Download (The Art of the Infinite The Pleasures of Mathematics)
E then or something akin to music structure itselfThere s a lot to
Make Fun Of In Thatfun of in that but for me I have to say Suaredances Really This was published in 2003Note I am apparently the 3rd person to have checked out this copy from the library The person before me checked it out on 16 August 2004 and it was marked returned on 30 March 2007 I m going to assume that was a faculty member Wow I loved this book It really opened my mind around how numbers Are Represented And ConstructedThis represented and constructedThis one of the best books I have read that explores the foundations of numbers in a very understandable format The approachdevelopment of math knowledge in the book was entertaining with a mix of history and inspiring proofs and examples I wished I read this book when I was in high school Topics I really appreciated include the explanation of number fields In particular I really enjoyed the explanation of why a heptagon can t be constructed with compass and ruler through the previously developed understanding of fields Additional tools would be neededOf course I ve known a lot about numbers for years and I use Real and Complex numbers every day as an engineer But I never had such an appreciation for how to constructrepresent numbers exactlyAs a side note The book such an appreciation for how to constructrepresent numbers exactlyAs a side note The book t talk about this but floating point numbers are popular for approximating real numbers Floating point numbers can be problematic because of truncation and rounding errors that occur in calculations This book has inspired me to learn about Exact Reals and has given me the ability to followunderstand papers on various strategies for exact reals as an alternative to floating point numbers. Metry into the unlikely realm where parallel lines meet Along the way deft character studies of great mathematicians and eually colorful lesser ones illustrate the opposed yet intertwined modes of mathematical thinking the intutionist notion that we discover mathematical truth as it exists and the formalist belief that math is true because we invent consistent rules for it Less than All wrote William Blake cannot satisfy Man The Art of the Infinite shows us some of the ways that Man has grappled with All and reveals mathematics as one of the most exhilarating expressions of the human imaginati. ,
One of my favorite books on math The essence of mathematics lies entirely on its freedom said Georg Cantor THE man who figured out that there are countable and uncountable infinities Wow Infinite freedom man who figured out that there are countable and uncountable infinities Wow Infinite freedom at least freedom within a playground nested with infinities Hilbert s paradise as you are about to learn in this book Hey Robert and Ellen managed to make number theory palatable for the layperson with an entire chapter on Cantor s work An infinite gold mine as a chapter And there is much The whole thing is a vivid narrative about mathematical beauty everywhere playful with subtle humor and deep erudition That is history geometry philosophy poetry infinite entertainment Mathematics is something that I find interesting but definitely wish I knew about So I went to my local library looking for a good book on math to give me an introduction to the subject When I found this book I thought I d found what I was looking for Boy was I wrongThe book is written in this weird florid prose and ust the way it was written made it impossible to read I
tried really hard but I couldn t get past the first few pages Finally I took it backreally hard but I couldn t get past the first few pages Finally I took it back the library and looked for a better alternative I gave it two stars because it probably would have been a decent book had it not been for the weird writing style I ust needed something less flowery and technical If you can handle the flowery prose then you might enjoy this book but I ust couldn t handle it Prose so purple I claim it was abused This book needed an editor to cut out the blathering that the authors thought clever The references to Rimbaud and Proust to cite ust a couple were completely unnec. Robert Kaplan's The Nothing That Is A Natural History of Zero was an international best seller translated into ten languages The Times called it elegant discursive and littered with uotes and allusions from Auinas via Gershwin to Woolf and The Philadelphia Inuirer praised it as absolutely scintillating In this delightful new book Robert Kaplan writing together with his wife Ellen Kaplan once again takes us on a witty literate and accessible tour of the world of mathematics Where The Nothing That Is looked at math through the lens of zero The Art of the Infinite takes infinity in its countless. ,
Essary and distractingI read the first 3 chapters and then skipped to the last the chapter on Georg Cantor and aleph null aleph one and transfinite numbers Fun fact Cantor was a conspiracy theoristI was excited when I read this in the introductionMany small things estrange math from its proper audience One is the remoteness of its machine made diagrams These reinforce the mistaken belief that it is all very far away on a planet visited only by graduates of the School for Space Cadets Diagrams printed out from computers communicate a second and subtler falsehood they lead the reader to think he is seeing the things themselves rather than pixellated approximations to themAn insightful remark if somewhat overwrought Hand drawn diagrams will make the text feel less imposing and let the reader know that however true They Are Humble Human Calculations Brilliant RightUnfortunately are humble human calculations Brilliant rightUnfortunately text is ridiculously remote A sampleHave negative numbers definitively moved mathematical thought into abstraction where the dance of symbols becomes vivid instead of figures Or do you the dance of symbols becomes vivid instead of figures Or do you the visual proof in the appendix to this chapter not only convincing but illuminating Notice that in our dances the
Same Steps Axioms Of Additivesteps axioms of additive multiplicative inverses and distributivity occur again and again This is because like suaredances in the confines of a barn little room to maneuver leads to intricate patterns The elaborate these become each linking onto the last the such patterns will all seem to lodge in a sense at once ancestral and abstract than sight It is as if the predominance in our brains of the visual cortex masked a different deeper apprehension of tim. Guises as a touchstone for understanding mathematical thinking Tracing a path from Pythagoras whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret the existence of irrational numbers; through Descartes and Leibniz; to the brilliant haunted Georg Cantor who proved that infinity can come in different sizes the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics The Kaplans guide us through the Republic of Numbers where we meet both its upstanding citizens and shadowy dwellers; and we travel across the plane of geo.
Robert M. Kaplan