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e-Book Introduction to the Theory of Numbers (Dover Books on Mathematics) download

e-Book Introduction to the Theory of Numbers (Dover Books on Mathematics) download

by Mathematics,Harold N. Shapiro

ISBN: 0486466698
ISBN13: 978-0486466699
Language: English
Publisher: Dover Publications (August 8, 2008)
Pages: 480
Category: Mathematics
Subategory: Math Science

ePub size: 1186 kb
Fb2 size: 1725 kb
DJVU size: 1703 kb
Rating: 4.6
Votes: 487
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But in the last years, I have realised that there are a handful of affordable introductions to number theory, number theoy for dummies like me (for example Elements of Number Theory, or LeVeque's Elementary Theory of Numbers (Dover Books on Mathematics)). This book is not exactly that kind, but I must declare that it is one that has much to admire and to enjoy, even at a distance.

The Holy Grail of Number Theory George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text Number Theory (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field - number theory.

Number Theory (Dover Books on Mathematics).

Published August 8th 2008 by Dover Publications (first published January 1983).

Selected chapters, sections, and exercises are appropriate for undergraduate courses. The first Starting with the fundamentals of number theory, this text advances to an intermediate level. Published August 8th 2008 by Dover Publications (first published January 1983). Introduction to the Theory of Numbers (Dover Books on Mathematics).

Dover books on mathematics include authors Paul J. Cohen ( Set Theory and the Continuum Hypothesis ), Alfred . Of all the technical areas in which we publish, Dover is most recognized for our magnificent mathematics list. Cohen ( Set Theory and the Continuum Hypothesis ), Alfred Tarski ( Undecidable Theories ), Gary Chartrand ( Introductory Graph Theory ), Hermann Weyl ( The Concept of a Riemann Surface ), Shlomo Sternberg ( Dynamical Systems ), and multiple math book works by C. R. Wylie in geometry. And Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers remains one of the most widely used textbooks we have ever published.

First Course in Mathematical Logic by Patrick Suppes In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presentation and context to permit relatively easy comprehension.

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.

Free mathematics textbooks, monographs, lecture notes, and other documents: algebra .

Free mathematics textbooks, monographs, lecture notes, and other documents: algebra, analysis, discrete mathematics, geometry, topology, linear algebra, probability, statistics. Introduction to the Theory of Dissipative Systems Constantin I. Chueshov ACTA, Published in 2002, 419 pages.

An Introduction to the Theory of Numbers is a classic book in the field of number theory, by G. H. Hardy and E. M. Wright. The book grew out of a series of lectures by Hardy and Wright and was first published in 1938. List of important publications in mathematics. Compare prices (2). Compare prices.

Starting with the fundamentals of number theory, this text advances to an intermediate level. Author Harold N. Shapiro, Professor Emeritus of Mathematics at New York University's Courant Institute, addresses this treatment toward advanced undergraduates and graduate students. Selected chapters, sections, and exercises are appropriate for undergraduate courses.The first five chapters focus on the basic material of number theory, employing special problems, some of which are of historical interest. Succeeding chapters explore evolutions from the notion of congruence, examine a variety of applications related to counting problems, and develop the roots of number theory. Two "do-it-yourself" chapters offer readers the chance to carry out small-scale mathematical investigations that involve material covered in previous chapters.
Comments:
Malak
Andrew Wile's said that the first text he reaches for when first getting acquainted with specific area of number theory is Davenport's "Higher Arithmetic." I think many feel similarly and that book is coincidentally the text that I first used.

However, as I learned more number theory, beyond Davenport's work, it has always struck me how unfortunate it was that Davenport didn't discuss things like Bertrand's postulate or any of the elementary results using calculus of a real variable. As a first go at these topics, Shapiro's work is unparalleled in my opinion - I simply can't recommend it highly enough. As I've pointed out in other reviews, no amount of mathematical rigor can substitute for clarity of thought and clarity of prose. Though H. N. Shapiro seems to have moved away from number theory in recent years (in terms of publications), it's clear that he was, minimally, a dedicated student of the subject and uncommonly able see all the ideas with 20/20 vision, through what is often encumbered formalisms. Many proofs and theoretical explanations I have not seen written about in such a clear manner anywhere else, undoubtedly.

In addition to the quality of writing, I also want to point out the excellent and quite rare selection of topics. There are discussions of many things other books ignore at an elementary level, such as the divisor function for polynomials and Dirichlet's divisor problem for arithmetic progressions. Also, in one place are the three most notable proofs of Bertrand's postulate with an interesting discussion on how they relate. There are also some nice and surprisingly broad discussions of algebraic topics.

Again, this is a fantastic book that seems to suffer from undue neglect.

Agamaginn
Die Zahlen...yes, maybe it was God himself who created them, as Kronecker once declared. I always felt a kind of religious fear of (interger) numbers. But in the last years, I have realised that there are a handful of affordable introductions to number theory, number theoy for dummies like me (for example Pettofrezzo-Byrkit's Elements of Number Theory, or LeVeque's Elementary Theory of Numbers (Dover Books on Mathematics)). This book is not exactly that kind, but I must declare that it is one that has much to admire and to enjoy, even at a distance. The author is a wellknown researcher and scholar, his Thesis advisor was Emil Artin. But he has avoided to cite his own work (for example, there is no mention in the book to his celebrated Tauberian theorem, which appears in Apostol's Introduction to Analytic Number Theory (Undergraduate Texts in Mathematics)) section 4.6). Erudition, elegance, freshnesh and an incredible amount of originality are offered here in spades. Starting from such simple things as GCD and unique factorization, the book leads us to arithmetic functions and shows that they form a valuated integral domain, where convolution is the product. In this context, the properties of some conspicuous arithmetic functions (like Euler's phi or Moebius' mu) seem no more extravagant oddities, but just pearls on a crown, on a ring. But there is no overkill. The algebraic hardcore is always under control, and the link with the glorious history of number theory is permanent. Of course, a little group theory is used for better understanding of congruences and primes in arithmetic progression. The chinese remainders theorem is offered in full but crystal clear generality. Simultaneous polynomial congruences are then introduced. A chapter on quadratic congruences includes two proofs of the reciprocity law. The rest of the book gives an elmentary proof of the prime number theorem and the Dirichlet theorem on primes in an arithmeic progression, which is proved in two different ways. Another jewel is the proof of a Theorem by I. Shur on the existence of primes in "integer intervals of arbitrry lenght".

Falya
Although I bought this gem years ago at a Chicago Borders (oh, Borders...), I plan to buy a backup or two through Amazon in the near future -- even while my copy, though well-used, is in pristine shape. That's just how I treat my most treasured books, and this is indeed among them. The other reviews here splendidly articulate all of this work's virtues, so I needn't rehearse them again; let me just reinforce the other reviewers' comments by stating that this work does an excellent job of carrying its student along from simple fundamentals, through all of the elements of number theory, into an amazingly thorough and comprehensible rendering of the Prime Number Theorem. Every theorem is deduced with perfect clarity, and every example is useful. I cannot recommend this book highly enough: if you are interested in studying number theory beyond the basics (well-covered in works by LeVeque, Dudley and Andrews), but do not plan on postdoctoral work in mathematics (i.e. if mathematics is recreational and aesthetic), this is for you.

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