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A collection of articles which explore the ways in which computers are used in mathematical research, taken from results of a conference at University College, Cardiff in 1986.
Advances in computer technology have had a tremendous impact on mathematics in the last two decades. In June of 1989, an international conference was held at MIT, bringing together mathematicians and computer scientists, to survey the work that has been done in computational mathematics, to report recent results in this field, and to discuss research directions as well as educational issues. This book presents a fascinating collection of contributions on topics ranging from computational algebra, and parallel computing, to mathematics education. Mathematicians interested in the computational aspects of their discipline as well as computer scientists interested in mathematical applications will enjoy the integrative view provided by this book.
The NATO Advanced Research Workshop on Mathematics Education and Technology was held in Villard-de-Lans, France, between May 6 and 11, 1993. Organised on the initiative of the BaCoMET (Basic Components of Mathematics Education for Teachers) group (Christiansen, Howson and Otte 1986; Bishop, Mellin-Olsen and van Dormolen 1991), the workshop formed part of a larger NATO programme on Advanced Educational Technology. Some workshop members had already participated in earlier events in this series and were able to contribute insights from them: similarly some members were to take part in later events. The problematic for the workshop drew attention to important speculative developments in the applications of advanced information technology in mathematics education over the last decade, notably intelligent tutoring, geometric construction, symbolic algebra and statistical analysis. Over the same period, more elementary forms of information technology had started to have a significant influence on teaching approaches and curriculum content: notably arithmetic and graphic calculators; standard computer tools, such as spreadsheets and databases; and computer-assisted learning packages and computer microworlds specially designed for educational purposes.
The Basics of Computer Arithmetic Made Enjoyable and Accessible-with a Special Program Included for Hands-on Learning "The combination of this book and its associated virtual computer is fantastic! Experience over the last fifty years has shown me that there's only one way to truly understand how computers work; and that is to learn one computer and its instruction set-no matter how simple or primitive-from the ground up. Once you fully comprehend how that simple computer functions, you can easily extrapolate to more complex machines." -Fred Hudson, retired engineer/scientist "This book-along with the virtual DIY Calculator-is an incredibly useful teaching and learning tool. The interesting trivia nuggets keep you turning the pages to see what's next. Students will have so much fun reading the text and performing the labs that they won't even realize they are learning." -Michael Haghighi, Chairperson of the Business and Computer Information Systems Division, Calhoun Community College, Alabama "At last, a book that presents an innovative approach to the teaching of computer architecture. Written with authority and verve, witty, superbly illustrated, and enhanced with many laboratory exercises, this book is a must for students and teachers alike." -Dr. Albert Koelmans, Lecturer in Computer Engineering, University of Newcastle upon Tyne, UK, and the 2003 recipient of the EASIT-Eng. Gold Award for Innovative Teaching in Computer Engineering Packed with nuggets of information and tidbits of trivia, How Computers Do Math provides an incredibly fun and interesting introduction to the way in which computers perform their magic in general and math in particular. The accompanying CD-ROM contains a virtual computer/calculator called the DIY Calculator, and the book's step-by-step interactive laboratories guide you in the creation of a simple program to run on your DIY Calculator. How Computers Do Math can be enjoyed by non-technical individuals; students of computer science, electronics engineering, and mathematics; and even practicing engineers. All of the illustrations and interactive laboratories featured in the book are provided on the CD-ROM for use by high school, college, and university educators as lecture notes and handouts. For online resources and more information please visit the author's website at www.DIYCalculator.com.
Computing is an exact science and the systematic study of any aspect necessarily involves the use of mathematical models. Moreover, the rate at which the subject is evolving demands a facility for developing new mathematical systems to keep pace with new computing systems and this requires an appreciation of how mathematics works. An understanding of the underlying mathematical structure facilitates the construction of suitable computer programs to perform computations. Assuming no specific knowledge of mathematics, the authors describe all the basic concepts required and progress from sets (rather than numbers) through a variety of algebraic structures that permit the precise description, specification and subsequent analysis of many problems in computing. The material included provides the essential mathematical foundations for core topics of computer science and extends into the areas of language theory, abstract machine theory and computer geometry. Computer Mathematics will be of interest to undergraduate students of computer science and mathematics, post-graduate computing 'conversion' course students and computer professionals who need an introduction to the mathematics that underpins computer science theory.
Best-selling author Nigel Cook's new second edition of Introductory Computers Mathematics provides a complete math course for those learning computer technology. Employing an “integrated math applications” approach, this book reinforces all math topics with extensive applications to show readers the value of math as a tool. Specific chapters in the section on Basic Math discuss fractions; decimal numbers; positive and negative numbers; exponents and the metric system; algebra, equations and formulas; geometry and trigonometry; and logarithms and graphs. Computer Math topics cover analog to digital, number systems and codes, logic gates, Boolean expressions and algebra, binary arithmetic, and an introduction to computers and programming. For individuals preparing for a career in computer technology.
To date, much of the literature prepared on the topic of integrating mathematics history into undergraduate teaching contains, predominantly, ideas from the 18th century and earlier. This volume focuses on nineteenth- and twentieth-century mathematics, building on the earlier efforts but emphasizing recent history in the teaching of mathematics, computer science, and related disciplines. From Calculus to Computers is a resource for undergraduate teachers that provides ideas and materials for immediate adoption in the classroom and proven examples to motivate innovation by the reader. Contributions to this volume are from historians of mathematics and college mathematics instructors with years of experience and expertise in these subjects. Examples of topics covered are probability in undergraduate statistics courses, logic and programming for computer science, undergraduate geometry to include non-Euclidean geometries, numerical analysis, and abstract algebra.
Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current sta
This volume is intended to be used as a textbook for a special topic course in computer science. It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision. The work incorporates many new research ideas, and focuses on the role of continuous mathematics. Audience: This book will be valuable to graduate students interested in theoretical computer topics, algorithms, expert systems, neural networks, and software engineering.
Computer Mathematics for Programmers presents the Mathematics that is essential to the computer programmer. The book is comprised of 10 chapters. The first chapter introduces several computer number systems. Chapter 2 shows how to perform arithmetic operations using the number systems introduced in Chapter 1. The third chapter covers the way numbers are stored in computers, how the computer performs arithmetic on real numbers and integers, and how round-off errors are generated in computer programs. Chapter 4 details the use of algorithms and flowcharting as problem-solving tools for computer programming. Subsequent chapters focuses on specific mathematical topics such as algebra, sets, logic, Boolean algebra, matrices, graphing and linear programming, and statistics. Students of computer programming will find the text very useful.
