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C++ for Mathematicians

An Introduction for Students and Professionals

C++ for Mathematicians by Edward Scheinerman
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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
CRC Press; June 2006
521 pages; ISBN 9781420010985
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Title: C++ for Mathematicians
Author: Edward Scheinerman
 
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