Solved and unsolved problems in number theory
Posted By: math007 | Date: 10 Nov 2007 02:56 | Comments: 4



Daniel Shanks, "Solved and unsolved problems in number theory"
Publisher: Chelsea Pub. Co | Pages: 258 | ISBN: 0828402973 | DjVu | 3 MB

The investigation of three problems, that of perfect numbers, that of periodic decimals, and that of Pythagorean numbers has given rise to much of elementary number theory, and the author shows how each result gives rise to further results and conjectures. He treats not only results and theorems ("solved problems") but also questions that are still open and conjectures ("unsolved problems"), making this a most exciting and unusual treatment. The author, a past editor of Mathematics of Computation, presents research done in the fifteen years between the first and second editions, with emphasis on results that were achieved with the aid of computers. The volume includes a substantial Bibliography.

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Elementary Number Theory
Posted By: tot167 | Date: 17 Feb 2008 13:28 | Comments: 1


Gareth A. Jones, Josephine M. Jones " Elementary Number Theory"
Springer | 1998-07-31 | ISBN:3540761977 | 200 pages | Djvu | 4,2 Mb


This book gives an undergraduate-level introduction to Number Theory, with the emphasis on fully explained proofs and examples; exercises (with solutions) are integrated into the text. The first few chapters, covering divisibility, prime numbers and modular arithmetic, assume only basic school algebra, and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares; in particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

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Elementary Number Theory
Posted By: tot167 | Date: 13 May 2008 09:47 | Comments: 1


Peter Hackman “Elementary Number Theory"
Linköpings universitet, Sweden | 2007 | ISBN: N/A | 411 pages | PDF | 1,19 Mb

Interesting and partly non-traditional book in elementary number theory for undergraduates in mathematics and computer science with some background in general algebra. A lot of material is included here, some topics are unusual. Autor “strongly advocate the use of computers as a means of generating and investigating examples” but he points that “this text is not conceived as a book on computational number theory”. Various original (more elegant and concise) proofs of theorems are presented in this book, found by the author himself…

Contents (chapters):

Preface
A Divisibility, Unique Factorization
B Congruences. The CRT (Chinese Remainder Theorem)
C Primitive Roots
D Quadratic Reciprocity
E Some Diophantine Problems
F Multiplicative Functions
G Continued Fractions
H “QCF” and Pell’s Equation
J Special Topics
K Z[i], Other Number Rings
L Primality and Factorization
Bibliography
Tables

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Elementary Number Theory, Group Theory and Ramanujan Graphs
(London Mathematical Society Student Texts)
(Paperback)
by Giuliana Davidoff (Author), Peter Sarnak (Author), Alain Valette



إقتباس:

Elementary Number Theory
(Hardcover)
by David M. Burton

Editorial Reviews

Product Description
This text provides a simple account of classical number theory, as well as some of the historical background in which the subject evolved. It is intended for use in a one-semester, undergraduate number theory course taken primarily by mathematics majors and students preparing to be secondary school teachers. Although the text was written with this audience in mind, very few formal prerequisites are required. Much of the text can be read by students with a sound background in high school mathematics.

Hardcover: 432 pages
Publisher: McGraw-Hill Science/Engineering/Math; 5 edition
(July 19, 2001)
Language: English
ISBN-10: 0072325690
ISBN-13: 978-0072325690
Product Dimensions: 9.3 x 6.6 x 0.9 inches
Shipping Weight: 1.6 pounds

Elementary Number Theory
(Hardcover)
by David M. Burton


Editorial Reviews

Product Description
Elementary Number Theory, Sixth 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.


Product Details

Hardcover: 448 pages
Publisher: McGraw-Hill Science/Engineering/Math; 6 edition
(September 27, 2005)
Language: English
ISBN-10: 0073051888
ISBN-13: 978-0073051888
Product Dimensions: 9.3 x 6 x 0.9 inches
Shipping Weight: 1.6 pounds

Elementary Methods in Number Theory
by Melvyn B. Nathanson

Editorial Reviews

Product Description
Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erdös-Selberg elementary proof of the prime number theorem, and Dirichlets theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Warings problems for polynomials, Liouvilles method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets.

Book Info
Discusses divisibility, prime numbers, and congruences and provides an introduction to Fourier analysis on finite abelian groups. Discusses the abc conjecture and its consequences in elementary number theory. DLC: Number theory.


Product Details

Hardcover: 440 pages
Publisher: Springer; 1 edition
(December 21, 1999)
Language: English
ISBN-10: 0387989129
ISBN-13: 978-0387989129
Product Dimensions: 9.4 x 6.4 x 1.6 inches
Shipping Weight: 2 pounds



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Elementary Number Theory in Nine Chapters, Second Edition
by James J. Tattersall

Editorial Reviews

Review
"Every chapter has a remarkable collection of exercises of various degrees of difficulty and contains a wealth of historical information, which makes interesting reading." Mathematical Reviews

The book is easy to read...The feature of the book that pleased me the most is the number of problems that are included. Not only does each section end with a large selection of problems, but each chapter also carries a number of supplementary exercises.
Michele Intermont

Product Description
Intended to serve as a one-semester introductory course in number theory, this second edition has been revised throughout. In particular, the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler. In addition, a wealth of new exercises have been included to fully illustrate the properties of numbers and concepts developed in the text. The book will serve as a stimulating introduction for students new to number theory, regardless of their background. First Edition Hb (1999) 0-521-58503-1 First Edition Pb (1999) 0-521-58531-7

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