Programming with Mathematica® : An Introduction

Starting from first principles, this book covers all of the foundational material needed to develop a clear understanding of the Mathematica language, with a practical emphasis on solving problems. Concrete examples throughout the text demonstrate how Mathematica language, can be used to solve problems in science, engineering, economics/finance, computational linguistics, geoscience, bioinformatics, and a range of other fields. The book will appeal to students, researchers and programmers wishing to further their understanding of Mathematica language. Designed to suit users of any ability, it assumes no formal knowledge of programming so it is ideal for self-study. Over 290 exercises are provided to challenge the reader s understanding of the material covered and these provide ample opportunity to practice using the language. Mathematica language notebooks containing examples, programs and solutions to exercises are available from (http://www.cambridge.org/wellin) www.cambridge.org/wellin . Contents......Page 7 Preface......Page 13 1.1 Overview of basic operations......Page 21 1.2 Getting started......Page 34 1.3 Getting help......Page 45 2.1 Expressions......Page 49 2.2 Definitions......Page 60 2.3 Predicates and Boolean operations......Page 68 2.4 Attributes......Page 73 3 Lists......Page 77 3.1 Creating and displaying lists......Page 78 3.2 The structure of lists......Page 87 3.3 Operations on lists......Page 90 4 Patterns and rules......Page 103 4.1 Patterns......Page 105 4.2 Transformation rules......Page 122 4.3 Examples and applications......Page 129 5 Functional programming......Page 135 5.1 Introduction......Page 136 5.2 Functions for manipulating expressions......Page 138 5.3 Iterating functions......Page 152 5.4 Programs as functions......Page 157 5.5 Scoping constructs......Page 166 5.6 Pure functions......Page 173 5.7 Options and messages......Page 184 5.8 Examples and applications......Page 190 6 Procedural programming......Page 209 6.1 Loops and iteration......Page 210 6.2 Flow control......Page 228 6.3 Examples and applications......Page 239 7.1 Fibonacci numbers......Page 251 7.2 Thinking recursively......Page 254 7.3 Dynamic programming......Page 259 7.4 Classical examples ·......Page 264 8.1 Numbers in Mathematica......Page 271 8.2 Numerical computation......Page 285 8.3 Arrays of numbers......Page 302 8.4 Examples and applications......Page 311 9 Strings......Page 329 9.1 Structure and syntax......Page 330 9.2 Operations on strings......Page 336 9.3 String patterns ·......Page 345 9.4 Regular expressions......Page 352 9.5 Examples and applications......Page 363 10 Graphics and visualization......Page 383 10.1 Structure of graphics......Page 385 10.2 Efficient structures......Page 406 10.3 Sound......Page 416 10.4 Examples and applications......Page 422 11.1 Manipulating expressions......Page 469 11.2 The structure of dynamic expressions......Page 490 11.3 Examples and applications......Page 501 12 Optimizing Mathematica programs......Page 513 12.1 Measuring efficiency......Page 514 12.2 Efficient programs......Page 516 12.3 Parallel processing......Page 535 12.4 Compiling......Page 543 13 Applications and packages......Page 553 13.1 Random walk application......Page 554 13.2 Overview of packages......Page 575 13.3 Contexts......Page 578 13.4 Creating packages......Page 583 2 The Mathematica language......Page 595 3 Lists......Page 598 4 Patterns and rules......Page 602 5 Functional programming......Page 608 6 Procedural programming......Page 634 7 Recursion......Page 641 8 Numerics......Page 646 9 Strings......Page 658 10 Graphics and visualization......Page 671 11 Dynamic expressions......Page 686 12 Optimizing Mathematica programs......Page 696 13 Applications and packages......Page 701 Bibliography......Page 707 Index......Page 715 This practical, example-driven introduction is designed for Mathematica users, new and accomplished, who wish to learn the foundations of the Mathematica programming language in order to apply it to the task of solving concrete problems in science, engineering, economics and finance, computational linguistics, geoscience, bioinformatics and so on. This practical, example-driven introduction teaches the foundations of the Mathematica language so it can be applied to solving concrete problems. Paul Wellin. Includes Bibliographical References And Index.