Solving Mathematical Problems: A Personal Perspective by Terence Tao (PDF)

Description

Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I saw Dr. Tao on the Stephen Colbert show a few months ago and was dazzled by his brilliance. I am an internist but I like to think of myself as a polymath who can read and think about anything. I was good in math in school and was an A student in calculus in college. It’s been many years since I’ve thought about math.I bought this book to see how the author thinks. It’s amazing to me, as someone who regards himself as “smart,” how quickly I became humbled by the mind of Terence Tao. After ten pages I knew I was in over my head but I stretched my mind for a while before putting the book aside. I am not sure what kind of background is necessary to understand this book, but I can tell you that college calculus and medical school is not the path to understanding.To say Terence Tao is a genius is not enough. He is so much smarter than the average intellectual that the market for him and his book is quite limited. It must be wonderful to wake up every day and start thinking if you’re Terence Tao.

⭐I came across this book after reading about Terence Tao, a recent Fields medalist. It’s interesting to see a book like this by such an accomplished mathematician. The book gives practical approaches to solving the types of math problems encountered in math olympiad competitions. I am not, nor have I ever been, a math olympian, but I found the book to be entertaining and useful for intellectual fortification purposes.

⭐I really liked this book. It is written by one of the most brilliant mathematicians of our generation. It presents some of the problem solving techniques math contestants should master in a mature though approachable manner. I wouldn’t suggest it as the only book to consult when designing a training curriculum for high level math contestants, but it is definitelly a good reference, and nicely written.

⭐the publisher’s ethics in releasing this “second edition”(does anyone remember the first?) are verymuch in line with what’s coming out of wallstreet lately — this is a shameless exploitationof the author’s recent medal received long afterhe “wrote” this book — this slim volume is in factthin not only in terms of page count but also in termsof originality — in the sense that it ain’t got any –problems , almost all of which are painfully well known,are laboriously treated to several pages of wastefulverbiage before finally revealing the one or two linesolution — there is no reason on earth why anyone whohas even a modest problem book collection should considerthis hack job —

⭐Terence Tao is an extremely smart man and this is a very hard book.

⭐very good book

⭐It’s easy to set a very hard and complicated math question. But it’s not so easy to set a hard question that appears simple and easy to understand but requires ingenuity to solve. That’s why this book is delighting.

⭐This charming book explains why math olympiad puzzles are fun, and gives 15 year old insights ( in two senses — most of the text was written by the 15 year old Terence Tao, but revised with some additional good exercises 15 years later by 30 year old Fields medalist Terence Tao.) The style is chatty, and the advice and worked examples are very good and do not require any math beyond pre-calculus. The level of difficulty is just right for would be high school math competitors, and adults with some math who enjoy a mild challenge.

⭐First, the bad news.The front cover of this book gives its author as “Terence Tao, Fields Medal winner 2006”. Well … yes, and no. The thing is, this book was written when Tao was 15 years old. It reflects the precocious skill and insight of an outstandingly gifted 15-year-old, who had won a gold medal at the International Mathematical Olympiad at age 13 (most participants are 17-ish), but not really those of the outstandingly gifted 31-year-old who won the Fields.It’s only about 100 pages long; the problems it discusses are mostly relatively easy (meaning, say, national high-school mathematics competition level or thereabouts, rather than IMO, so not *that* easy). It doesn’t give away any very deep secrets (if there are any) about how to solve such problems. Write down what you know, look for symmetries, simplify step by step, etc.; the real rocket science, as it were, is hidden away in the bits of Tao’s brain that instinctively know what symmetries to look for, what steps are likely to lead in the right direction, and so on.The good news: You wouldn’t know it was written by a 15-year-old if the preface didn’t tell you. It *is* a book about mathematics written by someone with a Fields-medal-quality brain, and a book about Olympiad-style problems written by one of the greatest-ever exponents of that art. It contains some nice problems, with solutions by (I repeat myself) one of the finest minds in the business. It’s also quite cheap.If you’re interested in this, you should also look at Paul Zeitz’s “The art and craft of problem-solving”; it has more pages and more substance to it, but it’s twice the price and wasn’t written by a Fields medalist.

⭐It is a good book covering examples of Olympiad mathematic competition

⭐This is a wonderful book to read — discusses approaches and thinking processes. This is a book of techniques not tricks. I enjoyed the “Let us try this way; hmmm that is a blind end. But we have a new clue/possibility here ….” style of writing. The tone is informal and informative, without being chatty or hand-waving.

⭐i love this book

⭐It is really Good.

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