## Archive for the ‘math’ Category

### A Mathematician’s Apology

I just finished reading “A Mathematician’s Apology,” written by the number theorist G. H. Hardy in 1940. I sort of assumed I had already read it when I was younger, but this turns out to be completely false. How do I know that I’ve never read it? Before opening it this time, I thought it […]

Filed under: books, math, reviews | 1 Comment

### Pascal’s rule for Beta functions

Recently I became acquainted something called the Beta function. It is defined in terms of the Gamma function (a continuous generalization of the factorial function): The first thing I’m tempted to do here is try to write this in terms of a binomial coefficient. If we replace each by the (equivalent for integers) , then […]

Filed under: math | 2 Comments

### Happy Pi Day 2013

I just got back from SIGCSE in Denver, which aside from Euclid Hall Bar and Kitchen, has a restaurant called Pi Kitchen and Bar. This would have been a fortuitous place to be today, Pi day (3/14). We have a programming exam scheduled for today in COS 126. In case you are a student taking the […]

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Stephen Tosh and I co-taught the online course Math 600 for the University of Waterloo last term, in September and October. The course is part of the Master’s of Mathematics for Teachers program, which is an online Master’s degree for high-school math teachers. The students were a very interesting mix of people from all over […]

Filed under: math, teaching, waterloo | 6 Comments

### The Math of Khan

I have been following some of the material produced by Khan Academy, in particular their recent and awesome software environment. They started producing Python tutorial videos back in 2011, but earlier this year they made a dramatic switch to a JavaScript dialect and an in-browser graphical immediate interpreter. That is to say, if you write […]

Filed under: math, programming, randomness | 2 Comments

### Joint Meeting

No, this is not about sharing joints (even in moderation). This week I am at the joint meeting of the American Math Society and Math Association of America in Boston, MA. It is a huge conference with around 7000 participants, but more cohesive than many other mega-conferences including Informs and ISMP that I have visited. The […]

Filed under: CS Circles, geometry, math, travel | Leave a Comment

### The Matrix

The Matrix Here is a factoid which might be a nice exercise. Fix integers 1 ≤ q ≤ p. Consider the p×p matrix where the entry in row i and column j is: 1, if i+j mod p is one of {0, 1, …, q-1}; 0, otherwise. This matrix is a cyclic matrix with q […]

Filed under: diagrams, math | 1 Comment