An Introduction to Modern Mathematical Computing With Mathematica [Hardcover]

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 Ms 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.

An essential read for mathematicians, this volume looks beyond the syntax and semantics of Mathematica and other programs. It focuses on why they are necessary tools for anyone who engages in mathematics, as well as showing how to create better proofs.

Preface.- Conventions and Notation.- 1. Number Theory.- 2. Calculus.- 3. Linear Algebra.- 4. Visualisation and Geometry: a Postscript.- Sample Quizzes.- Index.- References.-

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 lã#