Computer Science with Mathematica

Extended Table of Contents

Preface

About this Book

Overview of Contents - Comments on Exercises - Electronic Resources - Notation and Terminology - Colophon

 1 From Problems to Programs

From Problems to Programs - Computers - Programming Languages - Computer Science

 2 Mathematica's Programming Language

Arithmetic and Logic - Definitions -Simple Program Structures - Structure of Expressions - Help with Problems - Exercises

 3 Iteration and Recursion

The Greatest Common Divisor - The 3x+1 Problem - Advanced Topic: Loop Invariants - Application: Differential Equations - Exercises

 4 Structure of Programs

Complex Parametric Lines - The First Package - Optional Arguments - A Template Package - Exercises

 5 Abstract Data Types

Definition of Abstract Data Types - Example: Modular Numbers - Design of Abstract Data Types - Exercises

 6 Algorithms for Searching and Sorting

Searching Ordered Data - Sorting Data - Binary Trees - Exercises

 7 Complexity of Algorithms

Complexity of Computations - Example: Computing the n-th Fibonacci Number - Special Topic: Dynamic Programming - Long-Integer Arithmetic and Fast Multiplication - Exercises

 8 Operations on Vectors and Matrices

Vectors and Matrices - Inner and Outer Products - Linear Algebra - Programs with Arrays - Application: Aggregation - Exercises

 9 List Processing and Recursion

Symbolic Expressions and Lists - List Processing - Exercises

10 Rule-Based Programming

Pattern Matching - Rules and Term Rewriting - Simplification Rules and Normal Forms - Application: Trigonometric Simplifications - Exercises

11 Functions

A Notation for Functions (lambda Calculus) - Functions as Values - Example: Simulation of Shift Registers - Exercises

12 Theory of Computation

Computable Functions - Models of Computation - Turing Machines - Recursive Functions Are Turing Computable - Exercises

13 Databases

Database Design - Relational Databases - Data Entry and Queries - Commercial Databases - Exercises

14 Object-Oriented Programming

Introduction - Example: Bank Accounts - Principles of Object-Oriented Programming - Application: Collections - Exercises

Appendix A Further Reading

A Guide to the Literature - References

Appendix B More Information About Mathematica

Computations You Can Do with Mathematica - The Code for the Illustrations in this Book - Mathematica's Evaluation Method - Syntax of Operators

Index