Mathematical Intuition
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Mathematical Intuition
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Author : R.L. Tieszen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
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 2012-12-06 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.
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: Springer Science & Business Media
Release Date : 2005-12-19
Intuition In Science And Mathematics written by H. 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.
All The Mathematics You Missed
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Author : Thomas A. Garrity
language : en
Publisher: 清华大学出版社有限公司
Release Date : 2004
All The Mathematics You Missed written by Thomas A. Garrity and has been published by 清华大学出版社有限公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Chance Logic And Intuition An Introduction To The Counter Intuitive Logic Of Chance
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Author : Steven Tijms
language : en
Publisher: World Scientific
Release Date : 2021-02-18
Chance Logic And Intuition An Introduction To The Counter Intuitive Logic Of Chance written by Steven Tijms and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-18 with Mathematics categories.
Chance rules our daily lives in many different ways. From the outcomes of the lottery to the outcomes of medical tests, from the basketball court to the court of law. The ways of chance are capricious. Bizarre things happen all the time. Nevertheless, chance has a logic of its own. It obeys the rules of probability. But if you open a standard book on probability, you may very well feel far removed from everyday life. Abstract formulas and mathematical symbols stare back at you with almost every turn of the page.This book introduces you to the logic of chance without the use of mathematical formulas or symbols. In Part One, you will meet the fascinating pioneers of the mathematics of probability, including Galileo Galilei and Blaise Pascal. Their stories will introduce you, step by step, to the basics of probability. In Part Two, various examples in all areas of daily life will show you how chance defies our expectations time and again. But armed with the basic rules of probability and a good dose of inventiveness, you will be able to unravel the counter-intuitive logic of chance.
Intuition In Mathematics And Physics
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Author : Ronny Desmet
language : en
Publisher:
Release Date : 2016-06-16
Intuition In Mathematics And Physics written by Ronny Desmet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-16 with categories.
Despite the many revolutions in science and philosophy since Newton and Hume, the outdated idea of an inevitable war between the abstractions of science and the deep intuitions of humankind is reconfirmed, again and again. The history of science is interpreted and presented as a succession of victories over the army of our misleading intuitions, and each success of science is marketed as a defeat of intuition. Instead of endorsing the modern dogma that a truth cannot be scientific unless it hurts the deep intuitions of mankind, and that we cannot be scientific unless we tame the authority of our intuition, the authors of this collection highlight developments in 20th and early 21st century science and philosophy that have the potential to support, or even further, Whitehead's philosophical integration of the abstractions of mathematics and physics with the deep intuitions of humankind. Instead of accepting the authority of science-inspired philosophers to reduce and disenchant nature and humankind in the name of our most successful scientific theories, the authors stress the contemporary relevance of Whitehead's philosophical research program of thinking things together - science and intuition; facts and values - to promote the fundamental coherence that is required to start building an ecological civilization.
Intuitive Topology
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Author : Viktor Vasilʹevich Prasolov
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Intuitive Topology written by Viktor Vasilʹevich Prasolov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book is an introduction to elementary topology presented in an intuitive way, emphasizing the visual aspect. Examples of nontrivial and often unexpected topological phenomena acquaint the reader with the picturesque world of knots, links, vector fields, and two-dimensional surfaces. The book begins with definitions presented in a tangible and perceptible way, on an everyday level, and progressively makes them more precise and rigorous, eventually reaching the level of fairly sophisticated proofs. This allows meaningful problems to be tackled from the outset. Another unusual trait of this book is that it deals mainly with constructions and maps, rather than with proofs that certain maps and constructions do or do not exist. The numerous illustrations are an essential feature. The book is accessible not only to undergraduates but also to high school students and will interest any reader who has some feeling for the visual elegance of geometry and topology.
Phenomenology Logic And The Philosophy Of Mathematics
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Author : Richard L. Tieszen
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-06
Phenomenology Logic And The Philosophy Of Mathematics written by Richard L. Tieszen 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 2005-06-06 with Mathematics categories.
In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.
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.
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.