c++ for mathematicians - an introduction for students and professionals (2006)

[...]... important, thank you to my wife, Amy, and our children, Jonah, Naomi, Danny, and Rachel, for the world of love and happiness I share with them Ed Scheinerman Baltimore May 24, 2006 Part I Procedures Chapter 1 The Basics 1.1 What is C++? C++ is a computer programming language Computers are electronic information-processing machines Data and programs in these machines are saved, moved, and transformed... colleague.” I am fortunate to have such a colleague Thank you, Joanne Houlahan for your help (and patience) with getting me unstuck from computer woes I greatly appreciate my department chair, Daniel Naiman, for his support and encouragement for this project It gives me great joy to acknowledge the contributions of my father, Ira, and my son Jonah to the front cover Grandpa took the cover photo and grandson... (and errorprone) concept through the use of call-by-reference and STL container classes A mathematician shouldn’t be worrying about exotic data structures such as red–black trees; we just want to insert and delete elements in a set and not to worry about how the computer manages the set There are, however, a few instances where a rudimentary understanding of pointers is necessary • The name of a C++. .. moved, and transformed in the form of electrical voltages These electrical voltages can be interpreted as a zeros and ones The zeros and ones can be aggregated and interpreted as words, numbers, images, sounds, and so on Long ago, information—be it data or programs—could be entered into the Figure 1.1: A PDP-8 computer with front panel switches for entering instructions and data (Image courtesy of the... the standard cout is std::cout, where std stands for the “standard” namespace In the iostream file, cout and endl are defined to have the full names std::cout and std::endl It is possible to delete line 2 from the program, but then it would be necessary to replace cout with std::cout (and likewise for endl) However, for our purposes, it is much easier to declare: we are going to be using the standard... we omit those Nei- xxii C++ for Mathematicians ther multiple inheritance nor pure virtual functions are for us We do not explain how to make C++ programs work with other languages such as assembly language We don’t create our own namespaces For these and other C++ topics that are useful to large software engineering projects, please refer to any of several excellent, comprehensive C++ reference books... requires us to fuss with formidable formulas and solve elaborate equations Computer algebra systems such as Maple and Mathematica are extremely useful for such work • Visualization The computer can draw precise pictures and diagrams; often these images provide key insights to understanding problems • Examples and counterexamples The computer can run through millions of examples and try myriad possibilities... by Klemens Krause.) 3 4 C++ for Mathematicians computer by manipulating switches on the front of the machine Today, there are better methods Computer programming languages convert text into the requisite binary instructions C++ is a compiled language This means that before the program is run, it is first translated into a form that the machine can use directly The C++ files (and a typical project contains... to the C++ language and supporting libraries, and (D) answers to nearly every exercise No pointers! (almost) The C++ concepts covered in this book are not exhaustive There are aspects of the language that are relevant only to computer scientists and software engineers For example, C++ provides a number of exotic casting operators (such as reinterpret_cast) that are not of interest to mathematicians; ... C++ enables you to create correct programs quickly Furthermore, there is an extensive collection of C++ programs freely available on the Web that can be customized and used for your purposes (we discuss a few of these in Chapter 13) In addition, C++ is available for free on most computer systems See Appendix A for more information about different versions of C++ for various computing envi- xix xx C++ . h1" alt="" C++ for Mathematicians An Introduction for Students and Professionals Edward Scheinerman Cover photograph: Ira Scheinerman Cover design concept: Jonah Scheinerman Published. Standard Book Number-13: 97 8-0 97 8-1 -5 848 8-5 8 4-9 (Softcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and. Rosewood Drive, Danvers, MA 01923, 97 8-7 5 0-8 400. CCC is a not -for- profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy