Lecture highlights:

We just talk about the category of smooth maps between subsets of Euclidean spaces in this lecture.

- We prove that these maps indeed form a category.
- Graphs are naturally equivalent to the domain of their function.
- We provide a physical understanding of this category. We do calculus on them.

Please introduce mengnifolds next lecture…

## Meth

Pure maths is much easier than applied maths. ‘Genuine’ applied maths. Its hard because it deals with real world problems. Conceptually simple, but technically can be very difficult.

If originally problem is hard, we just consider a problem which is similar in spirit, but easier technically. It’s sort of a fake problem. Pure maths is not necessarily realistic!

The difficulty of pure mathematics lies in the language. I stayed in Hong Kong for over thirty years, but I still don’t know Cantonese. Because I don’t have the need. Most people don’t have the need to learn mathematical language, so they think it is hard.

It’s like a French boy telling his mum that he wants milk in French. But if you don’t know French, you will think ‘Wow! I don’t understand!’. That is because you don’t understand the language.

## Lecture Notes

Sorry guys (to the two people reading these posts). From now on I will only irregularly include very incomplete notes of the lecture. I need to save the time to read his notes instead. However, the Meth section is likely to continue.