## Primality Testing for Beginners

Author: Lasse Rempe-Gillen, Rebecca Waldecker
Publisher: American Mathematical Soc.
ISBN: 0821898833
Category: Mathematics
Page: 240
View: 2639
How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises.

## Applied Number Theory

Author: Harald Niederreiter,Arne Winterhof
Publisher: Springer
ISBN: 3319223216
Category: Mathematics
Page: 442
View: 1386
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.

## Library recommendations for undergraduate mathematics

Author: Lynn Arthur Steen,Mathematical Association of America
Publisher: Mathematical Assn of Amer
ISBN: N.A
Category: Mathematics
Page: 194
View: 505

## For the Learning of Mathematics

Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
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## Guiding Children's Learning of Mathematics

Author: Leonard Kennedy,Steve Tipps,Art Johnson
Publisher: Cengage Learning
ISBN: 049509191X
Page: 576
View: 6883
Trust Kennedy, Tipps and Johnson's market-leading text, GUIDING CHILDREN'S LEARNING OF MATHEMATICS, Eleventh Edition, to give you a thorough introduction to mathematics methods and to provide you with a practical resource guide to teaching pre-school through sixth grade level mathematics. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

## Basic Mathematics for College Students

Author: Alan S. Tussy,R. David Gustafson,Diane Koenig
Publisher: Cengage Learning
ISBN: 1439044422
Category: Mathematics
Page: 944
View: 4097
Offering a uniquely modern, balanced approach, Tussy/Gustafson/Koenig's BASIC MATHEMATICS FOR COLLEGE STUDENTS, Fourth Edition, integrates the best of traditional drill and practice with the best elements of the reform movement. To many developmental math students, mathematics is like a foreign language. They have difficulty translating the words, their meanings, and how they apply to problem solving. Emphasizing the language of mathematics, the text's fully integrated learning process is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically. It blends instructional approaches that include vocabulary, practice, and well-defined pedagogy with an emphasis on reasoning, modeling, communication, and technology skills. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

## Catalog of Copyright Entries. Third Series

1965: January-June
Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
ISBN: N.A
Page: 1394
View: 5895
Includes Part 1, Number 1: Books and Pamphlets, Including Serials and Contributions to Periodicals (January - June)

## (K)ein Gespür für Zahlen

So bekommt man den Durchblick in Mathe
Author: Barbara Oakley
Publisher: MVG Verlag
ISBN: 3864157811
Category: Mathematics
Page: 352
View: 4319
Mathematik versteht man oder eben nicht. Der eine ist dafür natürlich begabt, dem anderen bleibt dieses Fach für immer ein Rätsel. Stimmt nicht, sagt nun Barbara Oakley und zeigt mit ihrem Buch, dass wirklich jeder ein Gespür für Zahlen hat. Mathematik braucht nämlich nicht nur analytisches Denken, sondern auch den kreativen Geist. Denn noch mehr als um Formeln geht es um die Freiheit, einen der vielen möglichen Lösungsansätze zu finden. Der Weg ist das Ziel. Und wie man zum richtigen Ergebnis kommt, ist eine Kunst, die man entwickeln, entdecken und in sich wecken kann. Die Autorin vermittelt eine Vielfalt an Techniken und Werkzeugen, die das Verständnis von Mathematik und Naturwissenschaft grundlegend verbessern. (K)ein Gespür für Zahlen nimmt Ihnen — vor allem wenn Sie sich in Schule, Uni oder Beruf mathematisch oder naturwissenschaftlich beweisen müssen — nicht nur die Grundangst, sondern stärkt Ihren Mut, Ihren mathematischen Fähigkeiten zu vertrauen. So macht Mathe Spaß!

## Integrating Literature in the Content Areas

Author: Sharon Kane
Publisher: Taylor & Francis
ISBN: 1351813390
Category:
Page: N.A
View: 6884
This practical, accessible resource will help future and practicing teachers integrate literature into their middle school or high school classrooms, while also addressing content area standards and improving the literacy skills of their students. Two introductory chapters are followed by five chapters that each cover a different genre: Chapter 3, Informational Books; Chapter 4, Fiction; Chapter 5, Biography, Autobiography, and Memoir; Chapter 6, Poetry; and Chapter 7, How-to and Hands-on Books. Each genre chapter consists of four parts: Part 1: Discusses the genre and how content area teachers can use books within that genre to further content learning and enhance literacy skills. Part 2: Offers hands-on instructional strategies and activities using literature, with activities for use in a variety of disciplines. Part 3: Presents individual author studies (three or four per chapter) with bibliographies and guidelines for using the authors' books in content area courses. Part 4: Features an annotated bibliography of specially selected children and young adult literature for that genre, organized by content area. The annotations provide information about the book, which can be used to prepare booktalks, and teaching ideas for using in a specific content area. Altogether these sections contain more than 600 annotated entries tabbed by subject area, including art, English/language arts, languages and culture, math and technology, music, PE/health, science, and social studies/history.

## An Introduction to Cryptography

Author: Richard A. Mollin
Publisher: CRC Press
ISBN: 9781584881278
Category: Mathematics
Page: 392
View: 7017
INTRODUCTION FOR THE UNINITIATED Heretofore, there has been no suitable introductory book that provides a solid mathematical treatment of cryptography for students with little or no background in number theory. By presenting the necessary mathematics as needed, An Introduction to Cryptography superbly fills that void. Although it is intended for the undergraduate student needing an introduction to the subject of cryptography, it contains enough optional, advanced material to challenge even the most informed reader, and provides the basis for a second course on the subject. Beginning with an overview of the history of cryptography, the material covers the basics of computer arithmetic and explores complexity issues. The author then presents three comprehensive chapters on symmetric-key cryptosystems, public-key cryptosystems, and primality testing. There is an optional chapter on four factoring methods: Pollard's p-1 method, the continued fraction algorithm, the quadratic sieve, and the number field sieve. Another optional chapter contains detailed development of elliptic curve cryptosystems, zero-knowledge, and quantum cryptography. He illustrates all methods with worked examples and includes a full, but uncluttered description of the numerous cryptographic applications. SUSTAINS INTEREST WITH ENGAGING MATERIAL Throughout the book, the author gives a human face to cryptography by including more than 50 biographies of the individuals who helped develop cryptographic concepts. He includes a number of illustrative and motivating examples, as well as optional topics that go beyond the basics presented in the core data. With an extensive index and a list of symbols for easy reference, An Introduction to Cryptography is the essential fundamental text on cryptography.

## The AAAS science book list

a selected and annotated list of science and mathematics books for secondary school students, college undergraduates and nonspecialists
Author: Hilary J. Deason,American Association for the Advancement of Science
ISBN: N.A
Category: Reference
Page: 439
View: 8758

## Mathematical Reviews

Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6872

## Prime Numbers, Friends Who Give Problems

A Trialogue with Papa Paulo
Author: Paulo Ribenboim
Publisher: World Scientific
ISBN: 9814725838
Category: Mathematics
Page: 336
View: 7410
'" Prime Numbers, Friends Who Give Problems is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime numbers, up to the most famous problems. The humorous conversations and the inclusion of a back-story add to the uniqueness of the book. Concepts and results are also explained with great care, making the book accessible to a wide audience. Contents:What are Prime Numbers?Division is Harder than MultiplicationAnother Paulo! Is a Dialogue of Three Possible?How Natural Numbers are Made Out of PrimesTell Me Which is the Largest Prime?Trying Hard to Find PrimesA Formula, A Formula, PleasePaulo Came with a LassoBeautiful Old Elementary ArithmeticThe Old Man Still KnowsCan You Tell Me All About Congruences?Homework CheckedTesting for Primality and FactorizationFermat Numbers are Friendly. Are They Primes?This World is PerfectUnfriendly Numbers from a Friend of Fermat''sPaying My DebtMoney and PrimesSecret MessagesNew Numbers and FunctionsPrinceps GaussGathering ForcesThe After "Math" of GaussPrimes After Dinner: Bad Dreams?Primes in Arithmetic ProgressionSelling PrimesThe Great Prime MysteriesMysteries in Sequences: More But Not AllThe End and the Beginning Readership: College students, high school teachers and beginners interested in number theory and important facts about prime numbers. "'

## Algorithmen - Eine Einführung

Author: Thomas H. Cormen,Charles E. Leiserson,Ronald Rivest,Clifford Stein
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110522012
Category: Computers
Page: 1339
View: 8883
Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.

## Choice

Publication of the Association of College and Research Libraries, a Division of the American Library Association
Author: N.A
Publisher: N.A
ISBN: N.A
Page: N.A
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## Computational Number Theory

Author: Abhijit Das
Publisher: CRC Press
ISBN: 1482205823
Category: Computers
Page: 614
View: 480
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 practitioners of cryptography in industry. Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. It then discusses elliptic curves, primality testing, algorithms for integer factorization, computing discrete logarithms, and methods for sparse linear systems. The text also shows how number-theoretic tools are used in cryptography and cryptanalysis. A dedicated chapter on the application of number theory in public-key cryptography incorporates recent developments in pairing-based cryptography. With an emphasis on implementation issues, the book uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners.

## Finite-Elemente-Methoden

Author: Klaus-Jürgen Bathe
Publisher: Springer Verlag
ISBN: 9783540668060
Category: Technology & Engineering
Page: 1253
View: 9250
Dieses Lehr- und Handbuch behandelt sowohl die elementaren Konzepte als auch die fortgeschrittenen und zukunftsweisenden linearen und nichtlinearen FE-Methoden in Statik, Dynamik, Festkörper- und Fluidmechanik. Es wird sowohl der physikalische als auch der mathematische Hintergrund der Prozeduren ausführlich und verständlich beschrieben. Das Werk enthält eine Vielzahl von ausgearbeiteten Beispielen, Rechnerübungen und Programmlisten. Als Übersetzung eines erfolgreichen amerikanischen Lehrbuchs hat es sich in zwei Auflagen auch bei den deutschsprachigen Ingenieuren etabliert. Die umfangreichen Änderungen gegenüber der Vorauflage innerhalb aller Kapitel - vor allem aber der fortgeschrittenen - spiegeln die rasche Entwicklung innerhalb des letzten Jahrzehnts auf diesem Gebiet wieder.

## Basic Math and Pre-Algebra For Dummies

Author: Mark Zegarelli
Publisher: John Wiley & Sons
ISBN: 1118791991
Category: Mathematics
Page: 384
View: 5437
Basic Math & Pre-Algebra For Dummies, 2nd Edition (9781118791981) is now being published as Basic Math & Pre-Algebra For Dummies, 2nd Edition (9781119293637). While this version features an older Dummies cover and design, the content is the same as the new release and should not be considered a different product. Tips for simplifying tricky basic math and pre-algebra operations Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations. Explanations and practical examples that mirror today's teaching methods Relevant cultural vernacular and references Standard For Dummies materials that match the current standard and design Basic Math & Pre-Algebra For Dummies takes the intimidation out of tricky operations and helps you get ready for algebra!

Author: N.A
Publisher: N.A
ISBN: N.A
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Page: N.A
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