The first edition of "Computer Simulations with Mathematica" drew on the capabilities of Mathematica to prototype algorithms and to write code in a variety of programming styles, choosing the appropriate style for the problem at hand. Today, running very large simulations in Mathematics is quite feasible, within an order of magnitude of complied C and Fortran code. This new edition takes advantage of these features and includes the following significant additions: Java has become a commonly used tool for working with scientific applications. This book fully incorporates Java programs to run the simulations that are described and implemented in the book. This is one of the first books to describe and take advantage of Mathematica 6, which contains a fantastic array of new visualization functions and dynamic interactive graphics machinery. Several websites are maintained with Mathematica notebooks, C source code and compiled C Binaries for various platforms. A minimal background in Mathematica programming is assumed.