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This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. For the last four years I’ve been working on a book for programmers who want to learn mathematics. It’s finally done, and you can buy it today. The website for the book is pimbook.org, which has purchase links—paperback and ebook—and a preview of the first pages. Yo
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. Update 2017-01-09: Laci claims to have found a workaround to the previously posted error, and the claim is again quasipolynoimal time! Updated arXiv paper to follow. Update 2017-01-04: Laci has posted an update on his paper. The short version is that one small step
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. There’s a well-understood phenomenon in machine learning called overfitting. The idea is best shown by a graph: overfittingLet me explain. The vertical axis represents the error of a hypothesis. The horizontal axis represents the complexity of the hypothesis. The bl
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. The Mona LisaLeonardo da Vinci’s Mona Lisa is one of the most famous paintings of all time. And there has always been a discussion around her enigmatic smile. He used a trademark Renaissance technique called sfumato, which involves many thin layers of glaze mixed wi
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. Here’s a simple puzzle with a neat story. A rich old woman is drafting her will and wants to distribute her expansive estate equally amongst her five children. But her children are very greedy, and the woman knows that if he leaves her will unprotected her children
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. A professor at Stanford once said, If you really want to impress your friends and confound your enemies, you can invoke tensor products… People run in terror from the $ \otimes$ symbol. He was explaining some aspects of multidimensional Fourier transforms, but this
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. A lot of people who like functional programming often give the reason that the functional style is simply more elegant than the imperative style. When compelled or inspired to explain (as I did in my old post, How I Learned to Love Functional Programming), they ofte
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. Problem: Prove that generalized versions of Mario Brothers, Metroid, Donkey Kong, Pokemon, and Legend of Zelda are NP-hard. Solution: http://arxiv.org/pdf/1203.1895v1.pdf Discussion: Three researchers (including Erik Demaine, a computer science professor at MIT famo
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. For a list of all the posts on Category Theory, see the Main Content page. It is time for us to formally define what a category is, to see a wealth of examples. In our next post we’ll see how the definitions laid out here translate to programming constructs. As we’v
This article was ported from my old Wordpress blog here, If you see any issues with the rendering or layout, please send me an email. Dear reader, this post has an interactive simulation! We encourage you to play with it as you read the article below. In our series of posts on cellular automata, we explored Conway’s classic Game of Life and discovered some interesting patterns therein. And then in
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