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Five Golden Rules: Great Theories Of 20th Century Mathematics And Why They Matter

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An accessible and engaging treatment of the world's greatest mathematical theorems. Devoted to one theorem, each chapter introduces the mathematicians who created the theorem and the history of math at that time. Explains, in simple terms, what the theorem says and how it was proved. Numerous diagrams, cartoons and examples illustrate how the theorem works and bring the ma An accessible and engaging treatment of the world's greatest mathematical theorems. Devoted to one theorem, each chapter introduces the mathematicians who created the theorem and the history of math at that time. Explains, in simple terms, what the theorem says and how it was proved. Numerous diagrams, cartoons and examples illustrate how the theorem works and bring the math to life.


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An accessible and engaging treatment of the world's greatest mathematical theorems. Devoted to one theorem, each chapter introduces the mathematicians who created the theorem and the history of math at that time. Explains, in simple terms, what the theorem says and how it was proved. Numerous diagrams, cartoons and examples illustrate how the theorem works and bring the ma An accessible and engaging treatment of the world's greatest mathematical theorems. Devoted to one theorem, each chapter introduces the mathematicians who created the theorem and the history of math at that time. Explains, in simple terms, what the theorem says and how it was proved. Numerous diagrams, cartoons and examples illustrate how the theorem works and bring the math to life.

30 review for Five Golden Rules: Great Theories Of 20th Century Mathematics And Why They Matter

  1. 5 out of 5

    Patrick

    The Curse of Knowledge strikes again JDN 2456268 EDT 14:56. A review of Five Golden Rules by John Casti. It's a problem that plagues many nonfiction writers. Steven Pinker called it the Curse of Knowledge; Less Wrong refers to it as Inferential Distance. The problem is this: You know what you know, but you don't know what other people don't know. So it's hard to explain things without going over people's heads or seeming condescending. Five Golden Rules is supposed to be a book about cutting-edge The Curse of Knowledge strikes again JDN 2456268 EDT 14:56. A review of Five Golden Rules by John Casti. It's a problem that plagues many nonfiction writers. Steven Pinker called it the Curse of Knowledge; Less Wrong refers to it as Inferential Distance. The problem is this: You know what you know, but you don't know what other people don't know. So it's hard to explain things without going over people's heads or seeming condescending. Five Golden Rules is supposed to be a book about cutting-edge mathematics for people who don't know a lot of mathematics. It is in fact a book about cutting-edge mathematics for people who do know a lot of mathematics. I got quite a bit out of it, but I've studied abstract algebra and real analysis. Also, some of the topology still confused me, perhaps because I've never formally studied topology. How do you cut a hole in a surface and then stitch the hole closed with a Moebius strip? I'm still confused by higher-dimensional non-orientable surfaces. Also, I still don't quite get the deeper philosophical implications of Godel's incompleteness theorems. I've heard everything from "It undermines rationality itself" to "It's basically trivial". I assume the truth is somewhere in between? (I actually lean more towards the "basically trivial" side of things; a lot of paradoxes really seem like they are more statements about language than they are about truth. "It is raining in Bangladesh but Patrick Julius doesn't know that." "Patrick Julius cannot coherently assert this sentence." Both of these sentences could very well be true, but I can't assert them if they are. Is this a problem?) Casti is quite noncommital on what he thinks Godel implies. The basic format of the book centers around five seminal branches of 20th century mathematics: game theory, topology, computer science, singularity theory, and linear optimization. If you already have the basic knowledge of each field, you can get a lot out of the way Casti ties everything together with the passion of a real working mathematician. The joy he feels from exploring mathematics can be felt through the words. But if you don't at least know calculus, this book is going to make very little sense to you. He tries to make it non-mathematical, but fails really quite miserably. It's a much more pleasant read than your average math textbook, but it requires a comparable level of background knowledge. It's unfortunate really; I'd love to have a book that explains these deep mathematical concepts to people who don't know a lot of math. Unfortunately, Five Golden Rules isn't that book. Instead, it's a useful synthesis and a pleasant read for those of us who already have the necessary background.

  2. 4 out of 5

    Aathavan

    This book does a good job of explaining some of the main accomplishments of Mathematics of this last century. The ideas are well developed and explained with many examples - hypothetical and real. (I have read only Chptrs 1,2,5)

  3. 4 out of 5

    Grendelkhan

    It's not that I didn't enjoy this book, it's just that I can think of very little to say about it. I think I fall in a no-man's-land between the mathematically inclined who would find it dull and the lay reader who would consider the math to be so far over their head that it's not worth trying to understand directly, so an indirect approach, describing the applications of these six major mathematical concepts rather than their inherent logical elegance, would be indicated. That said, the section It's not that I didn't enjoy this book, it's just that I can think of very little to say about it. I think I fall in a no-man's-land between the mathematically inclined who would find it dull and the lay reader who would consider the math to be so far over their head that it's not worth trying to understand directly, so an indirect approach, describing the applications of these six major mathematical concepts rather than their inherent logical elegance, would be indicated. That said, the section I found most interesting was the one on the concept I was most familiar with, the halting problem; I'd encountered it in its barebones incarnation, following trivially from the invention of the universal Turing machine, back in my theory of computation classes, but before that, I'd seen it in Gödel Escher Bach as containing a deep analogy with Cantor's diagonalization and as the final reification of the Incompleteness Theorem. Seeing a topic I knew that well explained as to a novice was like learning it anew again, and I think I wasn't aware of the limits of a lay explanation because I already knew the full version. The other topics--the minimax theorem, Brouwer's fixed-point theorem, Morse's theorem and the simplex method--are, I'm quite sure, fascinating topics, and I was prompted to go read a bit more on my own, but the presentaiton in the book just doesn't square with my own style of learning and my level of understanding.

  4. 5 out of 5

    Ann

    Casti presents five important advance in 20th c. mathematics very clearly with interesting examples. I found the book quite engaging. If you are not very comfortable with mathematics, the book is a bit of a challenge but well worth the challege. I look forward to reading his second volume of important mathematics. Nice read to discover the importance of mathematics and get a feel for what these ideas are. The book also contains some important historical and personality notes.

  5. 5 out of 5

    kevin

    Despite the claims, this book is possibly not an easy read. It does help that I am somewhat familiar with 3 of the 5 golden rules and to a large extent, he did a great job simplifying some of the more complex notions. Highly recommended for those who had exposure in those topics, e.g., Game Theory, Turing machine, etc., and is feeling a little nostalgic, like me.

  6. 5 out of 5

    Ilya

    interesting overview of: * Game Theory (minmax) * Brower Fixed point theorem (Topology) * Morse's Singularity Theory, Catastrophe theory * The halting theorem Computability, Turing, Godel * Optimization, Linear/Dynamic Programming, Simplex Method interesting overview of: * Game Theory (minmax) * Brower Fixed point theorem (Topology) * Morse's Singularity Theory, Catastrophe theory * The halting theorem Computability, Turing, Godel * Optimization, Linear/Dynamic Programming, Simplex Method

  7. 5 out of 5

    Daniel Wright

    Took me forever. I understood a bit of the first chapter and it all went downhill from there...

  8. 4 out of 5

    Jim Foley

    Interesting presentation of 5 recently-developed brahces of math.

  9. 4 out of 5

    Quek

  10. 5 out of 5

    Frank E.

  11. 4 out of 5

    Abhishek

  12. 4 out of 5

    Jack

  13. 4 out of 5

    Giovanni

  14. 5 out of 5

    Caj Zell

  15. 4 out of 5

    Randall Scalise

  16. 5 out of 5

    Keith Mcgreggor

  17. 5 out of 5

    Hannah Jerao

  18. 4 out of 5

    Jing Zhu

  19. 5 out of 5

    Hereford

  20. 4 out of 5

    VENKATRAMAN C K

  21. 4 out of 5

    Andrew

  22. 4 out of 5

    Tadas Gedminas

  23. 4 out of 5

    Andy Juell

  24. 5 out of 5

    Xavier Alapont

  25. 4 out of 5

    TommyLovesEli

  26. 4 out of 5

    Shawn Fillinger

  27. 4 out of 5

    Matthew

  28. 4 out of 5

    John

  29. 4 out of 5

    John Taylor

  30. 4 out of 5

    Brooke Evans

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