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Author : C. P. Smith
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (1 download)
Download or read book On Representations of a Positive Integer as a Sum of Squares written by C. P. Smith and published by . This book was released on 1959 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : E. Grosswald
Publisher : Springer Science & Business Media
ISBN 13 : 1461385660
Total Pages : 262 pages
Book Rating : 4.4/5 (613 download)
Download or read book Representations of Integers as Sums of Squares written by E. Grosswald and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the academic year 1980-1981 I was teaching at the Technion-the Israeli Institute of Technology-in Haifa. The audience was small, but con sisted of particularly gifted and eager listeners; unfortunately, their back ground varied widely. What could one offer such an audience, so as to do justice to all of them? I decided to discuss representations of natural integers as sums of squares, starting on the most elementary level, but with the inten tion of pushing ahead as far as possible in some of the different directions that offered themselves (quadratic forms, theory of genera, generalizations and modern developments, etc.), according to the interests of the audience. A few weeks after the start of the academic year I received a letter from Professor Gian-Carlo Rota, with the suggestion that I submit a manuscript for the Encyclopedia of Mathematical Sciences under his editorship. I answered that I did not have a ready manuscript to offer, but that I could use my notes on representations of integers by sums of squares as the basis for one. Indeed, about that time I had already started thinking about the possibility of such a book and had, in fact, quite precise ideas about the kind of book I wanted it to be.
Author : Carlos J. Moreno
Publisher : CRC Press
ISBN 13 : 1420057235
Total Pages : 363 pages
Book Rating : 4.4/5 (2 download)
Download or read book Sums of Squares of Integers written by Carlos J. Moreno and published by CRC Press. This book was released on 2005-12-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's element
Author : Carl Douglas Olds
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.F/5 ( download)
Download or read book On the Number of Representations of the Square of an Integer as the Sum of an Odd Number of Squares written by Carl Douglas Olds and published by . This book was released on 1940 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carlos J. Moreno
Publisher : CRC Press
ISBN 13 : 1584884568
Total Pages : 368 pages
Book Rating : 4.5/5 (848 download)
Download or read book Sums of Squares of Integers written by Carlos J. Moreno and published by CRC Press. This book was released on 2005-12-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
Author : Abdul-Aziz K. Nafoosi
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.:/5 (487 download)
Download or read book Representation of Any Large Number as the Sum of Thirteen Squares of Positive Integers in Arithmetical Prgression written by Abdul-Aziz K. Nafoosi and published by . This book was released on 1960 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Manwah Lilian Wong
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)
Download or read book On the Representation of an Integer as the Sum of Squares written by Manwah Lilian Wong and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Melvyn B. Nathanson
Publisher : Springer Science & Business Media
ISBN 13 : 0387227385
Total Pages : 518 pages
Book Rating : 4.3/5 (872 download)
Download or read book Elementary Methods in Number Theory written by Melvyn B. Nathanson and published by Springer Science & Business Media. This book was released on 2008-01-11 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With many examples and exercises, and only requiring knowledge of a little calculus and algebra, this book will suit individuals with imagination and interest in following a mathematical argument to its conclusion.
Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1107159385
Total Pages : 491 pages
Book Rating : 4.1/5 (71 download)
Download or read book Elliptic and Modular Functions from Gauss to Dedekind to Hecke written by Ranjan Roy and published by Cambridge University Press. This book was released on 2017-04-18 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.
Author : W.A. Coppel
Publisher : Springer Science & Business Media
ISBN 13 : 0387894853
Total Pages : 620 pages
Book Rating : 4.3/5 (878 download)
Download or read book Number Theory written by W.A. Coppel and published by Springer Science & Business Media. This book was released on 2009-08-12 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.
Author : Leonard Eugene Dickson
Publisher : American Mathematical Soc.
ISBN 13 : 9780821819357
Total Pages : 830 pages
Book Rating : 4.8/5 (193 download)
Download or read book History of the Theory of Numbers written by Leonard Eugene Dickson and published by American Mathematical Soc.. This book was released on 1999 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kwok Y. Lam
Publisher : Birkhäuser
ISBN 13 : 3034882955
Total Pages : 376 pages
Book Rating : 4.0/5 (348 download)
Download or read book Cryptography and Computational Number Theory written by Kwok Y. Lam and published by Birkhäuser. This book was released on 2013-03-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer security as well as in the design and implementation of number theoretic cryptosystems and other related areas. Another goal of the meeting was to stimulate collaboration and more active interaction between mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government.
Author : G. H. Hardy
Publisher : Oxford University Press
ISBN 13 : 0199219869
Total Pages : 645 pages
Book Rating : 4.1/5 (992 download)
Download or read book An Introduction to the Theory of Numbers written by G. H. Hardy and published by Oxford University Press. This book was released on 2008-07-31 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.
Author : Thomas Koshy
Publisher : Elsevier
ISBN 13 : 0080547095
Total Pages : 801 pages
Book Rating : 4.0/5 (85 download)
Download or read book Elementary Number Theory with Applications written by Thomas Koshy and published by Elsevier. This book was released on 2007-05-08 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East
Author : David Burton
Publisher : McGraw Hill
ISBN 13 : 0077145089
Total Pages : 453 pages
Book Rating : 4.0/5 (771 download)
Download or read book EBOOK: Elementary Number Theory written by David Burton and published by McGraw Hill. This book was released on 2010-06-16 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton’s engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.
Author : Stanley Rabinowitz
Publisher : MathPro Press
ISBN 13 : 9780962640124
Total Pages : 548 pages
Book Rating : 4.6/5 (41 download)
Download or read book Index to Mathematical Problems, 1975-1979 written by Stanley Rabinowitz and published by MathPro Press. This book was released on 1999 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Guy
Publisher : Springer Science & Business Media
ISBN 13 : 0387266771
Total Pages : 455 pages
Book Rating : 4.3/5 (872 download)
Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
