elementary number theory with programming

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Elementary Number Theory With Programming

Author : Marty Lewinter
ISBN : 9781119062769
Genre : Mathematics
File Size : 42. 2 MB
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Filling a much-needed gap in the current literature, this book expertly bridges the subjects of number theory and programming and features a multitude of examples and programming exercises in each chapter. It provides an introduction to elementary number theory with fundamental coverage of computer programming and is appropriate for students of mathematics and computer science alike who need to become acquainted with the most famous theorems, problems, and concepts of number theory. In addition, the authors provide a comprehensive presentation of the methodology and applications for readers with various levels of experience, and while theorems are provided, the authors avoid the standard theorem/proof format to aid in reader comprehension. The book features sample programs and research challenges at the end of each chapter for readers to work through, as well as an appendix that provides select answers to the chapter exercises. The authors also maintain a supplementary material website that provides additional working examples of the computer programs. Topical coverage includes: special numbers; Fibonacci sequence, primes, and the Pell equation; Pascal's triangle; divisors and prime decomposition; modular arithmetic; number theoretic functions; Euler's Phi function; sums and partitions; and cryptography. Prerequisites include basic algebra and some knowledge of any computer language.

Elementary Number Theory Cryptography And Codes

Author : M. Welleda Baldoni
ISBN : 3540692002
Genre : Mathematics
File Size : 57. 29 MB
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In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.

Elementary Number Theory And Its Applications

Author : Kenneth H. Rosen
ISBN : 0321237072
Genre : Mathematics
File Size : 77. 9 MB
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Elementary Number Theory and Its Applicationsis noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises. The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years.

Elementary Number Theory

Author : James K. Strayer
ISBN : 9781478610403
Genre : Mathematics
File Size : 79. 55 MB
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In this student-friendly text, Strayer presents all of the topics necessary for a first course in number theory. Additionally, chapters on primitive roots, Diophantine equations, and continued fractions allow instructors the flexibility to tailor the material to meet their own classroom needs. Each chapter concludes with seven Student Projects, one of which always involves programming a calculator or computer. All of the projects not only engage students in solving number-theoretical problems but also help familiarize them with the relevant mathematical literature.

Algorithmic Cryptanalysis

Author : Antoine Joux
ISBN : 1420070037
Genre : Computers
File Size : 76. 50 MB
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Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program. Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applications. The final part addresses more sophisticated cryptographic applications, including LFSR-based stream ciphers and index calculus methods. Accounting for the impact of current computer architectures, this book explores the algorithmic and implementation aspects of cryptanalysis methods. It can serve as a handbook of algorithmic methods for cryptographers as well as a textbook for undergraduate and graduate courses on cryptanalysis and cryptography.

Elementary Number Theory

Author : Underwood Dudley
ISBN : 9780486134871
Genre : Mathematics
File Size : 82. 99 MB
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Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition.

Primes And Programming

Author : P. J. Giblin
ISBN : 0521409888
Genre : Mathematics
File Size : 46. 71 MB
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Peter Giblin describes, in the context of an introduction to the theory of numbers, some of the more elementary methods for factorization and primality testing; that is, methods independent of a knowledge of other areas of mathematics. Indeed everything is developed from scratch so the mathematical prerequisites are minimal. An essential feature of the book is the large number of computer programs (written in Pascal) and a wealth of computational exercises and projects, in addition to more usual theory exercises. The theoretical development includes continued fractions and quadratic residues, directed always towards the two fundamental problems of primality testing and factorization. There is time, all the same, to include a number of topics and projects of a purely "recreational" nature.

Untersuchungen Ber H Here Arithmetik

Author : Carl Friedrich Gauss
ISBN : 9780821842133
Genre : Mathematics
File Size : 62. 25 MB
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In this volume are included all of Gauss's number-theoretic works: his masterpiece, Disquisitiones Arithmeticae, published when Gauss was only 25 years old; several papers published during the ensuing 31 years; and papers taken from material found in Gauss's handwriting after his death. These papers include a fourth, fifth, and sixth proof of the Quadratic Reciprocity Law, researches on biquadratic residues, quadratic forms, and other topics. This reprint of the German translation from Latin of the second edition published in 1889 includes an extensive appendix and concludes with a commentary on the papers (with references, where appropriate, to the relevant pages of the Disquisitiones).

Special Relativity

Author : Nicholas M.J. Woodhouse
ISBN : 9783540466765
Genre : Science
File Size : 27. 82 MB
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Routineaufgaben Mit Python Automatisieren

Author : Al Sweigart
ISBN : 9783864919930
Genre : Computers
File Size : 42. 12 MB
Format : PDF, ePub
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Wenn Sie jemals Stunden damit verbracht haben, Dateien umzubenennen oder Hunderte von Tabelleneinträgen zu aktualisieren, dann wissen Sie, wie stumpfsinnig manche Tätigkeiten sein können. Wie wäre es, den Computer dazu zu bringen, diese Arbeiten zu übernehmen? In diesem Buch lernen Sie, wie Sie mit Python Aufgaben in Sekundenschnelle erledigen können, die sonst viel Zeit in Anspruch nehmen würden. Programmiererfahrung brauchen Sie dazu nicht: Wenn Sie einmal die Grundlagen gemeistert haben, werden Sie Python-Programme schreiben, die automatisch alle möglichen praktischen Aufgaben für Sie abarbeiten: • eine oder eine Vielzahl von Dateien nach Texten durchsuchen • Dateien und Ordner erzeugen, aktualisieren, verschieben und umbenennen • das Web durchsuchen und Inhalte herunterladen • Excel-Dateien aktualisieren und formatieren • PDF-Dateien teilen, zusammenfügen, mit Wasserzeichen versehen und verschlüsseln • Erinnerungsmails und Textnachrichten verschicken • Online-Formulare ausfüllen Schritt-für-Schritt-Anleitungen führen Sie durch jedes Programm und Übungsaufgaben am Ende jedes Kapitels fordern Sie dazu auf, die Programme zu verbessern und Ihre Fähigkeiten auf ähnliche Problemstellungen zu richten. Verschwenden Sie nicht Ihre Zeit mit Aufgaben, die auch ein gut dressierter Affe erledigen könnte. Bringen Sie Ihren Computer dazu, die langweilige Arbeit zu machen!

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