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Paradoxes In Mathematics

Author : Stanley J. Farlow
ISBN : 9780486791739
Genre : Mathematics
File Size : 60. 21 MB
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Students and puzzle enthusiasts will get plenty of enjoyment plus some painless mathematical instruction from 28 conundrums, including The Curve That Shook the World, Space Travel in a Wineglass, and Through Cantor's Looking Glass.

Mathematical Fallacies And Paradoxes

Author : Bryan Bunch
ISBN : 9780486137933
Genre : Mathematics
File Size : 21. 3 MB
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Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.

One Hundred Years Of Russell S Paradox

Author : Godehard Link
ISBN : 9783110199680
Genre : Mathematics
File Size : 48. 22 MB
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Die in diesem Band zusammengefassten Beiträge stellen die wesentlichen Forschungsergebnisse der internationalen Münchner Konferenz "100 Jahre Russell-Paradoxon" im Jahr 2001 dar, auf der an die Entdeckung des berühmten Russell Paradoxons vor 100 Jahren erinnert wurde. Die 31 Beiträge und der Einführungsessay des Herausgebers wurden alle - bis auf zwei Ausnahmen - ursprünglich für diesen Band verfasst.

A Cultural Paradox Fun In Mathematics

Author : Jeffrey A. Zilahy
ISBN : 9780557122646
Genre : Mathematical recreations
File Size : 82. 94 MB
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Do you think "math = awesome" is a true statement? After reading this book, you might change your answer to a yes. With "jargon avoidance" in mind, this recreational math book gives you the lowdown on why math is fun, interesting and relevant in today's society. Intended for anyone who is curious about math and where it is circa 2010. This book is less concerned with exploring the mathematical details than it is with exploring the overall impact of various discoveries and insights, and aims to be insightful, cutting edge-y and mathematically rigorous.

How Mathematicians Think

Author : William Byers
ISBN : 0691145997
Genre : Mathematics
File Size : 65. 79 MB
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To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

The Universal Book Of Mathematics

Author : David Darling
ISBN : 9780471270478
Genre : Mathematics
File Size : 88. 60 MB
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Reference book on mathematics.

Philosophy Of Mathematics

Author : Gerhard Preyer
ISBN : 9783110323689
Genre : Philosophy
File Size : 67. 83 MB
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One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.

The Power Of Paradox

Author : W. Brewster Willcox
ISBN : 9781469196732
Genre : Science
File Size : 46. 95 MB
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One thing this book is not is a tightly-reasoned argument that leads the reader inevitably to the books main thesis. It is rather, like its cover, a collage. It is a hundredmore or less observations into what is deep and meaningful in life, the reality around us, that gives the impression that reality is in fact a paradox, a friendly paradox. The book looks at theology, baseball, mathematics and the Bible. And it talks a lot about particle physics and quantum mechanics. Youll notice that it fails to mention rock stars and reality TV.

The Beginning Of All Things

Author : Hans Kng
ISBN : 9780802863591
Genre : Religion
File Size : 74. 18 MB
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Translated by John Bowden In an age when faith and science seem constantly to clash, can theologians and scientists come to a meeting of minds? Yes, maintains the intrepid Hans Küng, as he brilliantly argues here that religion and science are not mutually exclusive but complementary. Focusing on beginnings -- beginnings of time, of the world, of man, of human will -- Küng deals with an array of scientific precepts and teachings. From a unified field theory to quantum physics to the Big Bang to the theory of relativity -- even superstring and chaos theories -- he examines all of the theories regarding the beginning of the universe and life (of all kinds) in that universe. Küng seeks to reconcile theology with the latest scientific insights, holding that "a confrontational model for the relationship between science and theology is out of date, whether put forward by fundamentalist believers and theologians or by rationalistic scientists and philosophers." While accepting evolution as scientists generally describe it, he still maintains a role for God in founding the laws of nature by which life evolved and in facilitating the adventure of creation. Exhibiting little patience for scientists who do not see beyond the limits of their discipline or for believers who try to tell experts how things must have been, Küng challenges readers to think more deeply about the beginnings in order to facilitate a new beginning in dialogue and understanding.

Paradoxes And Sophisms In Calculus

Author : Sergiy Klymchuk
ISBN : 9780883857816
Genre : Mathematics
File Size : 72. 47 MB
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Paradoxes and Sophisms in Calculus offers a delightful supplementary resource to enhance the study of single variable calculus. By the word paradox the authors mean a surprising, unexpected, counter-intuitive statement that looks invalid, but in fact is true. The word sophism describes intentionally invalid reasoning that looks formally correct, but in fact contains a subtle mistake or flaw. In other words, a sophism is a false proof of an incorrect statement. A collection of over fifty paradoxes and sophisms showcases the subtleties of this subject and leads students to contemplate the underlying concepts. A number of the examples treat historically significant issues that arose in the development of calculus, while others more naturally challenge readers to understand common misconceptions. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences, and series are explored. The book could be useful for high school teachers and university faculty as a teaching resource; high school and college students as a learning resource; and a professional development resource for calculus instructors.

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