Chemistry is fun. Too hard for precise physics (pre quantum computing, see also quantum chemistry), but not too hard for some maths like social sciences.
And it underpins biology.
Technique to make cool sound instruments mathematically, either with electronic hardware components, or with a software synthesizer.
Good tutorials:
Best known techniques:
The meta of a game is the currently dominating know strategy or set of strategies, see also Section "Nash equilibrium".
A proof in some system for the formalization of mathematics.
Forms both a:
- division algebra if thought of with complex multiplication as the bilinear map of the algebra
- field
The missing link between basic and advanced by 
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01One of Ciro Santilli's strongest feeling in education is that material often falls in either of the two categories:
- hundreds of too basic popular science, e.g.:
- a 5 minute popular science video trying to explain quantum electrodynamics (an advanced subject) for someone who doesn't know what a Riemann integral is (a basic subject)
- a few full university courses that takes 20 hours to deliver the first punchline of the course
Ciro believes that there is often an important missing link between them, e.g.:
If we as a society are unable to provide this sweet Middle Way sweet-spot, it is unreasonable to expect that learners will ever have the motivation to advance, because it is just too boring! They are just more likely to go play video games instead.
It is Ciro's hope that OurBigBook.com will help to fill exactly that gap.
In Ciro's view, as of the 2020's this critical gap generally lies somewhere between the end of undergraduate studies, and at the start of postgraduate studies.
Let's take the gloves off more often, and give the full thing to interested students! Let students learn what they want to learn, and do that as soon as possible! Life is too short!
This problem is basically the knowledge version of the last mile problem. When we reach the end of graduate, there are enough directions of knowledge to go off into, that the probability that a great free tutorial exists is relatively low. Of course, as one approaches the realm of novel research, the branching is so wide that having perfect tutorials becomes impossible. Ciro's goal in life go push the last mile marker a bit further out.
Related:
- universityphysicstutorials.com/ by Adam Beatty mentions:
There are myriad resources for physics and maths. The Kahn Academy and Patrick JMT were the best for me. They really helped me out. The question is, what resources are there for the advanced undergraduate courses?
In this video, the noted chemist mentions how he managed to get into a chemistry research development before he even joined university, due to a somewhat exceptional situation. Section "The only reason for universities to exist should be the laboratories" also comes to mind. This is exactly the type of thing that Ciro Santilli wants to make much more widespread.
Stories of Ainan Celeste Cawley fighting to advance his kids education beyond school, and being forbidden to do so by a stupid educational system, also come to mind.
Bibliography:
DNS configuration of Ciro Santilli's website by Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01AKA how this GitHub page gets served under the domain: cirosantilli.com
Ciro only touches this very rarely, and always forgets and go into great pain whenever a change needs to done, so it is important to document it.
The last change was of 2019-07-07, when Ciro moved from the www subdomain www.cirosantilli.com to the APEX cirosantilli.com. A redirect is setup from the www subdomain to APEX.
GoDaddy DNS entries:
Type Name Value TTL
A @ 185.199.108.153 1 Hour
A @ 185.199.109.153 1 Hour
A @ 185.199.110.153 1 Hour
A @ 185.199.111.153 1 Hour
CNAME www cirosantilli.github.io 1 HourMoved cirosantilli.com to Porkbun 2022-02, unfortunatly records were not automatically updated and domain went down for a bit, upadded to new entries for IPv6 as well which are not documented by GitHub:
TYPE HOST ANSWER TTL PRIORITY OPTIONS
A cirosantilli.com 185.199.108.153 600
A cirosantilli.com 185.199.109.153 600
A cirosantilli.com 185.199.110.153 600
A cirosantilli.com 185.199.111.153 600
AAAA cirosantilli.com 2606:50c0:8000::153 600
AAAA cirosantilli.com 2606:50c0:8001::153 600
AAAA cirosantilli.com 2606:50c0:8002::153 600
AAAA cirosantilli.com 2606:50c0:8003::153 600
CNAME www.cirosantilli.com cirosantilli.github.io 600where the IPs are obtained from: help.github.com/en/articles/setting-up-an-apex-domain#configuring-a-records-with-your-dns-provider (archive).
- Custom domain:
cirosantilli.com - Enforce HTTPS: checked
And the CNAME file is tracked in this repository: CNAME.
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