In the previous post , we have seen how elliptic curves over the real numbers can be used to define a group. Specifically, we have defined a rule for point addition : given three aligned points, their sum is zero ($P + Q + R = 0$). We have derived a geometric method and an algebraic method for computing point…
Transcript of Stephen Wolfram's talk at SXSW 2015 on the present and future of computing: Wolfram Language, image recognition, language-design philosophy, tweetable programs, computational thinking for kids, natural language as input, symbolic programming, deployment, automation of programming, Internet of Things…
If you’re familiar with nearly any mainstream programming language, and I asked you to draw a diagram of an array, the array indices, and the array elements, odds are good you’d produce a diagram something like this: In this post, I want to persuade you to replace that image, or, at least, to augment it with an…
In fact, only of the lower house, the Sejm. During its current term, 460 deputies voted 5545 times since the 8th of November 2011. The Sejm website publishes the individual results of the votes as …
The article here sums up pretty well the debacle that North American tournament Scrabble players have been faced with since the…
First of all, don’t panic. I’m going to try in this post to introduce you to quantum field theory, which is probably the deepest and most intimidating set of…
A good colleague of mine, Rich Geldreich put up a interesting article talking about his viewpoints in future directions in lossless…
neural networks , deep learning , representations , NLP , recursive neural networks
Deep Learning is amazing. But why is Deep Learning so successful? Is Deep Learning just old-school Neural Networks on modern hardware? Is it just that we have so much data now the methods work b…
I'm assuming you're familiar with the basic idea of what a Turing machine is . There are a few parts to building one in Magic: a tape extending in two directions storing cells of a few different "colours"; a processing head that can read the current cell's colour, write a new colour and change its state if necessary…
True story: it’s possible to fly through your own secondary math education — honor roll bumper sticker on your mom’s minivan and all —Â but miss some of the Very Big Ideas of secondary …
A while back, John Regehr posted the Nibble Sort Programming Contest on his blog. The objective was to write a program that sorts the 4-bit components (nibbles) of 64-bit words as fast as possible. For example, 0x42badc0ffeed00d5 should result in 0xffeedddcba542000 after sorting.
Interesting applied project for your students , or as a warning for decisions under uncertainty / statistical significance. Real money on the line so the length of time and number of entries required to get a winner may be an interesting dataset after this is all done.
The aim of this course is to teach the basics of category theory, in a way that is accessible and relevant to computer scientists. The emphasis is on gaining a good understanding the basic definitions, examples, and techniques, so that students are equipped for further study on their own of more advanced topics if…
This post is a simplified version of the accompanying notebook to chapter 6 of my upcoming book Mastering SciPy. Click anywhere on this box for more information.
Our condolences Awesome Stories source John Nash and his wife Alicia were killed in a taxi accident on the New Jersey Turnpike Saturday afternoon. They were on their way back from Norway where he a…
Scheme's numbers are not like the rest of its library. They're older, and they're mostly borrowed from other languages (Maclisp and Common L...
I have recently been going through my book Maths 1001 making updates for a forthcoming foreign edition (of which more in future). So I have been looking over mathematical developments since approxi…
[An in-depth blog post by Daniel J. Bernstein, crossposted between the ECRYPT blog and the cr.yp.to blog .]
A few weeks ago, Hensen et al., of the Delft University of Technology and Barcelona, Spain, put out a paper reporting the first experiment that violates the Bell inequality in a way that closes off…
This is part 15 of Categories for Programmers. Previously: Representable Functors. See the Table of Contents. Most constructions in category theory are generalizations of results from other more sp…
I’ve been working on some other blog posts, including a conclusion of (or at least an installment in) this exciting series on zero knowledge proofs. That’s coming soon, but first I want…
Can we remove simple errors from math proofs? simple-talk interview source Stephen Johnson is one of the world’s top programmers. Top programmers are inherently lazy: they prefer to build too…
A leftover glow unlike any other — of neutrinos — has finally been seen.
An explanation of Variance, Covariance and Correlation in rigorous yet clear terms providing a more general and intuitive look at these essential concepts.
Introduction A Markov Chain is a set of transitions from one state to the next; Such that the transition from the current state to the next depends only on the current state, the previous and future states do not effect the probability of the transition. A transitions independence from future and past sates is called…
Greedy algorithms are among the simplest and most intuitive algorithms known to humans. Their name essentially gives their description: do the thing that looks best right now, and repeat until nothing looks good anymore or you’re forced to stop. Some of the best situations in computer science are also when greedy…
