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A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability.Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung a A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability.Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him. Math has a bad reputation: dull, difficult, detached from daily life. As a talking Barbie doll opined, "Math class is tough." But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function ("The year: 1972. The scene: Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey"), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.


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A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability.Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung a A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability.Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him. Math has a bad reputation: dull, difficult, detached from daily life. As a talking Barbie doll opined, "Math class is tough." But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function ("The year: 1972. The scene: Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey"), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.

30 review for Foolproof, and Other Mathematical Meditations

  1. 4 out of 5

    Brian Clegg

    The last time I enjoyed a popular maths book as much as this one was reading Martin Gardner’s Mathematical Puzzles and Diversions as a teenager. The trouble with a lot of ‘fun’ maths books is that they cover material that mathematicians consider fascinating, such as pairs of primes that are only two apart, which fail to raise much excitement in normal human beings. Here, all the articles have something a little more to them. So, even though Brian Hayes may be dealing with something fairly abstru The last time I enjoyed a popular maths book as much as this one was reading Martin Gardner’s Mathematical Puzzles and Diversions as a teenager. The trouble with a lot of ‘fun’ maths books is that they cover material that mathematicians consider fascinating, such as pairs of primes that are only two apart, which fail to raise much excitement in normal human beings. Here, all the articles have something a little more to them. So, even though Brian Hayes may be dealing with something fairly abstruse-sounding like the ratio of the volume of an n-dimensional hypersphere to the smallest hypercube that contains it, the article always has an interesting edge - in this case that although the ‘volume’ of the hypersphere grows up to the fifth dimension it gets smaller and smaller thereafter, becoming an almost undetectable part of the hypercube. If that doesn’t grab you, many articles in this collection aren’t as abstruse, covering everything from random walks to a strange betting game. What's more, an extra delight for me is that Hayes throws in a lot of computing reflections, even including snippets of code as a way of explaining some processes. I particularly loved the exploration of pseudorandom and quasirandom numbers (not the same thing) and their implications for Monte Carlo methods. The only times I felt Hayes loses it a bit is when he gets too heavily into research mode and gives us more detail than we need. For example, he digs into the origins of the story of the young Gauss adding up 1 to 100 almost instantaneously at school. His exploration of this mathematical legend is impressive, but he enumerates every possible source and route for the various versions of the legend to have originated, taking us to a level that feels unnecessarily complete. Similarly he lost me a bit when he tries to forensically examine why a Victorian mathematician who calculated pi to 707 places went wrong from the errors that he made in his calculations. But this kind of over-detailed analysis is rare. I suspect the ideal reader is someone who has an aged physics, maths or computer science degree, who is still aware of (say) what Monte Carlo methods or eigenvalues are in a vague sense, but needs some gentle reminders. The essential, however, is to have a sense of wonder in discovery. For people like us it’s a brilliant book.

  2. 5 out of 5

    Fernando Pestana da Costa

    The chapters in this book had their origin in articles published by the author in the American Scientist magazine between 1998 and 2014. It consists in a very fine selection of topics on Mathematics and mathematical related topics, some bent on the historical (like the one about the legend of young Gauss summing the terms of an arithmetic progression, or the one about Markov work on Pushkin's poem Eugene Oneguin), others about strange, somewhat counterintuitive behaviors (like the factoidal dist The chapters in this book had their origin in articles published by the author in the American Scientist magazine between 1998 and 2014. It consists in a very fine selection of topics on Mathematics and mathematical related topics, some bent on the historical (like the one about the legend of young Gauss summing the terms of an arithmetic progression, or the one about Markov work on Pushkin's poem Eugene Oneguin), others about strange, somewhat counterintuitive behaviors (like the factoidal distribution, or Zeno's wagering game). Even those about more standard stuff (so to speak), like the one titled "Playing ball in the nth dimension" have some nice surprises waiting the reader. I found this a very stimulating book on popularization of Mathematics.

  3. 5 out of 5

    Jake Cooper

    Hayes is to math what Mary Roach is to science: a tour guide I'd follow anywhere. Thoroughly researched, sparklingly written. A total charmer. Hayes is to math what Mary Roach is to science: a tour guide I'd follow anywhere. Thoroughly researched, sparklingly written. A total charmer.

  4. 5 out of 5

    Bonny

    I've learned to take publisher's blurbs with a grain of salt, but the one for Foolproof describes exactly what this interesting book delivers. Hayes is a scientist and writer, one who has the unique ability to make math understandable and accessible to non-mathematicians, and he has written a book that is accurate, informative, and highly enjoyable. His enthusiasm makes the reader want to truly understand the topics he covers in these 13 essays. I enjoyed and learned from each one of them, with I've learned to take publisher's blurbs with a grain of salt, but the one for Foolproof describes exactly what this interesting book delivers. Hayes is a scientist and writer, one who has the unique ability to make math understandable and accessible to non-mathematicians, and he has written a book that is accurate, informative, and highly enjoyable. His enthusiasm makes the reader want to truly understand the topics he covers in these 13 essays. I enjoyed and learned from each one of them, with the last one about proof in mathematics being my favorite. Who wouldn't love a discussion about proofs that prove something is impossible? The best popular math book that I have read previously is How Not to be Wrong by Jordan Ellenberg. Foolproof deserves a place right next to it on the shelf of excellent mathematics books.

  5. 5 out of 5

    Alex Gordon

    Interesting... Skimmed some. Like through the multiple pages of historical research on the short story of young gauss.. Also skimmed the many pages on factoidal randomness etc... I agree with the author on his point about history of rigorous study in math history Instead of justskipping that and just telling of the glorified "aha" moments making it seem like it didn't dome from work and study :)... I wish I had a list to share but knowing the man behind the math does make it easier to remember f Interesting... Skimmed some. Like through the multiple pages of historical research on the short story of young gauss.. Also skimmed the many pages on factoidal randomness etc... I agree with the author on his point about history of rigorous study in math history Instead of justskipping that and just telling of the glorified "aha" moments making it seem like it didn't dome from work and study :)... I wish I had a list to share but knowing the man behind the math does make it easier to remember for me... Back when I was spending long nights doing math homework I wrote a few history papers etc for english classes about math history etc... That really helped me... Aced that cal1 and cal2 class and still remember the struggle...

  6. 4 out of 5

    David02139

    An interesting survey of a number of topics in mathematics, with some counterintuitive results in probability and in n dimensional geometry. My mathematics is a bit rusty but I could understand most of the reasoning. This a a good book for those who want to have a broader knowledge of the different areas of mathematics and be surprised by some contradictions or results. The author gives the history behind each area which made each topic more understandable and interesting.

  7. 5 out of 5

    Colin

    I was a bit concerned, at first, about how much Hayes makes of not being a mathematician. That's usually a signal that maths is about to be dismissed or misunderstood - but on the contrary, the outsider's viewpoint makes Foolproof fascinating. The topics it covers are all either new to me or covered in a way that's unusual, and I rate this book very highly. I was a bit concerned, at first, about how much Hayes makes of not being a mathematician. That's usually a signal that maths is about to be dismissed or misunderstood - but on the contrary, the outsider's viewpoint makes Foolproof fascinating. The topics it covers are all either new to me or covered in a way that's unusual, and I rate this book very highly.

  8. 4 out of 5

    Kyle

    The premise of the book was that Brian as a non mathematician was writing for other non mathematicians about math. It was comprised of 13 separate topics, about a quarter which I found interesting, and others fell flat. One a few topics, he got way too far into the weeds and for someone not familiar with math, may get lost.

  9. 4 out of 5

    George Pollard

    Like another reviewer said this is one of the best pop-math books I’ve read. Everything is fresh and there’s little repetition of common stories and mathematics that are often repeated in other pop-math books.

  10. 5 out of 5

    Steve Gross

    More sophisticated than typical recreational mathematics books

  11. 5 out of 5

    James

  12. 4 out of 5

    Stefano

  13. 4 out of 5

    B SAI

  14. 4 out of 5

    Lena

  15. 4 out of 5

    Paul Vittay

  16. 4 out of 5

    Themos Kallos

  17. 5 out of 5

    Eduard Tita

  18. 5 out of 5

    Mandy

  19. 4 out of 5

    Sid Ravinutala

  20. 4 out of 5

    Gregory

  21. 5 out of 5

    Selina

  22. 5 out of 5

    Kt

  23. 4 out of 5

    Heather

  24. 4 out of 5

    Tristan

  25. 5 out of 5

    Dinab

  26. 4 out of 5

    Subhajit Das

  27. 4 out of 5

    Ali Temel

  28. 5 out of 5

    Raphael

  29. 4 out of 5

    Lubna Anees

  30. 4 out of 5

    Ryan Smith

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