CTK Insights

Archive for November, 2011

29 Nov

Thinking, fast and slow - and irrationally

Tweet Daniel Kahneman's - Thinking, fast and slow - an amazon.com selection as one of "Best Books of 2011" received an inspiring NY Times review by Jim Holt. Thinking, fast and slow is the first of Kahneman's books that I'll be reading on my Android tablet. Kahneman's earlier Judgement under Uncertainty; Choices, Values, and Frames; […]

25 Nov

Beneath a stone no water flows

TweetRecently, I've been reading and solving problems from a Russian publication by A. V. Shapovalov. As is now customary with popular books, in this book too every chapter is preceded by a suggestive epigraph cuing the reader to the content of the chapter. Every chapter in the book contains solved examples and exercises that come […]

24 Nov

Thought Provokers to Start a Class With, IV

TweetThe Bottleneck Principle The Bottleneck Principle is a problem-solving strategy according to which it may be useful to look into the circumstances in which the conditions of a problem at hand are either hardly or not at all satisfied. It is different from the Worst-Case Scenario in that the latter looks at the problem as […]

23 Nov

9 Algorithms That Changed the Future

Tweet In the Foreward to the new book by John McCormick, Chris Bishop wrote Computing is transforming our society in ways that are as profound as the changes wrought by physics and chemistry in the previous two centuries. Indeed, there is hardly an aspect of our lives that hasn't already been influenced, or even revolutionized, […]

17 Nov

Orbital Resonance and the Existence of Irrational Numbers

TweetI've been reading an outstanding collection An Invitation to Mathematics edited by D. Schleicher and M. Lackmann. There are 14 contributions by leading mathematicians, each introducing a direction of current mathematical research. The remarkable aspect of all the articles is that they all start at a level that could be appreciated by a curious high […]

11 Nov

Thought Provokers to Start a Class With, III

TweetThe Extreme Principle The Extreme Principle is a misnamed problem-solving tactic akin to the Worst-Case Scenario often used in combinatorics and computer science. It does not make any claim (like, say, the Pigeonhole Principle) per se, but only suggests that, for some problems, looking into extreme circumstances or elements within the conditions of the problem […]

11 Nov

On the Perimeters of Embedded Polygons

TweetThere are mathematical statements that appear counterintuitive. For example, when it comes to infinities, counterintuitive statements are abundant. At the other extreme, there are statements intuitively obvious that are rather hard to prove. Such, for example, is the famous Jordan Curve Theorem. Naturally, mathematics does not lack in statements of any intermediate kind. Here is […]

09 Nov

Enchanted by Fascinating Mathematical People

Tweet This is a beautifully illustrated collection of interviews and biographical etudes of 16 mathematicians of different backgrounds, varied professional interests, diverse level of achievement - all incredibly interesting as human beings. The sixteen interviewees lived and were active in the 1900s, though some are yet alive; the stories throw light - if only in […]

07 Nov

Thought provokers to start a class with, II

TweetThis Is Just Plain Counting I and many others think it's a good idea to start a math class with a simple non-traditional problem to get the students into the right mood for the class. My main source for the problems below is a Russian booklet by E. G. Kozlova intended for early and middle […]

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