Applied Number Theory

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Applied Number Theory

Harald Niederreiter,Arne Winterhof
Applied Number Theory Book PDF

Author : Harald Niederreiter,Arne Winterhof
Publisher : Springer
Page : 442 pages
File Size : 52,9 Mb
Release : 2015-09-01
Category : Mathematics
ISBN : 9783319223216

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Applied Number Theory by Harald Niederreiter,Arne Winterhof Pdf

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory. Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.

Number Theory

Don Redmond
Number Theory Book PDF

Author : Don Redmond
Publisher : CRC Press
Page : 778 pages
File Size : 48,8 Mb
Release : 1996-04-23
Category : Mathematics
ISBN : 0824796969

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Number Theory by Don Redmond Pdf

This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.

Number Theory

Don Redmond
Number Theory Book PDF

Author : Don Redmond
Publisher : CRC Press
Page : 772 pages
File Size : 49,9 Mb
Release : 2020-09-29
Category : Mathematics
ISBN : 9781000105360

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Number Theory by Don Redmond Pdf

This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.

Number Theory

Róbert Freud,Edit Gyarmati
Number Theory Book PDF

Author : Róbert Freud,Edit Gyarmati
Publisher : American Mathematical Soc.
Page : 549 pages
File Size : 43,9 Mb
Release : 2020-10-08
Category : Education
ISBN : 9781470452759

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Number Theory by Róbert Freud,Edit Gyarmati Pdf

Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.

An Experimental Introduction to Number Theory

Benjamin Hutz
An Experimental Introduction to Number Theory Book PDF

Author : Benjamin Hutz
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 49,8 Mb
Release : 2018-04-17
Category : Number theory
ISBN : 9781470430979

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An Experimental Introduction to Number Theory by Benjamin Hutz Pdf

This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.

Number Theory for Computing

Song Y. Yan
Number Theory for Computing Book PDF

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9783662040539

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Number Theory for Computing by Song Y. Yan Pdf

Taking readers from elementary number theory, via algorithmic, to applied number theory in computer science, this text introduces basic concepts, results, and methods, before going on to discuss their applications in the design of hardware and software, cryptography, and security. Aimed at undergraduates in computing and information technology, and presupposing only high-school math, this book will also interest mathematics students concerned with applications. XXXXXXX Neuer Text This is an essential introduction to number theory for computer scientists. It treats three areas, elementary-, algorithmic-, and applied number theory in a unified and accessible manner. It introduces basic concepts and methods, and discusses their applications to the design of hardware, software, cryptography, and information security. Aimed at computer scientists, electrical engineers and students the presentation presupposes only an understanding of high-school math.

Number Theory

Anonim
Number Theory Book PDF

Author : Anonim
Publisher : Academic Press
Page : 449 pages
File Size : 46,6 Mb
Release : 1986-05-05
Category : Mathematics
ISBN : 9780080873329

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Number Theory by Anonim Pdf

This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.

The Unreasonable Effectiveness of Number Theory

Stefan Andrus Burr,George E. Andrews
The Unreasonable Effectiveness of Number Theory Book PDF

Author : Stefan Andrus Burr,George E. Andrews
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 49,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821855018

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The Unreasonable Effectiveness of Number Theory by Stefan Andrus Burr,George E. Andrews Pdf

"Number theory is one of the oldest and noblest branches of mathematics; indeed, it was already ancient in the time of Euclid...for almost all of its history it has seemed to be among the purest branches of mathematics. It is only within the last few decades that a large number of applications have been encountered, at least by the mathematical community. The applications to cryptology are now famous; but it is not as well known that number theory has found an enormous number and variety of real-world applications in many different fields." - From the Preface This book is based on the AMS Short Course, The Unreasonable Effectiveness of Number Theory, held in Orono, Maine, in August 1991. This Short Course provided some views into the great breadth of application of number theory outside cryptology and highlighted the power and applicability of number-theoretic ideas. Because number theory is one of the most accessible areas of mathematics, this book will appeal to a general mathematical audience as well as to researchers in other areas of science and engineering who wish to learn how number theory is being applied outside of mathematics. All of the chapters are written by leading specialists in number theory and provides excellent introduction to various applications.

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 : 368 pages
File Size : 45,9 Mb
Release : 2020-03-06
Category : Mathematics
ISBN : 9781000673135

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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.

Handbook of Number Theory I

József Sándor,Dragoslav S. Mitrinovic,Borislav Crstici
Handbook of Number Theory I Book PDF

Author : József Sándor,Dragoslav S. Mitrinovic,Borislav Crstici
Publisher : Springer Science & Business Media
Page : 638 pages
File Size : 41,9 Mb
Release : 2005-11-17
Category : Mathematics
ISBN : 9781402042157

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Handbook of Number Theory I by József Sándor,Dragoslav S. Mitrinovic,Borislav Crstici Pdf

This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.

Number Theory and Geometry: An Introduction to Arithmetic Geometry

Álvaro Lozano-Robledo
Number Theory and Geometry An Introduction to Arithmetic Geometry Book PDF

Author : Álvaro Lozano-Robledo
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 40,5 Mb
Release : 2019-03-21
Category : Arithmetical algebraic geometry
ISBN : 9781470450168

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Number Theory and Geometry: An Introduction to Arithmetic Geometry by Álvaro Lozano-Robledo Pdf

Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.

Computational Number Theory

Abhijit Das
Computational Number Theory Book PDF

Author : Abhijit Das
Publisher : CRC Press
Page : 614 pages
File Size : 53,5 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781482205824

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Computational Number Theory by Abhijit Das Pdf

Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract

Directions in Number Theory

Ellen E. Eischen,Ling Long,Rachel Pries,Katherine E. Stange
Directions in Number Theory Book PDF

Author : Ellen E. Eischen,Ling Long,Rachel Pries,Katherine E. Stange
Publisher : Springer
Page : 339 pages
File Size : 55,7 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9783319309767

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Directions in Number Theory by Ellen E. Eischen,Ling Long,Rachel Pries,Katherine E. Stange Pdf

Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography. The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel research-mentorship model: women at all career stages, from graduate students to senior members of the community, joined forces to work in focused research groups on cutting-edge projects designed and led by experienced researchers. The goals for Women In Numbers 3 were to establish ambitious new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attended the WIN3 workshop, including 15 senior and mid-level faculty, 15 junior faculty and postdocs, and 12 graduate students.

Number Theory in Science and Communication

M.R. Schroeder
Number Theory in Science and Communication Book PDF

Author : M.R. Schroeder
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 43,6 Mb
Release : 2006-01-06
Category : Mathematics
ISBN : 9783540265986

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Number Theory in Science and Communication by M.R. Schroeder Pdf

Number Theory in Science and Communication introductes non-mathematicians to the fascinating and diverse applications of number theory. This best-selling book stresses intuitive understanding rather than abstract theory. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.

Advances In Number Theory And Applied Analysis

Pradip Debnath,Hari M Srivastava,Kalyan Chakraborty,Poom Kumam
Advances In Number Theory And Applied Analysis Book PDF

Author : Pradip Debnath,Hari M Srivastava,Kalyan Chakraborty,Poom Kumam
Publisher : World Scientific
Page : 463 pages
File Size : 54,8 Mb
Release : 2023-05-08
Category : Mathematics
ISBN : 9789811272615

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Advances In Number Theory And Applied Analysis by Pradip Debnath,Hari M Srivastava,Kalyan Chakraborty,Poom Kumam Pdf

Presently, the exploration of the applications of different techniques and tools of number theory and mathematical analysis are extensively prevalent in various areas of engineering, mathematical, physical, biological and statistical sciences. This book will present the most recent developments in these two fields through contributions from eminent scientists and mathematicians worldwide.The book will present the current state of the art development in these two areas through original new contributions and surveys. As such, readers will find several useful tools and techniques to develop their skills and expertise in number theory and applied analysis. New research directions are also indicated in each of the chapters. This book is meant for graduate students, faculty and researchers willing to expand their knowledge in number theory and mathematical analysis. The readers of this book will require minimum prerequisites of analysis, topology, number theory and functional analysis.