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.
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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.
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Solving Mathematical Problems: A Personal Perspective by Terence Tao. Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level.
Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions thro Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level.
Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout.
Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics. Get A Copy. Paperback , pages. More Details Original Title. Other Editions 3. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Solving Mathematical Problems , please sign up. Be the first to ask a question about Solving Mathematical Problems. Lists with This Book.
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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: 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. The answer is rather surprising, in fact you can make the area less than any chosen number. Tao has worked on the n-dimensional Kakeya problem where again the minimum volume can be made as small as one chooses, but the fractal dimension of the shape is unknown.
This problem sounds rather specialised, but on the contrary there are surprising connections to Fourier analysis and nonlinear waves. Another area in which Tao has worked is solving special cases of the equations of general relativity describing gravity.
Imposing cylindrical symmetry on the equations leads to the "wave maps" problem where, although it has yet to be solved, Tao's contributions have led to a great resurgence of interest since his ideas seem to have made a solution possible. One might imagine that with his remarkable output of research papers, Tao would not find time to write books.
However, this would be entirely wrong since he has produced both research monographs and undergraduate texts. Let us now look at these.
In Tao published a 2-volume textbook Analysis. The publisher describes the work as follows:- This two-volume introduction to real analysis is intended for honours undergraduates, who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of the number systems and set theory, and then goes on to the basics of analysis limits, series, continuity, differentiation, Riemann integration , through to power series, several-variable calculus and Fourier analysis , and finally the Lebesgue integral.
These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The course material is deeply intertwined with the exercises, as it is intended for the student to actively learn the material and to practice thinking and writing rigorously.
Also in , Tao published Nonlinear dispersive equations. Sebastian Herr begins a review as follows:- This monograph is a remarkable introduction to nonlinear dispersive evolution equations, in particular to their local and global well-posedness and scattering theory. Yet a third publication was Solving mathematical problems.
The publisher, Oxford University Press, describes the book as follows:- Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving mathematical problems includes numerous exercises and model solutions throughout.
Assuming only basic high-school mathematics, the text is ideal for general readers and students of 14 years and above with an interest in pure mathematics.