C++ for Mathematicians

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

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Description

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.show more

Product details

  • Paperback | 520 pages
  • 160 x 235 x 30mm | 748.44g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 22 black & white illustrations, 1 black & white halftones
  • 158488584X
  • 9781584885849
  • 2,479,928

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 Dshow more

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