Designed both as a guide to Mathematica as well as a detailed tour of modern mathematics. Ideal for teachers, researchers, and Mathematica enthusiasts. Illustrates the power of Mathematica by using the software's animations, three-dimensional graphics, high-precision number theory computations, and sophisticated geometric and symbolic programming techniques to attack a diverse collection of mathematical problems.
Introduction | Plotting | Prime Numbers | Rolling Circles | Surfaces | The Cantor Set, Real and Complex | The Quadratic Map | The Recursive Turtle | Parametric Plotting of Surfaces | Penrose Tiles | Fractals, Ferns, and Julia Sets | Custom Curves | Solving Equations | Differential Equations | Public-Key Encryption | Egyptian Fractions | The Ancient and Modern Euclidean Algorithm | Imaginary Primes and Prime Imaginaries | Certifying Primality | Check Digits and the Pentagon | New Directions for \[Pi] | Rearrangement of Series | Escher's Patterns | Computational Geometry | Coloring Planar Maps and Graphs | The Riemann Zeta Function | The Banach-Tarski Paradox
Tutorial and Reference