# Tag Archives: mathematics

# Basic Combinatorics

Because sometimes you need to count particular kinds of things.

- TopCoder post
- a small book: Basic Combinatorics
- Khan Academy

# Why Learn Math

From at least one, if not many more, perspective, I’m an old man, a somewhat established scholar. What could be more bizarre than wanting to quit everything else and spend six months learning all the math you wish you already knew? Apparently, I am not alone. Warren Henning, a software engineer, is doing much the same, and he explains his motives as follows in an essay on [Medium][]:

> To me, math is raw, untapped power. Statistics is helpful in computer programming, period. My dream is to learn the statistics, probability, and linear algebra needed to really understand machine learning and computer vision, which has had a major spurt of activity in the past 5–7 years. To realize this goal, I need a solid foundation so that I can truly understand what’s going on: why something works, when it won’t work, and what to do differently if it doesn’t.

[Medium]: https://medium.com/@warrenhenning/a-software-engineers-adventures-in-learning-mathematics-62140c59e5c

# Compound Interest

I gather that Al Bartlett is something of an internet legend when it comes to getting people to think about the power of *rates of change*, be it doubling, exponential, or compound interest. I wish the video was a little shorter. I’d like to share it with Lily.

# Winning at Monopoly with Math

I am a complete fool for articles like _Business Insider_’s [“How To Use Math To Crush Your Friends At Monopoly Like You’ve Never Done Before”][bi]. I like that the math involved can range from the simple — how the distribution of dice rolls affects where most people will land, given a particular starting point — to the complex. If the slide decks length puts you off — there’s sixty plus slides in there!, you can always scroll to the end and read the half dozen concluding slides that tell you what you should do. But, really, the fun is in the careful working through of the numbers.

[bi]: http://www.businessinsider.com/math-monopoly-statistics-2013-6

# Bezier Curves

As Father’s Day approaches, I found myself remembering all the time I spent in my own father’s office, playing with the various bits of office material as he tried to get work done. My father was an architect, and one place to park me was in front of the typewriter which was in the reception area and not in the immediate space where he worked, bent over a drafting table. I don’t know how many pages of his stationary I burned through writing various bits of nonsense, but maybe that love of typing, the sense of committing words to a page in a way that seemed more important than writing them by hand, was one of the things that later drove me to write. (In the same way that some painters say they paint because they love the smell of the paint itself.)

Sometimes, though, I would wander into his work space and play with the various tree stamps on pieces of tracing paper, or, perhaps best of all, I would get to handle the various hand tools which seemed to hold almost mystical power. Things like slide rules or scales. Or there was the entire collection of outlines of furniture in various scales that were in sheets of cut out plastic. Among those objects was a plastic curve maker:

Forgive the Amazon link: it was the best example of the exact thing I used to play with. In fact, I can remember my father letting me have it, and I took it home and drew my own version of a sports car, in profile, carefully considering the appropriate placement of the curves to be included. Later, when I started experimenting with drawing programs, I re-discovered the joy of curves, which I learned had a more interesting name, [Bezier curves][], named after the French engineer who used them to model, believe, curves on cars at Renault.

And now I find myself re-immersed in the world of math, not only because I find it fascinating and a possible research path for myself but also because I have a daughter who has a talent for math and I want to encourage it. I can only do that if I know enough to be useful to her. And so I start collecting links like this [Reddit thread][] on cure simulations. Check out these [animated Bezier curves][], for example, or this [Bezier curve simulation][].

Why should you care about Bezier curves?

[Bezier curves]: http://en.wikipedia.org/wiki/Bézier_curve

[Reddit thread]: http://www.reddit.com/r/InternetIsBeautiful/comments/27bsdl/curve_simulation/

[animated bezier curves]: http://www.jasondavies.com/animated-bezier/

[Bezier curve simulation]: http://tholman.com/bezier-curve-simulation/