Like Eureka!, only cooler

Concrete Mathematics

Stephen Hawking once said that his editor had warned him that each equation in his book would halve the readership.

With that in mind, and taking into account the number of readers of this blog (or lack thereof), would I dare put any equations?

You better believe it!

I just picked up my old copy of Concrete Mathematics, a book I have too long neglected. The ultimate goal, of course, is slaying the Beast, which I should try to complete before Donald E. Knuth passes away. While I wish him a very long life, long enough at least to complete Volume 5, and better yet 6 and 7, I should not take his remarkable health as an excuse to dither.

For the math notation, I use MathJax, a JavaScript library that can parse either MathMl, or much better LaTeX (which is based on TeX, another gift of Donald E. Knuth to the world).

The setup for this blog is based on this post.

The quality of rendering is variable: pretty good in Firefox, OK in Safari or Chrome, and no idea in IE or Opera. Of course, it is not as good as the output of LaTeX, but for the Web it is acceptable.

For instance, given the recurrence

$$ \begin{align} f(j) & = \alpha_j, &&\text{for $1 \leq j \lt d$}\\ f(dn + j) & = cf(n) + \beta_j, &&\text{for $0 \leq j \lt d$ and $n \geq 1$} \end{align} $$

then the solution is

$$f \left( ( b_m b_{m-1} \cdots b_1 b_0)_d \right) = \left( \alpha_{b_m} \beta_{b_{m-1}} \beta_{b_{m-2}} \cdots \beta_{b_1} \beta_{b_0} \right)_c$$

(refer to the book for explanations).

Isn’t this lovely?