The Mathematica® Programmer

The Mathematica Programmer covers the fundamental programming paradigms and applications of programming languages.

This book is organized into two parts encompassing 10 chapters. Part 1 begins with an overview of the programming paradigms. This part also treats abstract data types, polymorphism and message passing, object-oriented programming, and relational databases. Part 2 looks into the practical aspects of programming languages, including in lists and power series, fractal curves, and minimal surfaces.

This book will prove useful to mathematicians and computer scientists.

Foreword

Preface

About This Book

Contents of the Chapters

About the Programs

Notation and Terminology

Colophon

Part 1: Paradigms of Programming

1 Introduction

1.1 Mathematica's Programming Language

1.2 Pattern Matching and Term Rewriting

1.3 Programming Styles

2 Abstract Data Types

2.1 Data Types as a Programming Tool

2.2 The Definition of Abstract Data Types

2.3 A Practical Approach

2.4 Design Principles for Abstract Data Types

2.5 An Example: LISP in Mathematica

2.6 Built-in Functions and Data Types

2.7 An Exercise

2.8 Conclusions and Further Reading

3 Polymorphism and Message Passing

3.1 Polymorphic Operations

3.2 Three Implementation Methods

3.3 Data-Driven Programming and Rules

3.4 A Better Interface for Objects

3.5 Objects with Local State

3.6 Conclusions

4 Object-Oriented Programming

4.1 The Object-Oriented Paradigm

4.2 An Implementation in Mathematica

4.3 Abstract Classes and Polymorphic

4.4 An Advanced Example: Collections from SMALLTALK

4.5 Conclusions and Further Reading

4.6 The Complete Code of Classes.m

5 Databases

5.1 Database Design

5.2 Relational Databases

5.3 Fundamental Operations on Relations

5.4 Data Entry

5.5 Other Functions

5.6 Conclusions

5.7 The Complete Code of Databases.m

Part 2: Applications

6 Computations with Infinite Structures

6.1 Infinite Sets and Infinite Lists

6.2 Streams, Like Lists

6.3 Infinity at Last

6.4 More Applications

6.5 Really Taking Off

6.6 Conclusions and Further Reading

6.7 The Complete Code of Streams.m

7 Fibonacci on the Fast Track

7.1 Fibonacci Numbers

7.2 Complexity Measures

7.3 A Closed Formula

7.4 The Matrix Method

7.5 Conclusions and Further Reading

8 Fractal Curves

8.1 Self-Similarity

8.2 A Language for Polygons

8.3 Displaying Fractals

8.4 Variations on the Theme

8.5 The Fractal Dimension

8.6 Examples

8.7 Conclusions and Further Reading

8.8 The Complete Code of FractalCurves.m

9 Minimal Surfaces

9.1 A Formula for Minimal Surfaces

9.2 A Package for Plotting Minimal Surfaces

9.3 Analytic Continuations

9.4 Complex Contortions

9.5 Bonus Pictures

9.6 Further Reading

9.7 The Complete Code of MinimalSurfaces.m

10 System Programming

10.1 Working with Symbols

10.2 Housekeeping

10.3 Applying Functions to Symbols

10.4 A Crash Test

10.5 Options

10.6 Conclusions

10.7 The Complete Code of SystemProgramming.m

Appendices

Bibliography

Additional Program Listings

Index of Programs

Index