Intuition In Science And Mathematics
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Intuition In Science And Mathematics
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Author : Efraim Fischbein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-19
Intuition In Science And Mathematics written by Efraim Fischbein 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 2005-12-19 with Education categories.
In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.
Thinking About Equations
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Author : Matt A. Bernstein
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-20
Thinking About Equations written by Matt A. Bernstein and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Mathematics categories.
An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.
Intuition In Science And Mathematics
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Author : H. Fischbein
language : en
Publisher:
Release Date : 2014-01-15
Intuition In Science And Mathematics written by H. Fischbein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Mathematical Intuition
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Author : R.L. Tieszen
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-06-30
Mathematical Intuition written by R.L. Tieszen 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 1989-06-30 with Philosophy categories.
"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.
Everyday Practice Of Science
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Author : Frederick Grinnell
language : en
Publisher: Oxford University Press
Release Date : 2008-12-31
Everyday Practice Of Science written by Frederick Grinnell and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-31 with Science categories.
Scientific facts can be so complicated that only specialists in a field fully appreciate the details, but the nature of everyday practice that gives rise to these facts should be understandable by everyone interested in science. This book describes how scientists bring their own interests and passions to their work, illustrates the dynamics between researchers and the research community, and emphasizes a contextual understanding of science in place of the linear model found in textbooks with its singular focus on "scientific method." Everyday Practice of Science also introduces readers to issues about science and society. Practice requires value judgments: What should be done? Who should do it? Who should pay for it? How much? Balancing scientific opportunities with societal needs depends on appreciating both the promises and the ambiguities of science. Understanding practice informs discussions about how to manage research integrity, conflict of interest, and the challenge of modern genetics to human research ethics. Society cannot have the benefits of research without the risks. The last chapter contrasts the practices of science and religion as reflective of two different types of faith and describes a holistic framework within which they dynamically interact.
Mathematics Of Finance
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Author : Donald G. Saari
language : en
Publisher: Springer Nature
Release Date : 2019-08-31
Mathematics Of Finance written by Donald G. Saari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-31 with Mathematics categories.
This textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools. Financial interactions are characterized by a vast amount of data and uncertainty; navigating the inherent dangers and hidden opportunities requires a keen understanding of what techniques to apply and when. By exploring the conceptual foundations of options pricing, the author equips readers to choose their tools with a critical eye and adapt to emerging challenges. Introducing the basics of gambles through realistic scenarios, the text goes on to build the core financial techniques of Puts, Calls, hedging, and arbitrage. Chapters on modeling and probability lead into the centerpiece: the Black–Scholes equation. Omitting the mechanics of solving Black–Scholes itself, the presentation instead focuses on an in-depth analysis of its derivation and solutions. Advanced topics that follow include the Greeks, American options, and embellishments. Throughout, the author presents topics in an engaging conversational style. “Intuition breaks” frequently prompt students to set aside mathematical details and think critically about the relevance of tools in context. Mathematics of Finance is ideal for undergraduates from a variety of backgrounds, including mathematics, economics, statistics, data science, and computer science. Students should have experience with the standard calculus sequence, as well as a familiarity with differential equations and probability. No financial expertise is assumed of student or instructor; in fact, the text’s deep connection to mathematical ideas makes it suitable for a math capstone course. A complete set of the author’s lecture videos is available on YouTube, providing a comprehensive supplementary resource for a course or independent study.
Rational Intuition
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Author : Lisa M. Osbeck
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-25
Rational Intuition written by Lisa M. Osbeck and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-25 with Psychology categories.
Rational Intuition explores the concept of intuition as it relates to rationality through mediums of history, philosophy, cognitive science, and psychology.
The Outer Limits Of Reason
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Author : Noson S. Yanofsky
language : en
Publisher: MIT Press
Release Date : 2013-08-23
The Outer Limits Of Reason written by Noson S. Yanofsky and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-23 with Science categories.
This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Math Better Explained
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Author : Kalid Azad
language : en
Publisher:
Release Date : 2015-12-04
Math Better Explained written by Kalid Azad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-04 with categories.
Math, Better Explained is an intuitive guide to the math fundamentals. Learn math the way your teachers always wanted.
All The Mathematics You Missed
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Author : Thomas A. Garrity
language : en
Publisher: Cambridge University Press
Release Date : 2002
All The Mathematics You Missed written by Thomas A. Garrity and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
An essential resource for advanced undergraduate and beginning graduate students in quantitative subjects who need to quickly learn some serious mathematics.