数论导引
Author:
Publisher:
Published: 2007
Total Pages: 435
ISBN-13: 9787115156112
DOWNLOAD EBOOK →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。
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The Theory of Numbers
Author: Andrew Adler
Publisher: Jones & Bartlett Publishers
Published: 1995
Total Pages: 424
ISBN-13:
DOWNLOAD EBOOK →An Illustrated Theory of Numbers
Author: Martin H. Weissman
Publisher: American Mathematical Soc.
Published: 2020-09-15
Total Pages: 341
ISBN-13: 1470463717
DOWNLOAD EBOOK →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.
Topics from the Theory of Numbers
Author: Emil Grosswald
Publisher: Springer Science & Business Media
Published: 2010-02-23
Total Pages: 336
ISBN-13: 0817648380
DOWNLOAD EBOOK →Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate.
Recreations in the Theory of Numbers
Author: Albert H. Beiler
Publisher: Courier Corporation
Published: 1964-01-01
Total Pages: 383
ISBN-13: 0486210960
DOWNLOAD EBOOK →Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.
Algebraic Theory of Numbers
Author: Hermann Weyl
Publisher: Princeton University Press
Published: 1998
Total Pages: 244
ISBN-13: 9780691059174
DOWNLOAD EBOOK →This work explores the fundamental concepts in arithmetic. It begins with the definitions and properties of algebraic fields. The theory of divisibility is then discussed. There follows an introduction to p-adic numbers and then culminates with an extensive examination of algebraic number fields.
The Theory of Algebraic Numbers: Second Edition
Author: Harry Pollard
Publisher: American Mathematical Soc.
Published: 1975-12-31
Total Pages: 162
ISBN-13: 1614440093
DOWNLOAD EBOOK →This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Elements of the Theory of Numbers
Author: Joseph B. Dence
Publisher: Academic Press
Published: 1999-01-20
Total Pages: 542
ISBN-13: 9780122091308
DOWNLOAD EBOOK →Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors have created a two-pronged pedagogical approach that integrates analysis and algebra with classical number theory. Making greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses, this pedagogical approach helps to instill in the minds of the students the idea of the unity of mathematics. Elements of the Theory of Numbers is a superb summary of classical material as well as allowing the reader to take a look at the exciting role of analysis and algebra in number theory. * In-depth coverage of classical number theory * Thorough discussion of the theory of groups and rings * Includes application of Taylor polynomials * Contains more advanced material than other texts * Illustrates the results of a theorem with an example * Excellent presentation of the standard computational exercises * Nearly 1000 problems--many are proof-oriented, several others require the writing of computer programs to complete the computations * Clear and well-motivated presentation * Provides historical references noting distinguished number theory luminaries such as Euclid, de Fermat, Hilbert, Brun, and Lehmer, to name a few * Annotated bibliographies appear at the end of all of the chapters
A Selection of Problems in the Theory of Numbers
Author: Waclaw Sierpinski
Publisher: Elsevier
Published: 2014-05-16
Total Pages: 127
ISBN-13: 1483151468
DOWNLOAD EBOOK →A Selection of Problems in the Theory of Numbers focuses on mathematical problems within the boundaries of geometry and arithmetic, including an introduction to prime numbers. This book discusses the conjecture of Goldbach; hypothesis of Gilbreath; decomposition of a natural number into prime factors; simple theorem of Fermat; and Lagrange's theorem. The decomposition of a prime number into the sum of two squares; quadratic residues; Mersenne numbers; solution of equations in prime numbers; and magic squares formed from prime numbers are also elaborated in this text. This publication is a good reference for students majoring in mathematics, specifically on arithmetic and geometry.
An Introduction to the Theory of Numbers
