Springer Undergraduate Texts in Mathematics and Technology

An Introduction to Modern Mathematical Computing

With Mathematica®

Authors: Borwein, Jonathan, Skerritt, Matthew P.

  • 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
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eBook $44.99
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  • ISBN 978-1-4614-4253-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-1-4614-4252-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three “M’s” Maple, Mathematica and Matlab.

We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an "experimental mathematician" while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.

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).

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)


Table of contents (4 chapters)

  • Number Theory

    Borwein, Jonathan M. (et al.)

    Pages 1-76

  • Calculus

    Borwein, Jonathan M. (et al.)

    Pages 77-137

  • Linear Algebra

    Borwein, Jonathan M. (et al.)

    Pages 139-193

  • Visualization and Geometry: A Postscript

    Borwein, Jonathan M. (et al.)

    Pages 195-209

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4614-4253-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-1-4614-4252-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Modern Mathematical Computing
Book Subtitle
With Mathematica®
Authors
Series Title
Springer Undergraduate Texts in Mathematics and Technology
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-4253-0
DOI
10.1007/978-1-4614-4253-0
Hardcover ISBN
978-1-4614-4252-3
Series ISSN
1867-5506
Edition Number
1
Number of Pages
XVI, 224
Topics