The empowering quadratic

Most people openly hate mathematics. I did that too, before university. The question is why? I think it is often taught badly. Once grades are involved, it is very difficult to get it right. One thing changed when I turned from a hater to a fan of math. I realized that there was a storyline in most examples. So, maybe we could put the narrative back. As a little example, here is a story of the quadrative formula.

Abstraction, the fundamental idea of algebra

Using letters to denote numbers may look like just a simple trick of notation, but it is the fundamental idea of algebra. Abstraction allows us to do general computations, not just arithmetic calculations with actual quantities. Here is a handout for the first class of an Algebra/Pre-Calculus class. This also shows that if someone is able to solve an equation (no matter how simple), then he/she has already obtained the key skill needed for computer programming.

Informal introduction to the holonomy decomposition of transformation semigroups

An algebraic view of computation

I am not particularly interested in doing philosophy, as my research is about using computers to extend mathematical knowledge. But it turns out that this involves questions that are not mathematical or technical, but of fundamental nature. I write code and run computer experiments all the time, so the question `What is computation?’ is on my mind continuously. Here is an attempt, a draft version of a somewhat philosophical paper to address the question for the $(n+1)$th time.

Euler's Formula in College Algebra

Once complex numbers are introduced in a College Algebra/PreCalculus course, why not discuss Euler’s formula? Especially the equation $e^{\pi i}+1=0$, that looks good on a T-shirt. A full proof is out of question, but the power series definitions of the exponential and trigonometric functions provide a narrow, but walkable path up to the summit. With a computer algebra system it is easy to demonstrate how the approximations work, just by entering a few terms of the infinite sums.

Talk on finite computational structures