Ciro Santilli @cirosantilli 40

List of handbooks open as of 2022 at: www.maths.ox.ac.uk/members/students/undergraduate-courses/teaching-and-learning/handbooks-synopses Kudos, e.g. unlike the physics course of the University of Oxford which paywalled them. 2022 one: www.maths.ox.ac.uk/system/files/attachments/UG%20Handbook%202022.pdf

The Oxford mathematics Moodle has detailed course listings, and most PDFs are not paywalled.

E.g. the 2024 course:

By Ciro Santilli: Section "How to teach".

Others:

Some views:

There is a lot of "who kills who" useless fluff, and everything to do with the wife is boring, but too much gold otherwise.

It is amazing to see how seasons got better and better until the finale. The last season was amazing, Ciro Santilli actually watched all episodes of that one! This is clearly seen on the evolution of metacritic scores.

Published on the session reports of the Royal Prussian Academy of Sciences at Berlin 1918 page 464.

Is about Maxwell's equations in curved spacetime, and notably introduces gauge theory.

Viewable for free at: archive.org/details/mobot31753002089727/page/464/mode/2up.

This one is a little confusing: the upper case looks exactly like a letter P, but as the name suggests, it actually corresponds to the letter R. The letter P corresponds to pi instead.

Invertible matrices. Or if you think a bit more generally, an invertible linear map.

When the field $F$ is not given, it defaults to the real numbers.

Non-invertible are excluded "because" otherwise it would not form a group (every element must have an inverse). This is therefore the largest possible group under matrix multiplication, other matrix multiplication groups being subgroups of it.

www.nature.com/articles/206757a0 on Nature 181, 662-666. Paywalled as of 2022. Has some nice pictures in it.

This is one of the main reasons why Ciro Santilli invested in OurBigBook.com.

Ciro believes that the only thing students must be forced to learn is to speak read and write English and that a teacher's main job after that is to help students find their next big goals and also ties into the backward design philosophy.

Everything else, the student must choose.

This idea is generally known as self-directed learning.

This is most notable in University entry examinations of poor countries, where students often have to waste one extra year of their lives to go through preparation for the useless university entry exams. And then, surprise surprise, if they actually get in, they find that this is not what they really wanted to do, and they just go through to the end miserably because they understandably they don't want to risk another year of their lives.

And importantly: It must be easy to change your area of study.

Ciro saw this first hand École Polytechnique which was way freer than his university in Brazil.

Steve Jobs's university dropout stories from Steve Jobs' 2005 Stanford Commencement Address also come to mind.

Interesting projects:

Godfrey Hounsfield, 1979 Nobel Prize in Physiology and Medicine:^[ref]