An Introduction to Programming with Mathematica

1 Preliminaries. - 1. 1 Introduction. - 1. 2 Using Mathematica. - 1. 3 The Mathematica Language. - 1. 4 The Mathematica Interface. - 2 A Brief Overview of Mathematica. - 2. 1 Numerical and Symbolic Computations. - 2. 2 Functions. - 2. 3 Graphics. - 2. 4 Representation of Data. - 2. 5 Programming. - 3 List Manipulation. - 3. 1 Introduction. - 3. 2 Creating and Measuring Lists. - 3. 3 Working With the Elements of a List. - 3. 4 Working with Several Lists. - 3. 5 Higher-Order Functions. - 3. 6 Applying Functions to Lists Repeatedly. - 3. 7 Strings and Characters. - 4 Functions. - 4. 1 Introduction. - 4. 2 Programs as Functions. - 4. 3 User-Defined Functions. - 4. 4 Auxiliary Functions. - 4. 5 Anonymous Functions. - 4. 6 One-Liners. - 5 Evaluation of Expressions. - 5. 1 Introduction. - 5. 2 Creating Rewrite Rules. - 5. 3 Expressions. - 5. 4 Patterns. - 5. 5 Term Rewriting. - 5. 6 Transformation Rules. - 6 Conditional Function Definitions. - 6. 1 Introduction. - 6. 2 Conditional Functions. - 6. 3 ExampleClassifying Points. - 7 Recursion. - 7. 1 Fibonacci Numbers. - 7. 2 List Functions. - 7. 3 Thinking Recursively. - 7. 4 Recursion and Symbolic Computations. - 7. 5 Gaussian Elimination. - 7. 6 Trees. - 7. 7 Dynamic Programming. - 7. 8 Higher-Order Functions and Recursion. - 7. 9 Debugging. - 8 Iteration. - 8. 1 Newtons Method. - 8. 2 Vectors and Matrices. - 8. 3 Passing Arrays to Functions. - 8. 4 Gaussian Elimination Revisited. - 9 Numerics. - 9. 1 Types of Numbers. - 9. 2 Random Numbers. - 9. 3 Precision and Accuracy. - 9. 4 Numerical Computations. - 10 Graphics Programming. - 10. 1 Graphics Primitives. - 10. 2 Graphics Directives and Options. - 10. 3 Built-in Graphics Functions. - 10. 4 Graphics Programming. - 10. 5 Sound. - 11 Applications. - 11. 1 The Random Walk. - 11. 2 The Game of Life. - 11. 3 Implementing Languages. - 12 Contexts and Packages. - 12. 1 Introduction. - 12. 2 UsingPackages. - 12. 3 Contexts. - 12. 4 Packages. - 12. 5 Avoiding Name Collisions. - 12. 6 The BaseConvert Package. - 12. 7 The RandomWalks Package. - References. Language: English