C++ for Mathematicians

Book Description

The first book available on C++ programming that is written specifically for a mathematical audience, C++ for Mathematicians omits the language's more obscure features in favor of the aspects of greatest utility for mathematical work. Emphasizing the essential role of practice as part of the learning process, the book is ideally designed for undergraduate coursework as well as self-study. Each chapter provides many problems and solutions which complement the text and enable you to apply concepts right away. An accompanying CD ROM provides all numbered programs so that readers can easily use or adapt the code as needed.

Product Details

* Paperback: 520 pages
* Publisher: CRC; Bk&CD-Rom edition (June 6, 2006)
* Language: English
* ISBN-10: 158488584X
* ISBN-13: 978-1584885849



Table of Contents

List of Programs
List of Figures
Preface

I. PROCEDURES
The Basics
What is C++?
Hello C++

Numbers
The Integer Types
The Real Number Types
The bool and char Types
Checking the Size and Capacity of the Different Types
Standard Operations
Comparisons and Boolean Operations
Complex Numbers
Naming Variables

Greatest Common Divisor
The Problem
A First Approach
Euclid's Method
Looping With for, while, and do
An Exhaustive Approach to the GCD Problem
Extended GCD, Call by Reference, and Overloading

Random Numbers
Pseudo Random Number Generation
Uniform Random Values
More on Pseudo Random Number Generation
A Monte Carlo Program for the GCD Problem
Normal Random Values

Arrays
Euler's Totient
Array Fundamentals
A Procedure to Factor Integers
A Procedure to Calculate Euler's Totient
The Sieve of Eratosthenes
A Faster Totient
Computing pn for Large n
The Answer

II. OBJECTS
Points in the Plane
Data and Methods
Declaring the Point Class
Data Hiding
Constructors
Assignment and Conversion
Methods
Procedures using Arguments of Type Point
Operators

Pythagorean Triples
Generating Pythagorean Triples
Designing a Primitive Pythagorean Triple Class
Implementation of the PTriple Class
Finding and Sorting the Triples

Containers
Sets
Set Iterators
Multisets
Adjustable Arrays Via the Vector Class
Ordered Pairs
Maps
Lists, Stacks, and Assorted Queues

Modular Arithmetic
Designing the Mod Type
The Code
The Default Modulus: Static Class Variables and Methods
Constructors and Get/Set Methods
Comparison Operators
Arithmetic Operators
Writing Mod Objects to Output Streams
A Main to Demonstrate the Mod Class

The Projective Plane
Introduction to the Projective Plane, RP2
Designing the Classes PPoint and PLine
Inheritance
Protected Class Members
Class and File Organization for PPoint and PLine
The Parent Class PObject
The Classes PPoint and PLine
Discovering and Repairing a Bug
Pappus Revisited

Permutations
Ulam's Problem
Designing the Permutation Class
Finding Monotone Subsequences
Exercises

Polynomials
Procedure Templates
Class Templates
The Polynomial Class Template
The GCD Problem Revisited
Working in Binary

III. TOPICS
Using Other Packages
Arbitrary Precision Arithmetic: the GMP Package
Linear Algebra
Other Packages

Strings, Input/Output, and Visualization
Character Arrays
The String Class
Command Line Arguments
Reading and Writing Data in Files
String Streams
Formatting
A Class to Parse Files
Visualization

Odds and Ends
The switch Statement
Labels and the goto Statement
Exception Handling
Friends
Other Ways to Create Types
Pointers

IV. APPENDICES
A. Your C++ Computing Environment
Programming with a Command Window and a Text Editor
Programming with an Integrated Development Environment
General Advice on Debugging
B. Documentation with Doxygen
Doxygen Comments
Using Doxygen
C. C++ Reference
Variables and Types
Operations
Control Statements
Procedures
Classes
Standard Functions
D. Answers
Index

*Each Chapter Contains Exercises; Solutions can be found in Appendix D