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Benoit Mandelbrot, RIP
Nothing in the news media yet, but many folks on Twitter and colleague Nassim Taleb are reporting that the father of fractal geometry is dead at age 85. We’re n
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Medical researcher discovers integration, gets 75 citations
(Note: this post is `just for fun;’ no premeds, doctors, researchers, or nobel laureates were meant to be offended in the writing of this post.) The bane of many American physics grad student…
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First improvement of fundamental algorithm in 10 years
The max-flow problem, which is ubiquitous in network analysis, scheduling, and logistics, can now be solved more efficiently than ever.
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What if you had bought Apple stock instead of that iPod?
Currently, Apple's stock is at an all time high. A share today is worth over 40 times its value seven years ago. So, how much would you have today if you purchased stock instead of an Apple product? See for yourself in the table below. A huge thanks to everymac.com for the original prices and release dates. All values…
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Knuth's 'Earthshaking Announcement' due tomorrow
(I'm still looking for the catchiest way to appreciate the number MMXXVI. Exercise 7.2.1.6–122 gives 1234+.5*6+789 and -1+2345*6/7+8+9 and 1+(2/3)*45*67.8-9 ; other suggestions are welcome. The most elegant that I've seen so far is a beauty that was suggested independently by Arnaud Lefebvre and by Evangelos…
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Zero Zero
I've been thinking about something that we always did junior year when I was on my high school soccer team. When we'd score a goal, we reali...
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Math library functions that seem unnecessary
Functions include in the standard C math library that seem unnecessary at first glance and why they are necessary.
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Using Fibonacci Numbers to Convert from Miles to Kilometers and Vice Versa
I recently learned an interesting fact about Fibonacci numbers while watching a random number theory video on YouTube. Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No...
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Squaring two digit numbers in your head
All my life I've done mental arithmetic the 'wrong way': I've calculated from left-to-right, instead of right-to-left. So when I do somethi...
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Operational Transformation (algorithm behind Wave, Google Docs)
Almost exactly a year ago, Google made one of the most remarkable press releases in the Web 2.0 era. Of course, by "press release", I actually mean keynote at their own conference, and by "remarkable" I mean potentially-transformative and groundbreaking. I am referring of course to the announcement of Google Wave , a…
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Rotating Quine
My Quines are sometimes specialized for Japanese. But to attend RubyConf, I should write "global" Quines. v=0000;eval$s=%q~d=%!^Lcf<LK8, ...
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25 Best Hangman Words
Mathematica analysis of picking the optimal words to win the Hangman spelling game. Code and link to Wolfram Demonstration are included.
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Optimizing Your Wife
If a man can expect to meet exactly N eligible women in his life, what strategy should he use to maximize his chances of choosing the very best one? We typically make some idealized assumptions when solving this type of problem, such as assuming that he meets the women in random order of "goodness", that there is an…
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Issues in the Proof that P ≠ NP
Some further comments into the recent claimed proof that P is not equal to NP Yuri Manin is a great mathematician, who has worked in various areas and also is well known for his many excellent expo…
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Scott Aaronson explains his $200k bet (8 Signs A Claimed P≠NP Proof Is Wrong)
As of this writing, Vinay Deolalikar still hasn’t retracted his P≠NP claim, but a clear consensus has emerged that the proof, as it stands, is fatally flawed. The first reason is that weR…
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A review of probability theory
In preparation for my upcoming course on random matrices, I am briefly reviewing some relevant foundational aspects of probability theory, as well as setting up basic probabilistic notation that we…
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The "Soft Maximum" function
The soft maximum approximates the maximum function, and approaches it in the limit, but is easier to work with.
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How Game Theory Solved a Religious Mystery
"All will be well if you use your mind for your decisions, and mind only your decisions." Help me make more videos and posts! A monthly membership directly supports the channel and allows me to make more videos that inspire students and teachers around the world. You also get early access to new videos. Support with a…
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Mathematically correct but psychologically wrong
The snowball strategy says to pay off your smallest debt first, then the next smallest, and so on until you're out of debt. When I first heard of this I thought it was silly. Clearly the optimal strategy is to pay off the debt with the highest interest rate first. That assessment is mathematically correct,
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Divisibility by 7
How can you tell whether a number is divisible by 7? Almost everyone knows how to easily tell whether a number is divisible by 2, 3, 5, or 9. A few less know tricks for testing divisibility by 4, 6, 8, or 11. But not many people have ever seen a trick for testing divisibility
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P vs. NP for Dummies
A reader named Darren commented on my last post: I have this feeling that this whole P and NP thing is not only a profound problem that needs solving, but something that can be infinitely curious t…
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Update on Deolalikar’s Proof that P≠NP
An update on the P not equal to NP proof Timothy Gowers, Gil Kalai, Ken Regan, Terence Tao, and Suresh Venkatasubramanian are some of the top people who are trying to unravel what is up with the cl…
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Proving P!=NP: "...Ryan has taken the first real baby step in decades."
On October 8th, when in my graduate complexity course as we discussed the 1987 Razborov-Smolensky result that one can't compute the Mod p b...