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© 2012

An Introduction to Modern Mathematical Computing

With Mathematica®

  • Places primary importance on the mathematics, rather than being a 'how to' manual for making computations

  • Integrates numerous worked examples and introduces all key programming constructions

  • Includes exercises, sample tests, and a careful selection of 'explorations' suitable for either independent studies or for term projects

Textbook

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Jonathan M. Borwein, Matthew P. Skerritt
    Pages 1-76
  3. Jonathan M. Borwein, Matthew P. Skerritt
    Pages 77-137
  4. Jonathan M. Borwein, Matthew P. Skerritt
    Pages 139-193
  5. Jonathan M. Borwein, Matthew P. Skerritt
    Pages 195-209
  6. Back Matter
    Pages 211-224

About this book

Introduction

Thirty years ago, mathematical computation was difficult to perform and thus used sparingly. However, mathematical computation has become far more accessible due to the emergence of the personal computer, the discovery of fiber-optics and the consequent development of the modern internet, and the creation of Maple™, Mathematica®, and Matlab®.

An Introduction to Modern Mathematical Computing: With Mathematica® looks beyond teaching the syntax and semantics of Mathematica and similar programs, and focuses on why they are necessary tools for anyone who engages in mathematics. It is an essential read for mathematicians, mathematics educators, computer scientists, engineers, scientists, and anyone who wishes to expand their knowledge of mathematics. This volume will also explain how to become an “experimental mathematician,” and will supply useful information about how to create better proofs.

The text covers material in elementary number theory, calculus, multivariable calculus, introductory linear algebra, and visualization and interactive geometric computation. It is intended for upper-undergraduate students, and as a reference guide for anyone who wishes to learn to use the Mathematica program.

Also by J.M. Borwein and M.B. Skerritt: An Introduction to Modern Mathematical Computing: With Maple™, © 2011, ISBN: 978-1-4614-0121-6, 216 p. and 81 color illustrations.

Keywords

Mathematica Mathematical Computing Mathematical Modeling Mathematics Software Undergraduate Mathematics

Authors and affiliations

  1. 1., School of Mathematical and Physical ScieUniversity of NewcastleNewcastleAustralia
  2. 2., School of Mathematical and Physical ScieThe University of NewcastleCallaghanAustralia

About the authors

Jonathan M. Borwein is currently Laureate Professor in the School of Mathematical and Physical Sciences at the University of Newcastle (NSW) with adjunct appointments at Dalhousie and at Simon Fraser. He received his Doctorate from Oxford in 1974, and has published extensively in optimization, analysis and computational mathematics, and has received various prizes both for research and for exposition. He directs the University of Newcastle’s Priority Research Centre in Computer Assisted Research Mathematics and its Applications (CARMA).

Bibliographic information

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Reviews

From the reviews:

“There are two general approaches to computation: using computation as a numerical tool to approximate answers or using a computer algebra system to provide exact mathematical answers by symbolic manipulation. This book explores the second of these approaches, using the computer algebra system Mathematica. … Though this work does teach students how to use Mathematica, it does so with the goal of providing new insights into basic mathematics, which can then be applied to more advanced mathematics. … Summing Up: Recommended. Lower- and upper-division undergraduates.” (D. Z. Spicer, Choice, Vol. 50 (7), March, 2013)

“Three main chapters form the core of the book. In the first chapter, the authors talk about using a computer algebra system like Mathematica for problems in number theory … . Chapters 2 and 3 are devoted to calculus and linear algebra, respectively. … The mathematical content of the chapters is … elementary and written in a style easily understandable by nonspecialists. … a very good introduction for beginners to this interesting and important topic.” (Kai Diethelm, ACM Computing Reviews, March, 2013)