Mathematica in Action: Problem Solving Through Visualization and Computation

✍ Scribed by Stan Wagon (auth.), Stan Wagon (eds.)

• Publisher: Springer-Verlag New York
• Year: 2010
• Tongue: English
• Leaves: 591
• Edition: 3
• Category: Library

✦ Synopsis

In this third edition of Mathematica® in Action, award-winning author Stan Wagon guides beginner and veteran users alike through Mathematica's powerful tools for mathematical exploration. The transition to Mathematica 7 is made smooth with plenty of examples and case studies that utilize Mathematica's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting. Mathematica in Action also emphasizes the breadth of Mathematica and the impressive results of combining techniques from different areas. This material enables the reader to use Mathematica to solve a variety of complex problems.

Case studies ranging from elementary to sophisticated are provided throughout. Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, an illustration of the Banach—Tarski Paradox via hyperbolic geometry, new and surprising formulas for p, the discovery of shadow orbits for chaotic systems, and the use of powerful new capabilities for three-dimensional graphics. Visualization is emphasized throughout, with finely crafted graphics in each chapter.

Wagon is the author of eleven books on mathematics, including A Course in Computational Number Theory, named one of the ten best math books of 2000 by the American Library Association. He has written extensively on the educational applications of Mathematica, including the books VisualDSolve: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory.

From reviews of the second edition:

"In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to our understanding and enjoyment of mathematics."
—Richard Walker, The Mathematical Gazette

"The bottom line is that Mathematica in Action is an outstanding book containing many examples of real uses of Mathematica for the novice, intermediate, and expert user."
—Mark McClure, Mathematica in Education and Research

✦ Table of Contents

Front Matter....Pages i-xi
A Brief Introduction....Pages 1-22
Plotting....Pages 23-52
Prime Numbers....Pages 53-76
Rolling Circles....Pages 77-111
Three-Dimensional Graphs....Pages 113-140
Dynamic Manipulations....Pages 141-167
The Cantor Set, Real and Complex....Pages 169-178
The Quadratic Map....Pages 179-208
The Recursive Turtle....Pages 209-234
Parametric Plotting of Surfaces....Pages 235-265
Penrose Tiles....Pages 267-275
Complex Dynamics:Julia Sets and the Mandelbrot Set....Pages 277-300
Solving Equations....Pages 301-328
Optimization....Pages 329-362
Differential Equations....Pages 363-397
Computational Geometry....Pages 399-422
Check Digits and the Pentagon....Pages 423-429
Coloring Planar Maps....Pages 431-472
New Directions For π....Pages 473-490
The Banach–Tarski Paradox....Pages 491-504
The Riemann Zeta Function....Pages 505-522
Miscellany....Pages 523-556
Back Matter....Pages 557-578

✦ Subjects

Computational Mathematics and Numerical Analysis; Mathematical Software; Visualization; Applications of Mathematics