Theorems And Counterexamples In Mathematics

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Theorems And Counterexamples In Mathematics

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Author : Bernard R. Gelbaum
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Theorems And Counterexamples In Mathematics written by Bernard R. Gelbaum and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The gratifying response to Counterexamples in analysis (CEA) was followed, when the book went out of print, by expressions of dismay from those who were unable to acquire it. The connection of the present volume with CEA is clear, although the sights here are set higher. In the quarter-century since the appearance of CEA, mathematical education has taken some large steps reflected in both the undergraduate and graduate curricula. What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress. The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. The items included are presented in the spirit of a conversation among mathematicians who know the language but are interested in some of the ramifications of the subjects with which they routinely deal. Although such an approach might be construed as demanding, there is an extensive GLOSSARY jlNDEX where all but the most familiar notions are clearly defined and explained. The object ofthe body of the text is more to enhance what the reader already knows than to review definitions and notations that have become part of every mathematician's working context.

Theorems And Counterexamples In Mathematics

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Author : Sabita Mahanta
language : en
Publisher:
Release Date : 2014

Theorems And Counterexamples In Mathematics written by Sabita Mahanta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Logic, Symbolic and mathematical categories.

A Concise Handbook Of Mathematics Physics And Engineering Sciences

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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2010-10-18

A Concise Handbook Of Mathematics Physics And Engineering Sciences written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-18 with Mathematics categories.

A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students

Theorems In School

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Author : Paolo Boero
language : en
Publisher: Sense Publishers
Release Date : 2007

Theorems In School written by Paolo Boero and has been published by Sense Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Education categories.

This book, addressing mathematics educators, teacher-trainers and teachers, is published as a contribution to the endeavour of renewing the teaching of proof (and theorems) on the basis of historical-epistemological, cognitive and didactical considerations.

Geometric Algebra With Applications In Science And Engineering

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Author : Eduardo Bayro Corrochano
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28

Geometric Algebra With Applications In Science And Engineering written by Eduardo Bayro Corrochano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.

The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.

Optimization

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Author : Simon Serovajsky
language : en
Publisher: CRC Press
Release Date : 2024-07-30

Optimization written by Simon Serovajsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-30 with Mathematics categories.

Optimization: 100 Examples is a book devoted to the analysis of scenarios for which the use of well-known optimization methods encounter certain difficulties. Analysing such examples allows a deeper understanding of the features of these optimization methods, including the limits of their applicability. In this way, the book seeks to stimulate further development and understanding of the theory of optimal control. The study of the presented examples makes it possible to more effectively diagnose problems that arise in the practical solution of optimal control problems, and to find ways to overcome the difficulties that have arisen. Features Vast collection of examples Simple. accessible presentation Suitable as a research reference for anyone with an interest in optimization and optimal control theory, including mathematicians and engineers Examples differ in properties, i.e. each effect for each class of problems is illustrated by a unique example. Simon Serovajsky is a professor of mathematics at Al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimization and optimal control theory, mathematical physics, mathematical modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.

Real Analysis On Intervals

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Author : A. D. R. Choudary
language : en
Publisher: Springer
Release Date : 2014-11-20

Real Analysis On Intervals written by A. D. R. Choudary and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-20 with Mathematics categories.

The book targets undergraduate and postgraduate mathematics students and helps them develop a deep understanding of mathematical analysis. Designed as a first course in real analysis, it helps students learn how abstract mathematical analysis solves mathematical problems that relate to the real world. As well as providing a valuable source of inspiration for contemporary research in mathematics, the book helps students read, understand and construct mathematical proofs, develop their problem-solving abilities and comprehend the importance and frontiers of computer facilities and much more. It offers comprehensive material for both seminars and independent study for readers with a basic knowledge of calculus and linear algebra. The first nine chapters followed by the appendix on the Stieltjes integral are recommended for graduate students studying probability and statistics, while the first eight chapters followed by the appendix on dynamical systems will be of use to students of biology and environmental sciences. Chapter 10 and the appendixes are of interest to those pursuing further studies at specialized advanced levels. Exercises at the end of each section, as well as commentaries at the end of each chapter, further aid readers’ understanding. The ultimate goal of the book is to raise awareness of the fine architecture of analysis and its relationship with the other fields of mathematics.

Mathematics Studies Through Technology Precalculus Calculus And More

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Author : Vladimir Nodelman
language : en
Publisher: World Scientific
Release Date : 2024-12-16

Mathematics Studies Through Technology Precalculus Calculus And More written by Vladimir Nodelman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-16 with Mathematics categories.

This book caters to both prospective and current mathematics educators at the school and university levels, along with their students and anyone intrigued by the possibilities of integrating software into mathematics education.Mathematics, being a unified science, is best comprehended when its cohesive nature is emphasized and demonstrated to students. Educational software assumes a pivotal role in achieving this pedagogical goal.The book outlines the author's methodology in utilizing educational software for developing and applying computer models, grounded in a thorough analysis of the subject matter. This approach is vividly illustrated through examples employing a non-profit authoring program (VisuMatica) provided with the book, enabling users to:Through the guidance of this book, students will discover mathematics as clear, visible, friendly, and enjoyable.The author exemplifies this approach by focusing on the functional line of mathematics, spanning from school basics to advanced university courses in higher mathematics. Importantly, the assimilated ideas and techniques are readily applicable to teaching and learning other areas of mathematics.

Essentials Of Discrete Mathematics

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Author : David J. Hunter
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2015-08-21

Essentials Of Discrete Mathematics written by David J. Hunter and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Computers categories.

Written for the one-term course, the Third Edition of Essentials of Discrete Mathematics is designed to serve computer science majors as well as students from a wide range of disciplines. The material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and referred to throughout the text, providing a richer context for examples and applications. tudents will encounter algorithms near the end of the text, after they have acquired the skills and experience needed to analyze them. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linguistics, economics, and music.

Essays In Memory Of Imre Lakatos

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Author : Robert S. Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Essays In Memory Of Imre Lakatos written by Robert S. Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

The death of Imre Lakatos on February 2, 1974 was a personal and philosophical loss to the worldwide circle of his friends, colleagues and students. This volume reflects the range of his interests in mathematics, logic, politics and especially in the history and methodology of the sciences. Indeed, Lakatos was a man in search of rationality in all of its forms. He thought he had found it in the historical development of scientific knowledge, yet he also saw rationality endangered everywhere. To honor Lakatos is to honor his sharp and aggressive criticism as well as his humane warmth and his quick wit. He was a person to love and to struggle with. PAUL K. FEYERABEND ROBERT S. COHEN MARX W. WARTOFSKY TABLE OF CONTENTS Preface VII JOHN WORRALL / Imre Lakatos (1922-1974): Philosopher of Mathematics and Philosopher of Science JOSEPH AGASSI / The Lakatosian Revolution 9 23 D. M. ARMSTRONG / Immediate Perception w. W. BAR TLEY, III/On Imre Lakatos 37 WILLIAM BERKSON / Lakatos One and Lakatos Two: An Appreciation 39 I. B. COHEN / William Whewell and the Concept of Scientific Revolution 55 L. JONATHAN COHEN / How Can One Testimony Corroborate Another? 65 R. S. COHEN / Constraints on Science 79 GENE D'AMOUR/ Research Programs, Rationality, and Ethics 87 YEHUDA ELKANA / Introduction: Culture, Cultural System and Science 99 PA UL K.