Number theory revealed : an introduction

著者

書誌事項

Number theory revealed : an introduction

Andrew Granville

American Mathematical Society, c2019

大学図書館所蔵 件 / 全12件

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注記

Includes bibliographical references and index

収録内容

  • Gauss's Disquisitiones Arithmeticae
  • Preliminary chapter on induction
  • The Euclidean algorithm
  • Congruences
  • The basic algebra of number theory
  • Multiplicative functions
  • The distribution of prime numbers
  • Diophantine problems
  • Power residues
  • Quadratic residues
  • Quadratic equations
  • Square roots and factoring
  • Rational approximations to real numbers
  • Binary quadratic forms

内容説明・目次

内容説明

Number Theory Revealed: An Introduction presents a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations, as well as hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p, Fermat's Last Theorem for polynomials, and modern twists on traditional questions. This book provides careful coverage of all core topics in a standard introductory number theory course with pointers to some exciting further directions. An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach, adding additional material in further chapters and appendices. It is ideal for instructors who wish to tailor a class to their own interests and gives well-prepared students further opportunities to challenge themselves and push beyond core number theory concepts, serving as a springboard to many current themes in mathematics.

目次

Preliminary chapter on induction The Euclidean algorithm Congruences The basic algebra of number theory Multiplicative functions The distribution of prime numbers Diophantine problems Power residues Quadratic residues Quadratic equations Square roots and factoring Rational approximations to real numbers Binary quadratic forms Hints for exercises Recommended further reading Index.

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