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Terry Tao on how to compute non-converging infinite sums (2010)
The Riemann zeta function $latex {\zeta(s)}&fg=000000$ is defined in the region $latex {\hbox{Re}(s)>1}&fg=000000$ by the absolutely convergent series $latex \displaystyle \zeta(s) = \su…
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A Gentle Introduction to Data Compression
Joe Bertolami's portfolio and blog covering artificial intelligence, game development, computer graphics, data compression, and more.
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How to compile with continuations
In terms of unreasonable effectiveness, the transformation to continuation-passing style (CPS) ranks with the Y combinator .
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The Generalist – On Alexander Grothendieck
I never met Alexander Grothendieck. I was never in the same room with him. I never even saw him from a distance. But whenever I think about math — which is to say, pretty much every day ̵…
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Making of “Introduction to A*”
(Warning: these notes are rough – the main page is here and these are some notes I wrote for a few colleagues and then I kept adding to it until it became a longer page)
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A free, complete guide to Technical Analysis
Learn technical analysis - candlestick patterns, support & resistance, moving averages, RSI, MACD, Fibonacci retracements, Dow theory, and chart analysis.
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Planjure: A* and Dijkstra's in Om
I wrote Planjure to learn ClojureScript and Om. It’s a fun little program. You paint islands on a canvas and run path-planning algorithms to find the optimal path for your ship to traverse from start to finish. Sailing across blue ocean is faster than hiking through green islands. The three algorithms implemented are…
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New partition function record: p(10^20) computed
The partition function p ( n ) counts the number of partitions of n , i.e. the number of ways n can be written as a sum of positive integers when disregarding the order of the terms. For example, 4 has the five distinct partitions 4, 3+1, 2+2, 2+1+1, 1+1+1+1, so p (4) = 5. This week, I set a new record by computing…
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Selection bias and bombers (2008)
During WWII, statistician Abraham Wald told the RAF to add armor where it didn't seem planes needed it. But he was right.
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The Derivative of a Number
Are you kidding? Edward Barbeau is now a professor emeritus of mathematics at the University of Toronto. Over the years he has been working to increase the interest in mathematics in general, and e…
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The Firing Squad Problem
In 1957, John Myhill first posed an interesting problem that was closely related to computer programming, but did not require any related background to solve. Dubbed the "firing squad synchronization problem," the puzzle was passed along by word of mouth and first solved by Marvin Minsky and John McCarthy. However…
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Programming with Nothing (2011)
I love Ruby! I’ve used it every day for years and I’m not sick of it yet. It’s an easy language to love: it’s expressive, flexible and syntactically beautiful ; it has a unique combination of useful features like mixins , metaclasses and blocks ; it comes with a useful core library and comprehensive standard library …