mathematica in action: problem solving through visualization and computation

ISBN-13: 9780387753669 / Angielski / Miękka / 2010 / 580 str.

Stan Wagon

Opis

This book is an example-based introduction to techniques, from elementary to advanced, of using Mathematica, a revolutionary tool for mathematical computation and exploration. By integrating the basic functions of mathematics with a powerful and easy-to-use programming language, Mathematica allows us to carry out projects that would be extremely laborious in traditional programming environments. And the new developments that began with version 6 allowing the user to dyna- cally manipulate output using sliders or other controls add amazing power to the interface. Animations have always been part of Mathematica, but the new design allows the manipulation of any number of variables, an important enhancement. Mathematica in Action illustrates this power by using demonstrations and ani- tions, three-dimensional graphics, high-precision number theory computations, and sophisticated geometric and symbolic programming to attack a diverse collection of problems.. It is my hope that this book will serve a mathematical purpose as well, and I have interspersed several unusual or complicated examples among others that will be more familiar. Thus the reader may have to deal simultaneously with new mat- matics and new Mathematica techniques. Rarely is more than undergraduate mathematics required, however. An underlying theme of the book is that a computational way of looking at a mathematical problem or result yields many benefits. For example: Well-chosen computations can shed light on familiar relations and reveal new patterns. One is forced to think very precisely; gaps in understanding must be eliminated if a program is to work."

Recenzje

From the reviews of the third edition:

This book is a pleasing potpourri of Mathematica showpieces, picked to show the value of Mathematica for mathematics teaching and investigation... Although there is an introductory chapter explaining Mathematica, it is just enough to get you oriented and the examples go far beyond anything in this introduction. This book may motivate you to learn Mathematica but it won't teach it to you.

The book is full of interesting things. The first half focuses on visualization and the math is relatively elementary (nothing beyond multivariable calculus). The second half works on much harder problems. -MAA Reviews

"Beginners will benefit from the book as will more experienced Mathematica programmers as the explorations build from simple introductory concepts ... . The best feature of the book is that it teaches via interesting examples. ... The writing is remarkably good. ... The book contains a good number of color illustrations and is rich in Mathematica output. ... interesting explorations with clear and engaging writing are hard to come by. I'm delighted to have this book in my collection." (Playing with Mathematica, June, 2011)

Mathematica in Action is not a guidebook nor a reference manual. It is best described as a project book full of ideas and inspiration for research projects for anyone from high school students to professional mathematicians. It combines real mathematics with sophisticated coding... I highly recommend Mathematica in Action, both for its mathematical content and for its Mathematica content. You don't have to be a serious Mathematica user to enjoy this book or even use it. You can read it for mathematical ideas and inspiration without touching a keyboard, or, if you are a devotee of a different software system, you might be inspired to translate the examples into your favorite language. -The Mathematical Association of America, September, 2011

"This the third edition of the famous book 'Mathematica in Action' in which the author guides beginner as well as veteran users alike through Mathematica's powerful tools for mathematical exploration ... ." (T. C. Mohan, Zentralblatt MATH, Vol. 1198, 2010)

Spis treści

Preface.- A Brief Introduction.- Plotting.- Prime Numbers.- Rolling Wheels.- Surfaces.- Dynamic Manipulation.- The Cantor Set, Real and Complex.- The Quadratic Map.- The Recursive Turtle.- Parametric Plotting of Surfaces.- Penrose Tiles.- Complex Dynamics (by Mark McClure).- Solving Equations.- Optimization.- Differential Equations.- Computational Geometry.- Check Digits and the Pentagon.- Coloring Planar Maps.- New Directions for pi.- The Banach-Tarski Paradox.- The Riemman Zeta Function.- Miscellany.- References.- Index

Blurb

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