Size : 52,9 Mb
Release : 2008-02-21
Category : Mathematics
ISBN : 1420066617

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Fundamental Number Theory with Applications, Second Edition by Richard A. Mollin Pdf

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.

Number Theory and its Applications

Satyabrota Kundu,Supriyo Mazumder
Number Theory and its Applications Book PDF

Author : Satyabrota Kundu,Supriyo Mazumder
Publisher : CRC Press
Page : 366 pages
File Size : 45,5 Mb
Release : 2022-01-31
Category : Mathematics
ISBN : 9781000562484

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Number Theory and its Applications by Satyabrota Kundu,Supriyo Mazumder Pdf

Number Theory and its Applications is a textbook for students pursuing mathematics as major in undergraduate and postgraduate courses. Please note: Taylor & Francis does not sell or distribute the print book in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

Number Theory with Applications

W C Winnie Li
Number Theory with Applications Book PDF

Author : W C Winnie Li
Publisher : World Scientific Publishing Company
Page : 244 pages
File Size : 44,5 Mb
Release : 1996-02-16
Category : Mathematics
ISBN : 9789813104853

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Number Theory with Applications by W C Winnie Li Pdf

Novel and important applications of number theory to graph theory and vice versa had been made in the past decade. The two main tools used are based on the estimates of character sums and the estimates of the eigenvalues of Hecke operators, both are rooted in the celebrated Weil conjectures settled by Deligne in 1973. The purpose of this book is to give, from scratch, a coherent and comprehensive introduction to the topics in number theory related to the central tools, with the ultimate goal of presenting their applications. This book includes many important subjects in number theory, such as Weil conjectures, Riemann-Roch theorem, L-functions, character sum estimates, modular forms, and representation theory. Request Inspection Copy

Elementary Number Theory with Applications

Thomas Koshy
Elementary Number Theory with Applications Book PDF

Author : Thomas Koshy
Publisher : Elsevier
Page : 801 pages
File Size : 41,5 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9780080547091

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Elementary Number Theory with Applications by Thomas Koshy Pdf

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East

Elementary Number Theory and Its Applications

Kenneth H. Rosen
Elementary Number Theory and Its Applications Book PDF

Author : Kenneth H. Rosen
Publisher : Unknown
Page : 638 pages
File Size : 46,6 Mb
Release : 2000-01
Category : Number theory
ISBN : 0321204425

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Elementary Number Theory and Its Applications by Kenneth H. Rosen Pdf

The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage.The blending of classical theory with modern applications is a hallmark feature of the text. The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

Mathematics for the Liberal Arts

Donald Bindner,Martin J. Erickson,Joe Hemmeter
Mathematics for the Liberal Arts Book PDF

Author : Donald Bindner,Martin J. Erickson,Joe Hemmeter
Publisher : John Wiley & Sons
Page : 424 pages
File Size : 55,6 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118371749

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Mathematics for the Liberal Arts by Donald Bindner,Martin J. Erickson,Joe Hemmeter Pdf

Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes work Numerous figures and diagrams as well as hundreds of worked examples and exercises, aiding readers to further visualize the presented concepts Various real-world practical applications of mathematics, including error-correcting codes and the space shuttle program Vignette biographies of renowned mathematicians Appendices with solutions to selected exercises and suggestions for further reading Mathematics for the Liberal Arts is an excellent introduction to the history and concepts of mathematics for undergraduate liberal arts students and readers in non-scientific fields wishing to gain a better understanding of mathematics and mathematical problem-solving skills.

Emerging Applications of Number Theory

Dennis A. Hejhal,Joel Friedman,Martin C. Gutzwiller,Andrew M. Odlyzko
Emerging Applications of Number Theory Book PDF

Author : Dennis A. Hejhal,Joel Friedman,Martin C. Gutzwiller,Andrew M. Odlyzko
Publisher : Springer Science & Business Media
Page : 693 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215448

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Emerging Applications of Number Theory by Dennis A. Hejhal,Joel Friedman,Martin C. Gutzwiller,Andrew M. Odlyzko Pdf

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.

Number Theory

James Pommersheim,Tim Marks,Erica Flapan
Number Theory Book PDF

Author : James Pommersheim,Tim Marks,Erica Flapan
Publisher : Wiley
Page : 0 pages
File Size : 41,8 Mb
Release : 2010-02-15
Category : Mathematics
ISBN : 0470424133

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Number Theory by James Pommersheim,Tim Marks,Erica Flapan Pdf

Number Theory: A Lively Introduction with Proofs, Applications, and Stories, is a new book that provides a rigorous yet accessible introduction to elementary number theory along with relevant applications. Readable discussions motivate new concepts and theorems before their formal definitions and statements are presented. Many theorems are preceded by Numerical Proof Previews, which are numerical examples that will help give students a concrete understanding of both the statements of the theorems and the ideas behind their proofs, before the statement and proof are formalized in more abstract terms. In addition, many applications of number theory are explained in detail throughout the text, including some that have rarely (if ever) appeared in textbooks. A unique feature of the book is that every chapter includes a math myth, a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth Explorations, in which a series of exercises develop a topic that is related to the material in the section.

Number Theory and Its Applications

Cem Y. Yildrim,Serguei A. Stepanov
Number Theory and Its Applications Book PDF

Author : Cem Y. Yildrim,Serguei A. Stepanov
Publisher : CRC Press
Page : 364 pages
File Size : 40,5 Mb
Release : 2020-03-06
Category : Mathematics
ISBN : 9781000657418

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Number Theory and Its Applications by Cem Y. Yildrim,Serguei A. Stepanov Pdf

This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey.

Elementary Number Theory with Programming

Marty Lewinter,Jeanine Meyer
Elementary Number Theory with Programming Book PDF

Author : Marty Lewinter,Jeanine Meyer
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 43,7 Mb
Release : 2015-06-02
Category : Mathematics
ISBN : 9781119062769

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Elementary Number Theory with Programming by Marty Lewinter,Jeanine Meyer Pdf

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.

Fundamental Number Theory with Applications, Second Edition

Richard A. Mollin
Fundamental Number Theory with Applications Second Edition Book PDF

Author : Richard A. Mollin
Publisher : Chapman and Hall/CRC
Page : 384 pages
File Size : 53,5 Mb
Release : 2008-02-21
Category : Mathematics
ISBN : 1420066595

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Fundamental Number Theory with Applications, Second Edition by Richard A. Mollin Pdf

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.

Number Theory

George E. Andrews
Number Theory Book PDF

Author : George E. Andrews
Publisher : Courier Corporation
Page : 292 pages
File Size : 40,7 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486135106

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Number Theory by George E. Andrews Pdf

Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Number Theory with Computer Applications

Ramanujachary Kumanduri,Cristina Romero
Number Theory with Computer Applications Book PDF

Author : Ramanujachary Kumanduri,Cristina Romero
Publisher : Pearson
Page : 566 pages
File Size : 46,5 Mb
Release : 1998
Category : Mathematics
ISBN : UOM:39015047053387

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Number Theory with Computer Applications by Ramanujachary Kumanduri,Cristina Romero Pdf

Appropriate for most courses in Number Theory. This book effectively integrates computing algorithms into the number theory curriculum using a heuristic approach and strong emphasis on proofs. Its in-depth coverage of modern applications considers the latest trends and topics, such as elliptic curves--a subject that has seen a rise in popularity due to its use in the proof of Fermat's Last Theorem.