# education

## Programming is difficult

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.

## 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.