Today I'd like to share an idea. It's a very simple idea. It's not fancy and it's certainly not new. In fact, I'm sure many of you have thought about it already. But if you haven't—and even if you have!—I hope you'll take a few minutes to enjoy it with me. Here's the idea: Every matrix corresponds to a graph. So…
I have a confession to make: I have always found symbolic algebra more intuitive than geometric pictures. I think you’re supposed to feel the opposite way, and I greatly admire people who think and communicate in pictures, but for me, it’s usually a struggle.
We are very sorry to hear of the death of Michael Atiyah. Michael was a giant of mathematics. He held many positions including Savilian Professor of Geometry here in Oxford, President of the Royal Society, Master of Trinity College, Cambridge, the founding Directorship of the Isaac Newton Institute and Chancellor of…
A more polished version of this article appeared on Nautilus on 2019 February 28. This version has some more material. How I Learned to Stop Worrying and Love Algebraic Geometry In my 50s, too old …
Some weeks ago I got involved in a discussion on Twitter about, which books to recommend on the history of calculus. Somebody chimed in that Steven Strogatz’s new book would tell you all that you n…
How our mind falls short trying to short cut.
In part 1 of this series, we built a Sudoku solver based on translating Sudoku to SAT and then giving the resulting SAT instance to a SAT solver. We also benchmarked our solver and found out that it, unsurprisingly, loses to the state of the art of Sudoku solvers. Since
Once upon a time, my computer architecture professor mentioned that using a random eviction policy for caches really isn't so bad. That random eviction isn't bad can be surprising — if your cache fills up and you have to get rid of something, choosing the least recently used (LRU) is an obvious choice, since you're…
Would you believe me, if I claimed that an algorithm which has been on the books as "optimal" for 46 years, which have been analyzed in excruciating detail by geniuses like Knuth and taught in all CS courses in the world, can be optimized to run ten times faster ?
I. Allen Ginsberg’s famous poem on Moloch:What sphinx of cement and aluminum bashed open their skulls and ate up their brains and imagination? Moloch! Solitude! Filth! Ugliness! Ashcans and u…
From the highly eclectic blog of Mark Dominus
Peter Dorman points to this post on statistical significance and p-values by Timothy Taylor, editor of the Journal of Economic Perspectives, a highly influential publication of the American Economic Association.
In the previous post, I described a simple way to think about matrices, namely as bipartite graphs. Today I'd like to share a different way to picture matrices—one which is used not only in mathematics, but also in physics and machine learning. Here's the basic idea. An $m\times n$ matrix $M$ with real entries…
Discover the secrets behind hit music with our popular song chords analysis from 1300 tracks. Your songwriting journey begins here!
Lambdaclass's blog about distributed systems, machine learning, compilers, operating systems, security and cryptography.
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
Eller's algorithm creates 'perfect' mazes, having only a single path between any two cells, one row at a time. The algorithm itself is incredibly fast, and far more memory efficient than other popular algorithms (such as Prim's and Kruskal's) requiring storage proportional to only a single row. This makes it possible…
I’ve been helping a friend understand dynamic programming (DP for short), so I’ve been on the lookout for good resources. The topic is covered all across the web, but I found many of them focused on the code, and not enough on the beautiful visualizations that shed light into how DP works.
I am currently working my way through Higher-Order Perl , a highly recommended tome on effective and practical use of functional programming techniques in Perl. As you’d expect from a book that spends a lot of time discussing such concepts as function composition and recursion, the subject of tree traversal makes a…
The purpose of this article is to show you step-by-step examples of how to use the Fourier transform algorithm to multiply two numbers. The primary advantage of using fourier transforms to multiply numbers is that you can use the asymptotically much faster 'Fast Fourier Transform algorithm', to achieve better…
Consulting software engineer and research scientist. I build visualization systems for complex data and machine learning models.
Many times on this blog I've argued that the difference between pure and applied math is motivation. As my graduate advisor used to say, “Applied mathematics is not a subject classification. It's an attitude.” Traditionally there was general agreement regarding what is pure math and what is applied. Number theory and…
How to build a constraint programming solver in Julia. Part 1: Solving Sudoku using backtracking
What is the 🐞(n) of your API?
Every square has exactly 3 units and 20 peers. For example, here are the units and peers for the square C2 :
Many people are surprised to learn that `sed`, a seemingly simple text filtering program, is actually Turing complete. This realization prompts the question: how can a text processing utility achieve such computational power? The answer lies in sed's fundamental operations. Essentially, sed functions as a miniature...
I had an interesting discussion at work today (among people I think would all call themselves statisticians!) about the distinction(s) between statistics and machine learning. It is something I am …
