C++ for Mathematicians

C++ for Mathematicians: An Introduction for Students and Professionals

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Features

  • Introduces C++ programming language using examples that illustrate how C++ is used in mathematical research
  • Describes how to use C++ on different computer systems to help you start programming right away
  • Gives a clear and comprehensive introduction to the object-oriented method of programming
  • Discusses relevant topics including more advanced input/output, visualization, documentation, and selected special features of the C++ language
  • Includes a quick reference guide to the C++ language
  • Summary

    For problems that require extensive computation, a C++ program can race through billions of examples faster than most other computing choices. C++ enables mathematicians of virtually any discipline to create programs to meet their needs quickly, and is available on most computer systems at no cost. C++ for Mathematicians: An Introduction for Students and Professionals accentuates C++ concepts that are most valuable for pure and applied mathematical research.

    This is the first book available on C++ programming that is written specifically for a mathematical audience; it omits the language’s more obscure features in favor of the aspects of greatest utility for mathematical work. The author explains how to use C++ to formulate conjectures, create images and diagrams, verify proofs, build mathematical structures, and explore myriad examples. 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 learn quickly how to apply them to your own problems. An accompanying CD ROM provides all numbered programs so that readers can easily use or adapt the code as needed.

    Presenting clear explanations and examples from the world of mathematics that develop concepts from the ground up, C++ for Mathematicians can be used again and again as a resource for applying C++ to problems that range from the basic to the complex.

    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

    Editorial Reviews

    “For a mathematician like myself, Scheinerman’s new book is ideal. It concentrates on the portion of C++ that will be most useful to a mathematician. While developing the necessary tools and syntax of C++, the book presents example programs relevant to interesting and somewhat sophisticated mathematical problems. The reader can proceed as far as he/she wants. Even just reading the first few chapters of the book and writing some programs using the constructs introduced, there is sufficient [material] for many purposes within undergraduate mathematics … The strength of this book is the intermingling of interesting mathematics with the ideas and syntax of the C++ language. … The writing is very fluent and does not bog down in endless detail as so many programming books do … In summary, I recommend this book highly to frustrated mathematicians wishing to learn C++ programming. You will really enjoy the well-chosen examples and the light touch in the exposition.”
    —Jeffrey Nunemacher, MAA Reviews

     
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