Introduction

This section is for my personal notes on various topics. Note that most of my notes aren't actually here because I write them on my iPad.

Goals

When introducing a topic, this is the general path I follow:

1. Demonstrate the visual/intuitive interpretation of the concept.
2. Then, introduce the more formal description, which shows how the concept can be formulated and computed.
3. Finally, provide examples and exercises to solidify the understanding.

To many, it is more beneficial to gain a deep intuitive understanding of all the concepts, which prevents the concepts from being really abstract and hard to understand. It might even be beneficial to first understand the geometric visualizations, then look at the algebra. With that being said, different people have different learning styles, so it depends on the individual's preferences.

However, it is imperative to understand that the intuitive understanding, while important, might not be enough to solve problems. This is where the formulation comes in, which is why it is important to understand both the visual and algebraic interpretations of the concepts.

I prefer the intuition → formulation → computation → application path, which is contrary to most textbooks that start with the formulation.