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trick, that can be used in many mathematical situations. With such tricks, it is usually difficult, and in any case not desirable, to formalize them as lemmas: if you try to do so then almost certainly your formal lemma will not apply in all the situations where the trick does.

Of course, in many cases, the devil really is in the details, but nevertheless knowing the overall strategy of proof is extremely valuable when trying to read that proof.

Yong-Hui Says: November 3, 2008 at 5:57 pm | Reply I am in MSRI for the cofference discrete Rigity. Green will give the first lecture. I just happen to find a question for that tricki wiki: Whether is there a common-shared refference system for that tricki wiki? Similar to that of Mathscinet of ams math review It will be a basic instrument for a mathematical website.

Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol drew together international researchers with a variety of number-theoretic interests, and the book’s contents reflect the quality of the meeting. Topics covered include recent work on the Schur-Siegel-Smyth trace problem, Mahler measure and its generalisations, the merit factor problem, Barker sequences, K3-surfaces, self-inversive polynomials, Newman’s inequality, algorithms for sparse polynomials, the integer transfinite diameter, divisors of polynomials, non-linear recurrence sequences, polynomial ergodic averages, and the Hansen-Mullen primitivity conjecture. With surveys and expository articles presenting the latest research, this volume is essential for graduates and researchers looking for a snapshot of current progress in polynomials and number theory.• An invaluable resource to both students and experts in this area, with survey articles on the most important topics in the field • Expository articles introduce graduate students to some problems of active interest • The inclusion of new results from leading experts in the field provides a snapshot of current progress

Ergodic Theory: with a view towards Number Theory, by Einsiedler and Ward Terry Tao's blog Akshay Venkatesh's lecture notes Ben Green's lecture notes

For instance, the question of whether is equidistributed mod 1 is an old unsolved problem, equivalent to asking whether is normal base 10.

For instance, the question of whether is equidistributed mod 1 is an old unsolved problem, equivalent to asking whether is normal base 10.

[Incidentally, regarding the interactions between physics and number theory: physical intuition has proven to be quite useful in making accurate predictions about many mathematical objects, such as the distribution of zeroes of the Riemann zeta function, but has been significantly less useful in generating rigorous proofs of these predictions. In number theory, our ability to make accurate predictions on anything relating to the primes (or related objects) is now remarkably good, but our ability to actually prove these predictions rigorously lags behind quite significantly. So I doubt that the key to further rigorous progress on these problems lies with physics.]

Solving Mathematical Problems: A personal perspective. 2nd Edition, Terence Tao. Oxford University P ?The Journey of a thousand miles begins with one step? ? Lao Tzu Every so often, you come across a book that really stands out. I have recently been very fortunate to come across several such books, this being one of them. ?Solving mathematical problems? was written by Terence Tao when he was a 15 year old student and has now been slightly revised in this second edition. Like another of the reviewers at Amazon, I also came across this book after reading an article about Terence Tao winning the Fields medal (a bit like the Nobel prize for mathematics). Not only does it give a wonderful insight into the mind of a young Terence Tao, but also into the techniques used to elegantly solve some reasonably difficult problems, such as those posed as questions for the Maths Olympiad contests. [Terence competed in these challenges in his teens, winning bronze, silver and then gold.] Mathematical researchers are not always great e\ucators. Thankfully, Prof. Tao is.Mainly assuming only basic high-school pure mathematics, worked solutions to the problems are clearly and expertly described. Not only does he solve the problems but he also examines the steps, false starts and other solution possibilities that are part of the general approach to problem solving. I was only slightly disappointed that there were a handful of corrections in this second edition (available at Prof Tao?s blog here); one or two could perplex an unwary reader who might expect the work to be flawless. If you have an interest in mathematics, either as a high school student or a hobbyist, I would highly recommended reading this book. In the preface, Prof Tao remarks that if he wrote a book on the subject of competition problem-solving now, it would very different; now that is definitely a book I would like to read!….

Made to Stick: Why Some Ideas Survive and Others Die by Chip and Dan Heath helps us understand why our users (or our coworkers) can repeat the latest web hoax, but can’t remember anything about our projects. What we need to do is to create “sticky messages.” Sticky messages are not necessarily creative messages. In fact, there is formula that the brothers Heath have discovered that will help us to create sticky, memorable messages. That formula is: