Solving Mathematical. Problems. A Personal Perspective. Terence Tao. Department of If mathematics is likened to prospecting for gold, solving a good math-. Terence Tao was born in Adelaide, Australia, in In , , and he competed in the International Mathematical Olympiad for the Australian team, . book on mathematical problem solving which would be suitable for use in a (1) Clements, M.A. (), Terence Tao, Educational Studies in Mathematics.
|Language:||English, Spanish, German|
|Genre:||Politics & Laws|
|Distribution:||Free* [*Registration Required]|
Solving Mathematical Problems, by Terence Tao, is an updated version of a His book is easy to read and follow, and his suggested problem solving. Solving Mathematical. Problems. A Personal Perspective. KEBALANSEHSERIESYSTEENISTEREMKHATHIRE. Terence Tao. Department of Mathematics. Concerning “Solving Mathematical Problems: A Personal Perspective” by Terence Tao. Tom Verhoeff. June Introduction. Terence Tao, Fields medal.
His father, Billy Tao, is a Chinese-born paediatrician who has undertaken research on educating gifted children and on autism. Terry's mother, Grace, was born in Hong Kong and has a university degree in physics and mathematics.
Billy and Grace met while they were studying at the University of Hong Kong and they emigrated to Australia in Grace Tao taught physics, chemistry, science and mathematics in various secondary schools in Hong Kong before she emigrated to Australia and, once in Australia, also taught in secondary schools there. Terry, the subject of this biography, is their eldest child, having two younger brothers Trevor and Nigel. When Terry was two years old his parents realised that he was different from other children.
They saw him teaching five year old children to spell and to add numbers and, when they asked him how he had learnt these skills, he replied that he had been watching Sesame Street on television.
When he was three and a half years old his parents sent him to a private school but, six weeks later, they realised that he was not ready for schooling and also that the teachers did not know how to teach someone like him.
So they removed him from the school and he did not start schooling again until he was, like other children, five years old.
The article [ 4 ] is an evaluation of Terry's mathematical abilities just before his eighth birthday by which time he was attending Blackwood High School, Adelaide. Ken Clements writes that when he went into his home, Terry was Terence was small, even for a seven-year-old. After meeting his two brothers, I was accompanied by Terence to his father's study, where, after a brief chat, I began my usual assessment procedure for exceptionally bright primary school-age children.
Clements discovered that Terry knew the definition of a group and could solve graph sketching problems using the differential calculus.
He wondered how much his mother was teaching him but found that her role [ 4 ] She said that Terence likes to read mathematics by himself, and he often spent three or four hours after school reading mathematics textbooks.
By the time Terry reached the age of eleven, he was dividing his time between his studies at Blackwood High School and taking classes at Flinders University in Adelaide where he was taught by Garth Gaudry.
Even earlier, at the age of ten, he began participating in International Mathematical Olympiads. He won a bronze medal in , a silver medal in and a gold medal in , becoming the youngest ever gold medalist in the Mathematical Olympiad.
At the age of fourteen he began full-time university studies at Flinders University and was awarded a B. He continued to study at Flinders University for a Master's Degree advised by Garth Gaudry and was awarded the degree in August having written the thesis Convolution operators generated by right-monogenic and harmonic kernels.
Tao undertook research at Princeton University advised by Elias Stein. He was an assistant researcher at Princeton during and he was awarded a Sloan Postgraduate Fellowship in He was awarded his doctorate in June for his thesis Three regularity results in harmonic analysis.
In his research papers began to appear in print, four papers being published in that year. These are: Weak-type endpoint bounds for Riesz means; with Andrew C Millard On the structure of projective group representations in quaternionic Hilbert space; On the almost everywhere convergence of wavelet summation methods; and Convolution operators on Lipschitz graphs with harmonic kernels.
Following the award of his doctorate, Tao was appointed Hedrick Assistant Professor at the University of California at Los Angeles, a position he held from to He continued as an assistant professor at the University of California at Los Angeles where, at the age of twenty-four, he was promoted to full professor in In he was named the James and Carol Collins Professor there.
It is very difficult to write a biography of someone who is at the height of their creative powers as Tao is. Anything that one writes about his research contributions will be quickly outdated as he is contributing major results in such a wide range of different areas.
Yet he has produced such a fantastic collection of results, leading to the award of all the top prizes in mathematics, that one must try to at least give a vague picture of the work of this remarkable mathematician.
Before looking at his contributions we note the prizes and awards he has received although again this list is bound to become rapidly outdated as he continues to receive awards. He was a finalist in Australian of the Year in To gain some insight into his research contributions, let us first note that he received the Fields medal The article [ 1 ], describing the award of the Fields Medal, gives this overview:- Terence Tao is a supreme problem-solver whose spectacular work has had an impact across several mathematical areas.
He combines sheer technical power, an other-worldly ingenuity for hitting upon new ideas, and a startlingly natural point of view that leaves other mathematicians wondering, " Why didn't anyone see that before? The Press Release which announced the award of the Fields Medal to Tao listed his accomplishments in a number of areas which had led to the award of this most prestigious mathematical award.
First it describes his work with Ben Green on the distribution of prime numbers. They proved the remarkable result that the primes contain arithmetic progressions of any length.
To dismiss this fantastic achievement in a single sentence seems silly, but there is so much more to say. An area to which Tao has made many contributions is that of the Kakeya problem. Sort order. Dec 19, Murilo Andrade rated it liked it Shelves: I was quite disappointed after reading this book. 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.
Very easy to read, probably in one day you can finish it. Around pages, it contains only a few chapters on main olympiad topics. After each solved problem Tao proposes a few related or not ones to repeat the technique suggested.
There are no answers to the problems, but they are in general I was quite disappointed after reading this book.
There are no answers to the problems, but they are in general fairly easy. Main ideas I got from the book: Strategies in problem solving A bit like How to solve it, from Polya.
Heuristics to approach problems, with main ideas: Understand the problem Understand the data Understand the objective Select good notation Write down what you know, draw a diagram. Modify the problem slightly and significantly Prove results Simplify, exploit data and reach tactical goals. Basically, you should do this using a low risk approach.
Do not apply ideas blindly, but rather think ahead if it can attain the goal. Number Theory Try to relate the problem to things you know, e. Guess the answer e. Guess the easy options first, in order to save time.
Tao modifies the problems till one he can solve, following a logical path when taking decisions. Try small cases. Use the known facts you wrote down. Examples in algebra and analysis Always 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! Use induction! Euclidean Geometry Draw a picture! Sundry examples Choose a good notation!
Look for symmetries View 1 comment. Mar 10, Paulo Glez Ogando rated it really liked it Shelves: Terence Tao is one of the most famous and early mathematicians nowadays. He was the younger medal-winner in the IMO International Mathematical Olympiad , he won medals in three consecutive years, finally achieving the gold prize. In this book Tao aims to show the reader various tactics involved in solving mathematical problems at the IMO level, for which he assumes a basic level of mathematics, trying to avoid difficult or less known results or theorems.
A book much more famous in solving problem Terence Tao is one of the most famous and early mathematicians nowadays. A book much more famous in solving problems is How to Solve It: The latter is more theoretical, providing ways of thinking, meditation about problems and how to face them or some clues to solve them. But he offers a few examples in which you can apply them. In fact, he repeats himself continuously. In each of them he explains how to approach the solution, discarding unsuitable ways and why and choosing the best one.
Besides, he proposes a lot of problems the reader can try to solve, some of them similar to the yet solved ones, others simply a more general one. A good chance for fun, trying to apply the strategies he shows previously.
Rohan Reddy rated it really liked it Jul 10, Jie rated it it was amazing Jan 11, Armin Niakan rated it it was amazing Mar 09, Matteo rated it liked it Sep 14, Botkinbote rated it it was amazing May 29, Tanveer Muttaqueen rated it it was amazing Oct 28, Alexis Rosuel rated it really liked it Mar 10, Phillip rated it liked it Feb 09, Kaiser rated it really liked it Feb 21, Karl rated it liked it Jun 07, Sebastian rated it it was amazing Jun 18, Marc Donner rated it really liked it May 31, Yanzhang rated it liked it Dec 15, Scott Staniewicz rated it really liked it Jul 24,