Fundamentals of Number Theory

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Publisher : Courier Corporation
ISBN 13 : 0486141500
Total Pages : 292 pages
Book Rating : 4.03/5 ( download)

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Book Synopsis Fundamentals of Number Theory by : William J. LeVeque

Download or read book Fundamentals of Number Theory written by William J. LeVeque and published by Courier Corporation. This book was released on 2014-01-05 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect. The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, p-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of e, to mention a few. Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.

Fundamental Number Theory with Applications, Second Edition

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Publisher : CRC Press
ISBN 13 : 9781420066616
Total Pages : 384 pages
Book Rating : 4.17/5 ( download)

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Book Synopsis Fundamental Number Theory with Applications, Second Edition by : Richard A. Mollin

Download or read book Fundamental Number Theory with Applications, Second Edition written by Richard A. Mollin and published by CRC Press. This book was released on 2008-02-21 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Spiral Workbook for Discrete Mathematics

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Publisher : Open SUNY Textbooks
ISBN 13 : 9781942341161
Total Pages : 298 pages
Book Rating : 4.64/5 ( download)

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Book Synopsis A Spiral Workbook for Discrete Mathematics by : Harris Kwong

Download or read book A Spiral Workbook for Discrete Mathematics written by Harris Kwong and published by Open SUNY Textbooks. This book was released on 2015-11-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.

17 Lectures on Fermat Numbers

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Publisher : Springer Science & Business Media
ISBN 13 : 0387218505
Total Pages : 280 pages
Book Rating : 4.02/5 ( download)

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Book Synopsis 17 Lectures on Fermat Numbers by : Michal Krizek

Download or read book 17 Lectures on Fermat Numbers written by Michal Krizek and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.

Fundamentals of Number Theory

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Publisher :
ISBN 13 : 9781635491999
Total Pages : 309 pages
Book Rating : 4.91/5 ( download)

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Book Synopsis Fundamentals of Number Theory by : Emanuel Patterson

Download or read book Fundamentals of Number Theory written by Emanuel Patterson and published by . This book was released on 2017-05 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The branch of pure mathematics that is dedicated to study of integers is called number theory or arithmetic. Number theory studies the properties of prime numbers, rational numbers, and algebraic integers. This book elucidates the concepts and innovative models around prospective developments with respect to number theory. Such selected concepts that redefine this subject have been presented in it. It will provide comprehensive knowledge to the readers. Those in search of information to further their knowledge will be greatly assisted by this textbook. Coherent flow of topics, student-friendly language and extensive use of examples make this book an invaluable source of information.

Number Theory

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Publisher : Academic Press
ISBN 13 : 0080873324
Total Pages : 449 pages
Book Rating : 4.29/5 ( download)

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Book Synopsis Number Theory by :

Download or read book Number Theory written by and published by Academic Press. This book was released on 1986-05-05 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fundamentals of Set and Number Theory

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110550946
Total Pages : 446 pages
Book Rating : 4.48/5 ( download)

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Book Synopsis Fundamentals of Set and Number Theory by : Valeriy K. Zakharov

Download or read book Fundamentals of Set and Number Theory written by Valeriy K. Zakharov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language

Basic Number Theory.

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Publisher : Springer Science & Business Media
ISBN 13 : 3662059789
Total Pages : 332 pages
Book Rating : 4.84/5 ( download)

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Book Synopsis Basic Number Theory. by : Andre Weil

Download or read book Basic Number Theory. written by Andre Weil and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Itpzf}JlOV, li~oxov uoq>ZUJlCJ. 7:WV Al(JX., llpoj1. AE(Jj1. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set ofnotes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by ChevaIley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very welt It contained abrief but essentially com plete account of the main features of c1assfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I inc1uded such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather c10sely at some critical points.

Fundamentals of Discrete Math for Computer Science

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Publisher : Springer Science & Business Media
ISBN 13 : 1447140699
Total Pages : 424 pages
Book Rating : 4.96/5 ( download)

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Book Synopsis Fundamentals of Discrete Math for Computer Science by : Tom Jenkyns

Download or read book Fundamentals of Discrete Math for Computer Science written by Tom Jenkyns and published by Springer Science & Business Media. This book was released on 2012-10-16 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation with the reader through informal commentary and provocative questions. Features: no university-level background in mathematics required; ideally structured for classroom-use and self-study, with modular chapters following ACM curriculum recommendations; describes mathematical processes in an algorithmic manner; contains examples and exercises throughout the text, and highlights the most important concepts in each section; selects examples that demonstrate a practical use for the concept in question.

Fundamentals of Ramsey Theory

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Publisher : CRC Press
ISBN 13 : 0429775911
Total Pages : 256 pages
Book Rating : 4.18/5 ( download)

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Book Synopsis Fundamentals of Ramsey Theory by : Aaron Robertson

Download or read book Fundamentals of Ramsey Theory written by Aaron Robertson and published by CRC Press. This book was released on 2021-06-17 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before. The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises. This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapter The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTS Preface List of Figures List of Tables Symbols 1. Introduction 2. Integer Ramsey Theory 3. Graph Ramsey Theory 4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography Index Biography Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.