数论导引
Author | : |
Publisher | : |
Total Pages | : 435 |
Release | : 2007 |
Genre | : Number theory |
ISBN | : 9787115156112 |
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本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download An Introduction To The Theory Of Numbers PDF full book. Access full book title An Introduction To The Theory Of Numbers.
Author | : |
Publisher | : |
Total Pages | : 435 |
Release | : 2007 |
Genre | : Number theory |
ISBN | : 9787115156112 |
本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。
Author | : Leo Moser |
Publisher | : The Trillia Group |
Total Pages | : 95 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 1931705011 |
"This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text."--Publisher's description
Author | : Ivan Niven |
Publisher | : |
Total Pages | : 280 |
Release | : 1968 |
Genre | : Number theory |
ISBN | : |
Author | : Martin H. Weissman |
Publisher | : American Mathematical Soc. |
Total Pages | : 341 |
Release | : 2020-09-15 |
Genre | : Education |
ISBN | : 1470463717 |
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
Author | : Ivan Niven |
Publisher | : |
Total Pages | : 288 |
Release | : 1993 |
Genre | : Number theory |
ISBN | : 9780852266304 |
Author | : Andrew Adler |
Publisher | : Jones & Bartlett Publishers |
Total Pages | : 424 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : |
Author | : Oystein Ore |
Publisher | : Courier Corporation |
Total Pages | : 400 |
Release | : 2012-07-06 |
Genre | : Mathematics |
ISBN | : 0486136434 |
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Author | : G. H. Hardy |
Publisher | : Oxford University Press |
Total Pages | : 645 |
Release | : 2008-07-31 |
Genre | : Mathematics |
ISBN | : 0199219869 |
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 | : K. Ireland |
Publisher | : Springer Science & Business Media |
Total Pages | : 355 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475717792 |
This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.
Author | : Álvaro Lozano-Robledo |
Publisher | : American Mathematical Soc. |
Total Pages | : 488 |
Release | : 2019-03-21 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 147045016X |
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.