Ebook: An Introduction to Modern Mathematical Computing: With Mathematica®

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.

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This book provides the optimal introduction to MATLAB and Simulink, the primary tools in engineering, science, and industry for simulating dynamic systems. Using the latest versions of the software, the book also has 20 hands-on projects that provide a practical mastery of the subject areas including the code and executable files. Apart from a basic knowledge of mathematics and physics, no further specialist knowledge is necessary. There are also over 80, in-text, exercises where readers themselves can check their mastery of the material. A CD-ROM with source code accompanies the book