Intuition in Science and Mathematics

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Publisher : Springer Science & Business Media
ISBN 13 : 0306472376
Total Pages : 298 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Intuition in Science and Mathematics by : H. Fischbein

Download or read book Intuition in Science and Mathematics written by H. Fischbein and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Intuition in Science and Mathematics

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Publisher : Springer Science & Business Media
ISBN 13 : 9027725063
Total Pages : 234 pages
Book Rating : 4.0/5 (277 download)

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Book Synopsis Intuition in Science and Mathematics by : H. Fischbein

Download or read book Intuition in Science and Mathematics written by H. Fischbein and published by Springer Science & Business Media. This book was released on 1987-10-31 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Intuition in Science and Mathematics

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Author :
Publisher : Springer
ISBN 13 : 9789048184378
Total Pages : 226 pages
Book Rating : 4.1/5 (843 download)

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Book Synopsis Intuition in Science and Mathematics by : H. Fischbein

Download or read book Intuition in Science and Mathematics written by H. Fischbein and published by Springer. This book was released on 2010-10-28 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Intuition in Mathematics and Physics

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Publisher :
ISBN 13 : 9781940447131
Total Pages : 246 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Intuition in Mathematics and Physics by : Ronny Desmet

Download or read book Intuition in Mathematics and Physics written by Ronny Desmet and published by . This book was released on 2016-06-16 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Intuition

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Publisher : Springer Science & Business Media
ISBN 13 : 9400922930
Total Pages : 223 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Mathematical Intuition by : R.L. Tieszen

Download or read book Mathematical Intuition written by R.L. Tieszen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Intuition in Science and Mathematics

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Publisher :
ISBN 13 : 9789401737371
Total Pages : 244 pages
Book Rating : 4.7/5 (373 download)

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Book Synopsis Intuition in Science and Mathematics by : H. Fischbein

Download or read book Intuition in Science and Mathematics written by H. Fischbein and published by . This book was released on 2014-01-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:

How Students (mis-) Understand Science and Mathematics

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Publisher : Teachers College Press
ISBN 13 : 9780807770412
Total Pages : 148 pages
Book Rating : 4.7/5 (74 download)

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Book Synopsis How Students (mis-) Understand Science and Mathematics by : Ruth Stavy

Download or read book How Students (mis-) Understand Science and Mathematics written by Ruth Stavy and published by Teachers College Press. This book was released on 2000-01-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this long-awaited book, Timothy J. Lensmire examines the problems and promise of progressive literacy education. He does this by developing a series of striking metaphors in which, for example, he imagines the writing workshop as a carnival or popular festival and the teacher as a novelist who writes her student-characters into more and less desirable classroom stories. Grounded in Lensmire's own and others' work in schools, Powerful Writing, Responsible Teaching makes powerful use of Bakhtin's theories of language and writing and Dewey's vision of schooling and democracy. Lensmire's book is, at once, a defense, a criticism, and a reconstruction of progressive and critical literacy approaches.

Thinking About Equations

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Publisher : John Wiley & Sons
ISBN 13 : 1118210646
Total Pages : 189 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Thinking About Equations by : Matt A. Bernstein

Download or read book Thinking About Equations written by Matt A. Bernstein and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Encyclopedia of Mathematics Education

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Publisher : Springer
ISBN 13 : 9783030157883
Total Pages : 916 pages
Book Rating : 4.1/5 (578 download)

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Book Synopsis Encyclopedia of Mathematics Education by : Stephen Lerman

Download or read book Encyclopedia of Mathematics Education written by Stephen Lerman and published by Springer. This book was released on 2020-02-07 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Mathematics Education is a comprehensive reference text, covering every topic in the field with entries ranging from short descriptions to much longer pieces where the topic warrants more elaboration. The entries provide access to theories and to research in the area and refer to the leading publications for further reading. The Encyclopedia is aimed at graduate students, researchers, curriculum developers, policy makers, and others with interests in the field of mathematics education. It is planned to be 700 pages in length in its hard copy form but the text will subsequently be up-dated and developed on-line in a way that retains the integrity of the ideas, the responsibility for which will be in the hands of the Editor-in-Chief and the Editorial Board. This second edition will include additional entries on: new ideas in the politics of mathematics education, working with minority students, mathematics and art, other cross-disciplinary studies, studies in emotions and mathematics, new frameworks for analysis of mathematics classrooms, and using simulations in mathematics teacher education. Existing entries will be revised and new entries written. Members of the international mathematics education research community will be invited to propose new entries. Editorial Board: Bharath Sriraman Melony Graven Yoshinori Shimizu Ruhama Even Michele Artigue Eva Jablonka Wish to Become an Author? Springer's Encyclopedia of Mathematics Education's first edition was published in 2014. The Encyclopedia is a "living" project and will continue to accept articles online as part of an eventual second edition. Articles will be peer-reviewed in a timely manner and, if found acceptable, will be immediately published online. Suggested articles are, of course, welcome. Feel encouraged to think about additional topics that we overlooked the first time around, and to suggest colleagues (including yourself!) who will want to write them. Interested new authors should contact the editor in chief, Stephen Lerman, at [email protected], for more specific instructions.

Understanding Intuition

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Publisher : Academic Press
ISBN 13 : 0128141093
Total Pages : 244 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Understanding Intuition by : Lois Isenman

Download or read book Understanding Intuition written by Lois Isenman and published by Academic Press. This book was released on 2018-04-12 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding Intuition: A Journey In and Out of Science explores the biological and cognitive mechanisms that account for intuition, and examines the first-person experience. The book integrates both scientific and personal perspectives on this important yet elusive mental capacity. It uses specific encounters to illustrate that intuition is enhanced when we can attend to the subtle aspects of our inner experiences, such as bodily sensations, images, and differing kinds of intuitive evaluative feelings, all of which may emerge no further than on the fringe of awareness. This awareness of subtle inner experiences helps forge a more fluid exchange between the unconscious and conscious minds, and allows readers to calibrate their own intuitions. Over the course of the book, readers will gain a deeper appreciation and respect for the unconscious mind and its potential sophistication, and even its potential wisdom. Understanding Intuition is a timely and critical resource for students and researchers in psychology, cognitive science, theology, women’s studies, and neuroscience. Stresses the powerful influence of the unconscious mind and its important adaptive role Frames intuition as significant and novel unconscious insight Presents a systematic framework for understanding different kinds of intuition Examines the emotional underpinnings of intuition, giving special emphasis to the role of somatic feelings and their derivatives

Experiencing Geometry

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Publisher : Prentice Hall
ISBN 13 :
Total Pages : 438 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Experiencing Geometry by : David Wilson Henderson

Download or read book Experiencing Geometry written by David Wilson Henderson and published by Prentice Hall. This book was released on 2005 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: The distinctive approach of Henderson and Taimina's volume stimulates readers to develop a broader, deeper, understanding of mathematics through active experience--including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting, challenging problems encourage readers to gather and discuss their reasonings and understanding. The volume provides an understanding of the possible shapes of the physical universe. The authors provide extensive information on historical strands of geometry, straightness on cylinders and cones and hyperbolic planes, triangles and congruencies, area and holonomy, parallel transport, SSS, ASS, SAA, and AAA, parallel postulates, isometries and patterns, dissection theory, square roots, pythagoras and similar triangles, projections of a sphere onto a plane, inversions in circles, projections (models) of hyperbolic planes, trigonometry and duality, 3-spheres and hyperbolic 3-spaces and polyhedra. For mathematics educators and other who need to understand the meaning of geometry.

Teaching to Intuition

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Publisher : Dog Ear Publishing
ISBN 13 : 9781457518652
Total Pages : 194 pages
Book Rating : 4.5/5 (186 download)

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Book Synopsis Teaching to Intuition by : Edric Cane

Download or read book Teaching to Intuition written by Edric Cane and published by Dog Ear Publishing. This book was released on 2013-03-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edric's book is absolutely outstanding. His insight into kids' mental processes, and his techniques for building bridges between real-world experience and math processing are something pretty close to a paradigm shift. AND he knows how to write clearly, simply, conversationally. Howard and Marion Brady, educators, authors, What's Worth Learning. "I have never actually been thanked after a lesson, but today I was. Many times." A teacher tries a strategy based on teaching to her students' intuition, and a topic that had frustrated them no longer seems such a hurdle. Through very practical strategies that teachers can immediately borrow for their classes, Teaching to Intuition seeks to address the widespread estrangement from mathematics displayed by many. Focusing on essential elementary and middle school topics, at that early stage where gaps begin and where too many children lose ground and lose hope, Teaching to Intuition seeks to reconcile students with mathematics itself. It proposes strategies to connect the facts and processes of mathematics to our children's intimate sense of understanding and helps them see mathematics as an emanation of realities and thinking structures that are already theirs. Edric Cane has taught in Europe, in Africa, and at Oberlin College (Ohio) and Occidental College (Los Angeles). He taught math in a 95 percent minority school in the Los Angeles Unified School District. He has a PhD from the University of Michigan and spent two years as a Besse Scholar at Saint Antony's College (Oxford University, England). He now lives near Sacramento, California. The originality of Teaching to Intuition reflects to some degree the variety of his experiences and interests.

Street-Fighting Mathematics

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Publisher : MIT Press
ISBN 13 : 0262265591
Total Pages : 152 pages
Book Rating : 4.2/5 (622 download)

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Book Synopsis Street-Fighting Mathematics by : Sanjoy Mahajan

Download or read book Street-Fighting Mathematics written by Sanjoy Mahajan and published by MIT Press. This book was released on 2010-03-05 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Math, Better Explained

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Publisher :
ISBN 13 : 9781519711540
Total Pages : 98 pages
Book Rating : 4.7/5 (115 download)

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Book Synopsis Math, Better Explained by : Kalid Azad

Download or read book Math, Better Explained written by Kalid Azad and published by . This book was released on 2015-12-04 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math, Better Explained is an intuitive guide to the math fundamentals. Learn math the way your teachers always wanted.

Intuition and Science

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Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Intuition and Science by : Mario Bunge

Download or read book Intuition and Science written by Mario Bunge and published by . This book was released on 1962 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Intuition

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Publisher : St. Martin's Griffin
ISBN 13 : 1429907673
Total Pages : 209 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Intuition by : Osho

Download or read book Intuition written by Osho and published by St. Martin's Griffin. This book was released on 2007-04-01 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover your own deep well of wisdom in Intuition: Knowing Beyond Logic—from one of the greatest spiritual teachers of the twentieth century. Intuition deals with the difference between the intellectual, logical mind and the more encompassing realm of spirit. Logic is how the mind knows reality, intuition is how the spirit experiences reality. Osho’s discussion of these matters is wonderfully lucid, occasionally funny, and thoroughly engrossing. All people have a natural capacity for intuition, but often social conditioning and formal education work against it. People are taught to ignore their instincts rather than to understand and use them as a foundation for individual growth and development—and in the process they undermine the very roots of the innate wisdom that is meant to flower into intuition. In this volume, Osho pinpoints exactly what intuition is and gives guidelines for how to identify its functioning in others and ourselves. You will learn to distinguish between genuine intuitive insight and the “wishful thinking” that can often lead to mistaken choices and unwanted consequences. Includes many specific exercises and meditations designed to nourish and support each individual’s natural intuitive gifts. Osho challenges readers to examine and break free of the conditioned belief systems and prejudices that limit their capacity to enjoy life in all its richness. He has been described by the Sunday Times of London as one of the “1000 Makers of the 20th Century” and by Sunday Mid-Day (India) as one of the ten people—along with Gandhi, Nehru, and Buddha—who have changed the destiny of India. Since his death in 1990, the influence of his teachings continues to expand, reaching seekers of all ages in virtually every country of the world.

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being

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Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being by : George Lakoff

Download or read book Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being written by George Lakoff and published by . This book was released on 2000-11-02 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the cognitive science of mathematical ideas.