About this site

Object

This site aims to

The main point is to fill a strange issue from the current form of math and physics courses : while professionals should be aware of the presence of a big gap between undergraduate physics courses and high-level theoretical physics (and somehow similarly for pure math), they do not seem willing or aware of the possible means to bridge this gap, in the form of optimized coursed on basic concepts that would be more directly faithful to the high-level understanding. I happened to find out, get interested in, and work on, the development of such optimized paths. There are diverse concepts for which this goes, but also a special one that is key to many others : tensors. So much work is wasted learning physics because of trying to express stuff in some inconvenient language, as the perfect expression of those stuff would involve the language of tensors, but tensors are not supposed to be known at that level. This goes under the excuse that a teaching of tensors would look even harder to follow than that stuff inconveniently expressed without these - that is the way physics is usually learned at a high level : navigating through obscure, awkward ways to introduce tensors, then getting used to the expressive means it leads to. But this is only because the teaching of tensors itself suffers being usually done in some inefficient ways. A good initiation to tensors requires a renewed path through abstract algebra, that only few mathematicians or physicists are aware of. That is why this work actually starts by digging into the foundations of math.

Level, target

It may be situated in between undergraduate and graduate levels: by its way of rebuilding everything from the start, it aims to fill the role of (a subset in progress of) an undergraduate curriculum (1st university year), but the difficulty level with the care for powerful methods and deep and complete explanations, is comparable to graduate level (3rd year). Also, it takes some of its inspiration and concepts from existing graduate-level mathematics (in a simplified form).
It is thus mainly targeted at

(Such innovative works for the undergraduate level seem to be generally lacking in the world, while more works can be found on the foundations of mathematics at other levels).

Originality

It does not aim (nor exclude) to bring new ideas, results or theories (with few exceptions : the set generation principle; the page "Time in set theory" - interpretations of quantum physics), but focuses on developing new optimized paths to already known fundamental theories of mathematics and physics : putting things in the right order, to make high concepts look as clear, simple and fast to learn as possible. It combines the following advantages:

The set theory formalism presented here differs from the traditional ZF system, but aims to more directly fit the common use and notations of mathematics (without artificial encoding and abbreviation systems), and be cleaner on foundation and meaning.

Long introduction

I wrote this long introduction to the contents of this site and relations between logic and physics, for what was first supposed to be the news bulletin of the Iranian Association for Logic, but finally was a book "Logic around the world".

Why leave the system

I first made an introduction video on youtube (in 3 parts, total is more than 1 hour):

Also available in text version : Why learn physics by yourself
A shorter version (about 15 min) was done at Ukraine Crisis Media Center where I announced my offer of free physics courses in Ukraine for summer 2016. Full text version and video.

Reading advice

The first texts of mathematics are generally intended to be slowly read, respecting the order.

Writing history and notes

A first version was written in French, then partially corrected and translated to make the start of this site, which then continued directly in English on other subjects.
Now over 50 pages ready from the start on mathematics (entirely self-contained), plus more sections of maths and physics in bulk or draft; still incomplete (some French pages should be corrected before translation, and others are in plans to be directly written here).

I cannot ensure the perfection of the English vocabulary as I'm not native English speaker. Moreover I need to name some concepts that have not always a standard name in the mathematical literature; I know that my use of "functor" differs from (is more general than) its standard meaning in category theory, and thus breaks the standard convention, but I do not know any better word for what I need.

Would you like to help ?


I look for translators to provide versions of this work in other languages.

As this site is relatively recent, it is not well-known yet. So if you see it worth, please help spreading the word about it (look here for how).

About the author

Sylvain Poirier (one of maybe around 200 homonyms worldwide according to facebook search)
From Le Havre, France (and probably the only one from there)
PhD in Mathematics
(but I did not like the academic system; I learnt more mathematics and physics on my own since teenage, including General Relativity at 16).

I have the following other sites :
(Other sites on the web with the same are from homonyms)


For many years I was upset. Here is why. Now things seem to be going a little better in the sense that I found a programmer to start the work but more will be needed.

Contact

Email : trustforum at gmail.com
A facebook account I sometimes losed access to just because of their "security procedures"... and where I give some news, though I keep the main interesting long-term content in my web sites


Back to entry page, or Part 1 : First foundations of mathematics.