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Computer algebra systems have revolutionized the use of computers within mathematics research, and are currently extending that revolution to the undergraduate mathematics curriculum. But the power of such systems goes beyond simple algebraic or numerical manipulation. In this practical resource Roman Maeder shows how computer-aided mathematics has reached a level where it can support effectively many of the computations in science and engineering. Besides treating traditional computer science topics, he demonstrates how scientists and engineers can use these computer-based tools to do scientific computations. A valuable text for computer science courses for scientists and engineers, this book will also prove useful to Mathematica users at all levels. Covering the latest release of Mathematica, the book includes useful tips and techniques to help even seasoned users.
Preface; 1. About this book; 2. Computers and science; 3. Mathematica's programming language; 4. Iteration and recursion; 5. Structure of programs; 6. Abstract data types; 7. Algorithms for searching and sorting; 8. Complexity of algorithms; 9. Operations on vectors and matrices; 10. List processing and recursion; 11. Rule-based programming; 12. Functions; 13. Theory of computation; 14. Databases; 15. Object-oriented programming; Appendix A. Further reading; Appendix B. More information about Mathematica; Index.