![]() This was certainly a personal issue, as like I said, I went into this book, not really expecting what I got, and believing it would have been the usual, fascinating and enriching Mathematical literary composition, when in reality it was closer to a textbook. By the end of the book I was just reading to get an incredibly general impression of the essence of solving a mathematical problems, and found myself not really bothering to understand every statement and every step. I started this book hoping to get a deep insight into basic mathematical problem solving, and was doing all of the exercises, focusing on the logic of his solutions, and paying a great deal of attention to how Terence Tao worked through each problem. This book was aimed at the 14+ age category, I am 17 currently studying Advanced Higher Maths and a fair few areas were completely unknown to me, so I am not be sure how 14 year old me would have coped with this, I'm pretty sure I would not have gotten a single shred of it. But, nonetheless, this was coherent, a fairly good introduction to Problems from Mathematics Olympiads, and at times really quite interesting. This was not the case and I felt slightly idiotic when I realised I had purchased a textbook rather than I book on interesting Maths concepts and the history of the subject. I started reading this thinking it would be similar in content and arousal of interest as the other Maths texts I have read. The other, more personal, criticism is that many of the solutions depend heavily on modulo arithmetic, which again tends to lend itself towards abstract problems.Īll that said, I enjoyed reading it and will probably refer back to the individual chapters if I find myself working/struggling in one of those domains. My only criticisms of this book are that it is especially geared towards solving abstract mathematics problems (with a clear bias towards mathematics competitions) as opposed to applied problems that require abstract mathematics (as in much if physics). The personal tone of the author also reminds me of Div, Grad, Curl and all that which I think channels the goal perfectly - it is relatively easy for the reader to follow the thought process of Terry Tao. It acts as a nice survey of topics in mathematics (including number theory, analytic geometry, functional analysis, etc) and includes a legitimately fun "sundry" chapter at the end. The book is, as promised by the title, focused on methods for solving problems rather than a more rigorous treatment of any particular problem. I quite liked this book and would have found it extremely useful if I had managed to find it when I first started studying math and physics in university. Tao modifies the problems till one he can solve, following a logical path when taking decisions.Īlways try to use tactics that get you closer to the objective, unless all available direct approaches have been exhausted - In this case go sideways or backwards ! Guess the easy options first, in order to save time. Try to relate the problem to things you know, e.g. Do not apply ideas blindly, but rather think ahead if it can attain the goal. Simplify, exploit data and reach tactical goals.īasically, you should do this using a low risk approach. ![]() Modify the problem ( slightly and significantly ) Write down what you know, draw a diagram. Heuristics to approach problems, with main ideas: ![]() Main ideas I got from the book:Ī bit like How to solve it, from Polya. There are no answers to the problems, but they are in general fairly easy. After each solved problem Tao proposes a few related (or not) ones to repeat the technique suggested. Around 100 pages, it contains only a few chapters on main olympiad topics. Very easy to read, probably in one day you can finish it. There is not much to learn from it, as it has been written by Tao in his (mathematical) youth, and by that time he didn't have a solid writing style yet. I was quite disappointed after reading this book.
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