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, by Edward Frenkel
Download Ebook , by Edward Frenkel
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Product details
File Size: 11837 KB
Print Length: 306 pages
Publisher: Basic Books; Reprint edition (October 1, 2013)
Publication Date: October 1, 2013
Sold by: Hachette Book Group
Language: English
ASIN: B00BKRW5E6
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Amazon Best Sellers Rank:
#339,909 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
First of all, let's be honest and not mislead the general reader - this book covers a lot of highly advanced math. The author, Edward Frenkel, likely does as well as anyone could to outline the math in a way that a non-specialist audience can usefully grasp if they put in considerable effort and re-reading, but even then the reader needs to be comfortable with math at least at the undergrad level (calculus, differential equations, linear algebra, etc.). Don't expect to really 'understand' what Frenkel is talking about unless you have considerably greater math background, say grad school level and prior familiarity with the particular areas of math Frenkel covers.Being an engineer, I fall into the former category and came to this book already loving math, and I found the math in this book to often be quite tough going (especially in the second half of the book), though I did get a rough sense of what he was talking about (and I followed the advice to keep going in the tougher parts rather than getting bogged down). True, I could re-read the whole book to get a better understanding, but realistically it would make more sense to bone up on the prerequisite math using other books and then return to this book in a few years (yes, that long). Because I feel that the accessibility of this book for the general reader has been overstated by the book's endorsers and overestimated by the author, I'm deducting a star.That said, I did enjoy this book greatly and am glad that I read it. Besides the exposure to high-level math and the associated research and discovery process (at both the individual and collaborative levels), I found this window into Russian culture fascinating, and frankly I was rather surprised to see that the culture matches many of the stereotypes quite well (Frenkel relates many memorable stories in this regard). I was also inspired to see Frenkel's passion for math, his perseverance against serious adversity, and his resulting remarkable achievements, which he describes with considerable humility, all things considered. In that regard, I was also awed, yet again, to see the reach of some human minds (alas, not mine!) into the wondrous parallel universe of Platonic objective truth which we call 'mathematics' (or more precisely, perhaps we should give a different name to that universe, since 'mathematics' only reflects what we've discovered and mapped so far).Summing up, I can definitely recommend this book to anyone who already loves math and has decent mathematical 'maturity' in the sense of being able to handle math at a relatively abstract level. Those who don't have at least that background could mostly skip the math in the book and instead focus on the memoir aspect. Whether that would be worthwhile depends on the specific interests of the reader, and I only can say that I and apparently many other readers greatly enjoyed that aspect.
Although this book is readable by most, even a math major will only follow the Mathematical content to a certain extent. While Frenkel does a nice job of explaining how it all works together, I imagine the technical explanations will bog down the average reader. Also, Frenkel often toots his own horn which I imagine was difficult not to hold back on after doing cutting edge mathematics. At the same time, his intro about Math in Russia in the 1900’s was enough to make me want to finish the book out. I must admit that the last chapter or two was somewhat difficult to finish. I guess that I’m glad I read it, but I will not be reading it again.
You can clearly tell that the author loves mathematics, it jumps out at you as you read the book - the enthusiasm and excitement is clear in each page. At times, the excitement is so great that the mathematical terms and concepts jump off the page and the author seems to get lost in his thoughts. At those times, the reader can get lost also - lost in math, as the concepts are so hard to follow that reading them two or three times doesn't help. After these binges by the author, he tends to somewhat apologize that the reader's head may be spinning.But to me, as I love math also, even these pages are interesting. The mathematical terms, Lie Groups, automorphic functions, Riemann surfaces, etc. are another exciting world that I will never fully understand but can read in books like this one and get a level of some of the enthusiasm that I felt as a math major in college, prior to entering the business world.I agree, however, that the average reader may be turned off by all of this, and possibly not finish the book. However, if you have a love of math, either current, or dormant and want to revitalize it, then pick up and read this book. You will probably enjoy it like I did.
Edward has done an amazing thing - he has translated the concepts of advanced mathematics into an every day language that, with a little reflection, makes deeply difficult concepts readily accessible to the interested reader. Edward shows us that mathematics is not at all the solving equations that we did in school, but rather a whole world of deeply creative ideas that enables us to better understand our world.As someone deeply passionate about mathematics, but having very little talent, this book was able to open very many doors of understanding for me that previously were closed.The mathematics in here is not conceptually dumbed down and readers should expect to think and reflect to get the full value from the book.Stylistically the book alternates often between an autobiographical chapter and then a beautiful exposition of the mathematics Edward was studying. I disagree entirely with reviewers who have said the book is too autobiographical or that it is self-congratulatory. It is very clearly a passionate and cheerful exposition of Edward's favorite mathematics, which is balanced beautifully with his fascinating and interesting autobiography as a mathematician.There are many ways to read this book and benefit - however I find that because the mathematics he is discussing is so advanced, it will probably appeal most to people who are interested or intrigued with mathematics (and quantum physics). It will help mathematicians explain their concepts in simpler language, and help lay people understand part of why mathematics is so beautiful and powerful.The topics include group theory, knot theory, analysis, number theory, sheaf theory, abstract algebra, gauge theory, and the laglands program which ties many of these ideas together.While the book succeeds in presenting extremely advanced mathematical ideas in very simple language, any passionate reader should read the book multiple times to truly absorb the concepts and see the connections at a deeper level.For a comparison - The book is nowhere near as challenging, rigorous, or complicated as roger penrose's road to reality. At the same time, it is more conceptually focused than ian stewart's books. It is more rigorous than Steven Stroglat'z 'joy of x' - All of these characteristics form its strength - I will happily recommend this book to anyone interested in mathematics or wanting to understand quantum physics better.
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