Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators PDF Download
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Author: Alexei Volkov
Publisher: Springer
ISBN: 3319733966
Category : Education
Languages : en
Pages : 464
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Book Description
This volume traces back the history of interaction between the “computational” or “algorithmic” aspects of elementary mathematics and mathematics education throughout ages. More specifically, the examples of mathematical practices analyzed by the historians of mathematics and mathematics education who authored the chapters in the present collection show that the development (and, in some cases, decline) of counting devices and related computational practices needs to be considered within a particular context to which they arguably belonged, namely, the context of mathematics instruction; in their contributions the authors also explore the role that the instruments played in formation of didactical approaches in various mathematical traditions, stretching from Ancient Mesopotamia to the 20th century Europe and North America.
Author: Alexei Volkov
Publisher: Springer
ISBN: 3319733966
Category : Education
Languages : en
Pages : 464
Get Book Here
Book Description
This volume traces back the history of interaction between the “computational” or “algorithmic” aspects of elementary mathematics and mathematics education throughout ages. More specifically, the examples of mathematical practices analyzed by the historians of mathematics and mathematics education who authored the chapters in the present collection show that the development (and, in some cases, decline) of counting devices and related computational practices needs to be considered within a particular context to which they arguably belonged, namely, the context of mathematics instruction; in their contributions the authors also explore the role that the instruments played in formation of didactical approaches in various mathematical traditions, stretching from Ancient Mesopotamia to the 20th century Europe and North America.
Author: Cordelia Hall
Publisher: Springer Science & Business Media
ISBN: 1447136578
Category : Mathematics
Languages : en
Pages : 345
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Book Description
Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools such as proof checkers. These connections are emphasised throughout the book. Software tools (see Appendix A) enable the computer to serve as a calculator, but instead of just doing arithmetic and trigonometric functions, it will be used to calculate with sets, relations, functions, predicates and inferences. There are also special software tools, for example a proof checker for logical proofs using natural deduction.
Author: Robert N. McCullough
Publisher:
ISBN: 9780895827005
Category : Computer science
Languages : en
Pages : 0
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Book Description
Author: Hung T. Nguyen
Publisher: Springer Science & Business Media
ISBN: 9780792347224
Category : Mathematics
Languages : en
Pages : 440
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Book Description
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.
Author: Gerard O’Regan
Publisher: Springer Nature
ISBN: 3030342093
Category : Computers
Languages : en
Pages : 468
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Book Description
This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.
Author: Harold Abelson
Publisher: MIT Press
ISBN: 9780262510370
Category : Computers
Languages : en
Pages : 502
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Book Description
Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.
Author: John Vince
Publisher: Springer Science & Business Media
ISBN: 9781846280344
Category : Computers
Languages : en
Pages : 268
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Book Description
This is a concise and informal introductory book on the mathematical concepts that underpin computer graphics. The author, John Vince, makes the concepts easy to understand, enabling non-experts to come to terms with computer animation work. The book complements the author's other works and is written in the same accessible and easy-to-read style. It is also a useful reference book for programmers working in the field of computer graphics, virtual reality, computer animation, as well as students on digital media courses, and even mathematics courses.
Author: Clive Maxfield
Publisher: John Wiley & Sons
ISBN: 9780471741961
Category : Computers
Languages : en
Pages : 464
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Book Description
The Basics of Computer Arithmetic Made Enjoyable andAccessible-with a Special Program Included for Hands-onLearning "The combination of this book and its associated virtual computeris fantastic! Experience over the last fifty years has shown methat there's only one way to truly understand how computers work;and that is to learn one computer and its instruction set-no matterhow simple or primitive-from the ground up. Once you fullycomprehend how that simple computer functions, you can easilyextrapolate to more complex machines." -Fred Hudson, retired engineer/scientist "This book-along with the virtual DIY Calculator-is an incrediblyuseful teaching and learning tool. The interesting trivia nuggetskeep you turning the pages to see what's next. Students will haveso much fun reading the text and performing the labs that theywon't even realize they are learning." -Michael Haghighi, Chairperson of the Business and ComputerInformation Systems Division, Calhoun Community College,Alabama "At last, a book that presents an innovative approach to theteaching of computer architecture. Written with authority andverve, witty, superbly illustrated, and enhanced with manylaboratory exercises, this book is a must for students and teachersalike." -Dr. Albert Koelmans, Lecturer in Computer Engineering, Universityof Newcastle upon Tyne, UK, and the 2003 recipient of theEASIT-Eng. Gold Award for Innovative Teaching in ComputerEngineering Packed with nuggets of information and tidbits of trivia, HowComputers Do Math provides an incredibly fun and interestingintroduction to the way in which computers perform their magic ingeneral and math in particular. The accompanying CD-ROM contains avirtual computer/calculator called the DIY Calculator, and thebook's step-by-step interactive laboratories guide you in thecreation 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, andmathematics; and even practicing engineers. All of theillustrations and interactive laboratories featured in the book areprovided on the CD-ROM for use by high school, college, anduniversity educators as lecture notes and handouts. For online resources and more information please visit theauthor's website at ahref="http://www.diycalculator.com/"www.DIYCalculator.com/a.
Author: Richard Noss
Publisher: Springer Science & Business Media
ISBN: 9400916965
Category : Education
Languages : en
Pages : 288
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Book Description
This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.
Author: Ronald L. Graham
Publisher: Addison-Wesley Professional
ISBN: 0134389980
Category : Computers
Languages : en
Pages : 811
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Book Description
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
