Mathematics experiments

著者

    • Li, Shangzhi

書誌事項

Mathematics experiments

Shangzhi Li ... [et al.] ; [with a foreword by Weinan E.]

World Scientific, c2003

  • : hard
  • : pbk

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注記

"English translation from the Chinese edition Experiments in mathematics by Li Shangzhi et al., c1999, Higher education Press"--T.p. verso

Includes bibliographical references (p. 217)

内容説明・目次

巻冊次

: hard ISBN 9789812380494

内容説明

Owing to the advent of computers, experiments are becoming an increasingly important part of mathematics. This book provides guidance to students doing experiments in mathematics. The aim is to stimulate interest in mathematics through examples and experiments.Each experiment in the book starts with an interesting problem. The students are expected to work with these problems on computers, try to find the solutions themselves, and experience the scientific exploration in the process.The problems which the authors have chosen cover a wide spectrum in mathematics, ranging from calculus, number theory, coding and probability to geometry and chaos. They are introduced in a simple way and yet show great depth. The discussions are thorough but not lengthy.This book is useful not only to mathematics students, but also to students in all areas of sciences who are interested in learning some of the mathematical tools. It provides a hands-on approach to the most fundamental issues in mathematics — an approach which may help to revolutionize the teaching of mathematics.

目次

  • Fundamentals of calculus
  • how to calculate ?
  • best fractional approximation
  • series and limits
  • primes
  • probability
  • geometric transformations
  • simulating physical phenomena
  • iterates (1) - solving equations
  • find optimal solutions
  • the fastest approach
  • iterates (2) -fractals
  • iterates (3) - chaos
  • coding
  • machinery proof to the theorems of elementary geometry.
巻冊次

: pbk ISBN 9789812380500

内容説明

Owing to the advent of computers, experiments are becoming an increasingly important part of mathematics. This book provides guidance to students doing experiments in mathematics. The aim is to stimulate interest in mathematics through examples and experiments.Each experiment in the book starts with an interesting problem. The students are expected to work with these problems on computers, try to find the solutions themselves, and experience the scientific exploration in the process.The problems which the authors have chosen cover a wide spectrum in mathematics, ranging from calculus, number theory, coding and probability to geometry and chaos. They are introduced in a simple way and yet show great depth. The discussions are thorough but not lengthy.This book is useful not only to mathematics students, but also to students in all areas of sciences who are interested in learning some of the mathematical tools. It provides a hands-on approach to the most fundamental issues in mathematics - an approach which may help to revolutionize the teaching of mathematics.

目次

  • Fundamentals of calculus
  • how to calculate ?
  • best fractional approximation
  • series and limits
  • primes
  • probability
  • geometric transformations
  • simulating physical phenomena
  • iterates (1) - solving equations
  • find optimal solutions
  • the fastest approach
  • iterates (2) -fractals
  • iterates (3) - chaos
  • coding
  • machinery proof to the theorems of elementary geometry.

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