Sums of Squares of Square-free Numbers
| Author | : |
| Publisher | : |
| Total Pages | : |
| Release | : 1972 |
| Genre | : |
| ISBN | : |
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Sums Of Squares Of Square Free Numbers PDF Download
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Sums of Squares of Integers
| Author | : Carlos J. Moreno |
| Publisher | : CRC Press |
| Total Pages | : 363 |
| Release | : 2005-12-09 |
| Genre | : Computers |
| ISBN | : 1420057235 |
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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
Representations of Integers as Sums of Squares
| Author | : E. Grosswald |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 262 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461385660 |
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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.
Sums of Squares of Square-free Numbers
| Author | : Michael Keates |
| Publisher | : |
| Total Pages | : |
| Release | : 1972 |
| Genre | : |
| ISBN | : |
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Number Theory
| Author | : Wenpeng Zhang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 247 |
| Release | : 2006-06-05 |
| Genre | : Mathematics |
| ISBN | : 0387308296 |
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This book collects survey and research papers on various topics in number theory. Although the topics and descriptive details appear varied, they are unified by two underlying principles: first, readability, and second, a smooth transition from traditional approaches to modern ones. Thus, on one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated.
Elementary Number Theory with Applications
| Author | : Thomas Koshy |
| Publisher | : Elsevier |
| Total Pages | : 801 |
| Release | : 2007-05-08 |
| Genre | : Mathematics |
| ISBN | : 0080547095 |
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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
From Polynomials to Sums of Squares
| Author | : T.H Jackson |
| Publisher | : CRC Press |
| Total Pages | : 200 |
| Release | : 1995-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780750303293 |
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From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is complemented with illustrations that feature specific examples. Other than familiarity with complex numbers and some elementary number theory, very little mathematical prerequisites are needed. The accompanying disk enables readers to explore the subject further by removing the tedium of doing calculations by hand. Throughout the text there are practical activities involving the computer.
Number Theory
| Author | : George E. Andrews |
| Publisher | : Courier Corporation |
| Total Pages | : 292 |
| Release | : 2012-04-30 |
| Genre | : Mathematics |
| ISBN | : 0486135101 |
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Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Mathematical Constants
| Author | : Steven R. Finch |
| Publisher | : Cambridge University Press |
| Total Pages | : 634 |
| Release | : 2003-08-18 |
| Genre | : Mathematics |
| ISBN | : 9780521818056 |
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Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Elementary Number Theory with Programming
| Author | : Marty Lewinter |
| Publisher | : John Wiley & Sons |
| Total Pages | : 240 |
| Release | : 2015-05-08 |
| Genre | : Mathematics |
| ISBN | : 1119062772 |
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A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area. Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes: Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas Select solutions to the chapter exercises in an appendix Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set A related website with links to select exercises An Instructor’s Solutions Manual available on a companion website Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.
