Theories of Interval Arithmetic

Mathematical Foundations and Applications

Author: Hend Dawood

Publisher: LAP Lambert Academic Publishing

ISBN: 3846501549

Category: Mathematics

Page: 128

View: 3705

Scientists are, all the time, in a struggle with uncertainty which is always a threat to a trustworthy scientific knowledge. A very simple and natural idea, to defeat uncertainty, is that of enclosing uncertain measured values in real closed intervals. On the basis of this idea, interval arithmetic is constructed. The idea of calculating with intervals is not completely new in mathematics: the concept has been known since Archimedes, who used guaranteed lower and upper bounds to compute his constant Pi. Interval arithmetic is now a broad field in which rigorous mathematics is associated with scientific computing. This connection makes it possible to solve uncertainty problems that cannot be efficiently solved by floating-point arithmetic. Today, application areas of interval methods include electrical engineering, control theory, remote sensing, experimental and computational physics, chaotic systems, celestial mechanics, signal processing, computer graphics, robotics, and computer-assisted proofs. The purpose of this book is to be a concise but informative introduction to the theories of interval arithmetic as well as to some of their computational and scientific applications. Editorial Reviews "This new book by Hend Dawood is a fresh introduction to some of the basics of interval computation. It stops short of discussing the more complicated subdivision methods for converging to ranges of values, however it provides a bit of perspective about complex interval arithmetic, constraint intervals, and modal intervals, and it does go into the design of hardware operations for interval arithmetic, which is something still to be done by computer manufacturers." - Ramon E. Moore, (The Founder of Interval Computations) Professor Emeritus of Computer and Information Science, Department of Mathematics, The Ohio State University, Columbus, U.S.A. "A popular math-oriented introduction to interval computations and its applications. This short book contains an explanation of the need for interval computations, a brief history of interval computations, and main interval computation techniques. It also provides an impressive list of main practical applications of interval techniques." - Vladik Kreinovich, (International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems) Professor of Computer Science, University of Texas at El Paso, El Paso, Texas, U.S.A. "I am delighted to see one more Egyptian citizen re-entering the field of interval mathematics invented in this very country thousands years ago." - Marek W. Gutowski, Institute of Physics, Polish Academy of Sciences, Warszawa, Poland

A Philosophical and Mathematical Dictionary

Containing an Explanation of the Terms, and an Account of the Several Subjects, Comprised Under the Heads Mathemetics, Astronomy, and Philosophy Both Natural and Experimental; with an Historical Account of the Rise, Progress and Present State of These Sciences; Also Memoirs of the Lives and Writings of the Most Eminent Authors, Both Ancient and Modern, who by Their Discoveries Or Improvements Have Contributed to the Advancement of Them

Author: Charles Hutton

Publisher: London : Printed for the author


Category: Astronomy

Page: 760

View: 5533

Hints, Theoretical, Elucidatory, and Practical, for the Use of Teachers of Elementary Mathematics, and of Self-taught Students

With Especial Reference to Vol. I of Hutton's Course, and Simson's Euclid, as Text-books: Also a Selection of Miscellaneous Tables, and an Appendix on the Geometrical Division of Plane Surfaces

Author: Olinthus Gregory

Publisher: N.A


Category: Geometry

Page: 188

View: 6099

Elements of Probability Theory

Author: L. Z. Rumshiskii

Publisher: Elsevier

ISBN: 1483136000

Category: Mathematics

Page: 172

View: 2546

Elements of Probability Theory focuses on the basic ideas and methods of the theory of probability. The book first discusses events and probabilities, including the classical meaning of probability, fundamental properties of probabilities, and the primary rule for the multiplication of probabilities. The text also touches on random variables and probability distributions. Topics include discrete and random variables; functions of random variables; and binomial distributions. The selection also discusses the numerical characteristics of probability distributions; limit theorems and estimates of the mean; and the law of large numbers. The text also describes linear correlation, including conditional expectations and their properties, coefficient of correlation, and best linear approximation to the regression function. The book presents tables that show the values of the normal probability integral, Poisson distribution, and values of the normal probability density. The text is a good source of data for readers and students interested in probability theory.

Encyclopedia of Educational Theory and Philosophy

Author: D. C. Phillips

Publisher: SAGE Publications

ISBN: 1483364755

Category: Education

Page: 952

View: 3225

Education is a field sometimes beset by theories-of-the-day and with easy panaceas that overpromise the degree to which they can alleviate pressing educational problems. The two-volume Encyclopedia of Educational Theory and Philosophy introduces readers to theories that have stood the test of time and those that have provided the historical foundation for the best of contemporary educational theory and practice. Drawing together a team of international scholars, this invaluable reference examines the global landscape of all the key theories and the theorists behind them and presents them in the context needed to understand their strengths and weaknesses. In addition to interpretations of long-established theories, this work offers essays on cutting-edge research and concise, to-the-point definitions of key concepts, ideas, schools, and figures. Features: Over 300 signed entries by trusted experts in the field are organized into two volumes and overseen by a distinguished General Editor and an international Editorial Board. Entries are followed by cross references and further reading suggestions. A Chronology of Theory within the field of education highlights developments over the centuries; a Reader’s Guide groups entries thematically, and a master Bibliography facilitates further study. The Reader’s Guide, detailed index, and cross references combine for strong search-and-browse capabilities in the electronic version. Available in a choice of print or electronic formats, Encyclopedia of Educational Theory and Philosophy is an ideal reference for anyone interested in the roots of contemporary educational theory.