Elementary Number Theory

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Author: Kenneth H. Rosen

Publisher: Pearson

ISBN: 0134310055

Category: Mathematics

Page: 768

View: 4152

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps readers explore key concepts and push their understanding to new heights. Computational exercises and computer projects are also available. Reflecting many years of professors' feedback, this edition offers new examples, exercises, and applications, while incorporating advancements and discoveries in number theory made in the past few years.

Elementary Number Theory

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Author: James S. Kraft,Lawrence C. Washington

Publisher: CRC Press

ISBN: 1498702686

Category: Mathematics

Page: 411

View: 1532

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat’s, Euler’s, and Wilson’s theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous cryptographic topics, such as RSA and discrete logarithms, along with recent developments. The book offers many pedagogical features. The "check your understanding" problems scattered throughout the chapters assess whether students have learned essential information. At the end of every chapter, exercises reinforce an understanding of the material. Other exercises introduce new and interesting ideas while computer exercises reflect the kinds of explorations that number theorists often carry out in their research.

Elementary Number Theory with Applications

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Author: Thomas Koshy

Publisher: Academic Press

ISBN: 9780124211711

Category: Mathematics

Page: 716

View: 9560

In revising his well-regarded undergraduate text, Koshy incorporates new sections and exercises dealing with the latest discoveries and reinvigorates the standards in number theory, as well. Elementary Number Theory is the only number theory text that shows the student how modular systems can be employed to create beautiful designs, tying the theory to both geometry and art. This text is ideal for undergraduate mathematics and computer science students, and any Instructor teaching a course in number theory will find the content to be ideally suited for their current curricula.

Elementary Number Theory

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Author: David M. Burton

Publisher: Tata McGraw-Hill Education

ISBN: 9780070616073

Category: Number theory

Page: 434

View: 9348

Friendly Introduction to Number Theory, A: Pearson New International Edition

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Author: Joseph H. Silverman

Publisher: Pearson Higher Ed

ISBN: 1292055413

Category: Mathematics

Page: 472

View: 4672

For one-semester undergraduate courses in Elementary Number Theory. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet—number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.

Lineare Algebra

Einführung, Grundlagen, Übungen

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Author: Howard Anton

Publisher: Springer Verlag

ISBN: 9783827403247

Category: Mathematics

Page: 680

View: 4964

In Ihrer Hand liegt ein Lehrbuch - in sieben englischsprachigen Ausgaben praktisch erprobt - das Sie mit groem didaktischen Geschick, zudem angereichert mit zahlreichen Ubungsaufgaben, in die Grundlagen der linearen Algebra einfuhrt. Kenntnisse der Analysis werden fur das Verstandnis nicht generell vorausgesetzt, sind jedoch fur einige besonders gekennzeichnete Beispiele notig. Padagogisch erfahren, behandelt der Autor grundlegende Beweise im laufenden Text; fur den interessierten Leser jedoch unverzichtbare Beweise finden sich am Ende der entsprechenden Kapitel. Ein weiterer Vorzug des Buches: Die Darstellung der Zusammenhange zwischen den einzelnen Stoffgebieten - linearen Gleichungssystemen, Matrizen, Determinanten, Vektoren, linearen Transformationen und Eigenwerten.

Number Theory

Ramanujan Mathematical Society, January 3-6, 1996, Tiruchirapalli, India

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Author: Michel Waldschmidt,Ramanujan Mathematical Society

Publisher: American Mathematical Soc.

ISBN: 0821806068

Category: Mathematics

Page: 399

View: 3721

To observe the tenth anniversary of the founding of the Ramanujan Mathematical Society, an international conference on Discrete Mathematics and Number Theory was held in January 1996 in Tiruchirapalli, India. This volume contains proceedings from the number theory component of that conference. Papers are divided into four groups: arithmetic algebraic geometry, automorphic forms, elementary and analytic number theory, and transcendental number theory. This work deals with recent progress in current aspects of number theory and covers a wide variety of topics.

Algebraic Number Theory

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Author: H. Koch,Helmut Koch

Publisher: Springer Science & Business Media

ISBN: 9783540630036

Category: Mathematics

Page: 269

View: 8231

This book is an exposition of the main ideas of algebraic number theory. It is written for the non-expert. Therefore, beyond some algebra, there are almost no prerequisites.

Algebraic Number Theory

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Author: Edwin Weiss

Publisher: Courier Corporation

ISBN: 048615436X

Category: Mathematics

Page: 288

View: 8294

Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.

Number Theory in Mathematics Education

Perspectives and Prospects

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Author: Rina Zazkis,Stephen R. Campbell

Publisher: Routledge

ISBN: 1136501436

Category: Education

Page: 268

View: 791

This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education. Topics variously engaged include: *understanding particular concepts related to numerical structure and number theory; *elaborating on the historical and psychological relevance of number theory in concept development; *attaining a smooth transition and extension from pattern recognition to formative principles; *appreciating the aesthetics of number structure; *exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain; *reexamining previously constructed knowledge from a novel angle; *investigating connections between technique and theory; *utilizing computers and calculators as pedagogical tools; and *generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers. Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs. Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.

Meine Zahlen, meine Freunde

Glanzlichter der Zahlentheorie

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Author: Paulo Ribenboim

Publisher: Springer-Verlag

ISBN: 3540879579

Category: Mathematics

Page: 391

View: 3351

Paulo Ribenboim behandelt Zahlen in dieser außergewöhnlichen Sammlung von Übersichtsartikeln wie seine persönlichen Freunde. In leichter und allgemein zugänglicher Sprache berichtet er über Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer!), die klassischen Arbeiten von Gauß über binäre quadratische Formen, Eulers berühmtes primzahlerzeugendes Polynom, irrationale und transzendente Zahlen. Nach dem großen Erfolg von „Die Welt der Primzahlen" ist dies das zweite Buch von Paulo Ribenboim, das in deutscher Sprache erscheint.

A Classical Introduction to Modern Number Theory

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Author: Kenneth Ireland,Michael Rosen

Publisher: Springer Science & Business Media

ISBN: 147572103X

Category: Mathematics

Page: 394

View: 7881

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.

From Natural Numbers to Quaternions

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Author: Jürg Kramer,Anna-Maria von Pippich

Publisher: Springer

ISBN: 3319694294

Category: Mathematics

Page: 277

View: 1003

This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

Number Theory in Function Fields

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Author: Michael Rosen

Publisher: Springer Science & Business Media

ISBN: 9780387953359

Category: Mathematics

Page: 358

View: 1552

This work studies the arithmetic of polynomial rings over finite fields, A=F T], and its relation to elementary number theory, which is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of elementary number theory, it was noticed that Z has many properties in common with A=F T], thereby leading one to suspect that many results which hold for Z have analogues of the ring A. The first few chapters of this book illustrate this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. After presenting the needed foundational material about function fields, later chapters explore a variety of topics, including: the ABC-conjecture, Artin's conjecture on primitive roots, Drinfeld modules, the Brumer-Stark conjecture, class number formulae, and average value theorems.

Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit

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Author: Edward Frenkel

Publisher: Springer-Verlag

ISBN: 3662434210

Category: Mathematics

Page: 317

View: 9133

Number Theory

Diophantine, Computational and Algebraic Aspects. Proceedings of the International Conference held in Eger, Hungary, July 29-August 2, 1996

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Author: Kalman Gyoery,Attila Pethoe,Vera T. Sos

Publisher: Walter de Gruyter

ISBN: 3110809796

Category: Mathematics

Page: 612

View: 901

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

A Pythagorean Introduction to Number Theory

Right Triangles, Sums of Squares, and Arithmetic

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Author: Ramin Takloo-Bighash

Publisher: Springer

ISBN: 3030026043

Category: Mathematics

Page: 279

View: 396

Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.

Learning and Teaching Number Theory

Research in Cognition and Instruction

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Author: Stephen R. Campbell,Rina Zazkis

Publisher: Greenwood Publishing Group

ISBN: 9781567506532

Category: Education

Page: 245

View: 1055

Essential to developing deeper understandings of mathematics, number theory has received scant attention in mathematics education research. This volume redresses this matter and serves as a launch point for further research in this important area.