Index

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This is a section about Linear algebra!

Linear algebra is a very important subject about which there is a lot to say.

For example, this sentence. And then another one.


Linear algebra

This is a section about Fundamental theorem of calculus!

Fundamental theorem of calculus is a very important subject about which there is a lot to say.

For example, this sentence. And then another one.


Fundamental theorem of calculus

{title2=三西猴的主页}

Check out: \b[https://ourbigbook.com], a <personal knowledge base> that can publish from <lightweight markup> both to a multi-user \b[<mind melding>] dynamic website, or as a <static website>. It's like \b[<Wikipedia> + <GitHub> + <Stack Overflow> + <Obsidian (software)>]. Source code: \b[https://github.com/ourbigbook/ourbigbook].

<sponsor>[Sponsor me to work on this project]: 100k <USD> = I quit me job and work on it one year full time. Status: \b[~144k / 200k USD] reached: 1st year locked-in, 2nd year stretch goal open at 200k USD. How to donate: <sponsor>{full}.

I reached \b[100k USD] after a <sponsor/1000 Monero donation>, so I quit my job for 1 year starting 1st June 2024 to solve as many <STEM> courses as I can from a world leading university to try and kickstart \b[The Higher Education Revolution]. If I reach \b[200k USD], then I'll do it for two years instead. A second year greatly improve chances of success: year one I solve a bunch of courses, year two I come guns blazing with the content and expand further.

\b[Mission]: to live in a world where you can learn <university>-level <mathematics>, <physics>, <chemistry>, <biology> and <engineering> from perfect free <open source> books that anyone can write to get famous. More rationale: <OurBigBook.com>{full}

<Ciro Santilli's documentation superpowers>[Explaining things is my superpower], e.g. I was top user \#39 on <Stack Overflow> in 2023https://stackexchange.com/leagues/1/year/stackoverflow/2023-01-01{ref}<Ciro Santilli's Stack Overflow contributions>{ref} and I have a few 1k+ star educational <GitHub> repositorieshttps://github.com/cirosantilli/linux-kernel-module-cheat{ref}<Linux Kernel Module Cheat>{ref}https://github.com/cirosantilli/x86-bare-metal-examples{ref}https://github.com/search?o=desc&q=user%3Acirosantilli&s=stars&type=Repositories{ref}. Now I want to bring that level of awesomeness to <Master's degree>[masters level] <Mathematics> and <Physics>. But I can't do it alone! So I created <OurBigBook.com> to allow everyone to work together towards the perfect book of everything.

My life's goal is to bring hardcore <university>-level <STEM> <open educational content> to all ages. Sponsor me at https://github.com/sponsors/cirosantilli[] starting from 1<Dollar>[[$]]/month so I can work full time on it. Further information: <sponsor>{full}. Achieving what I call "<free gifted education>" is my <Nirvana>.

<Ciro Santilli's website>[This website] is written in <OurBigBook Markup>, and it is published on both https://cirosantilli.com (<static website>) and https://outbigbook.om/cirosantilli (multi-user <OurBigBook Web> instance). Its <source code> is located at: https://github.com/cirosantilli/cirosantilli.github.io[] and https://cirosantilli.com/_dir[also at `cirosantilli.com/_dir`] and it is <licensed> under <CC BY-SA 4.0> unless otherwise noted.

To contact Ciro, see: <contact>{full}. He likes to talk with random people of the <Internet>.

https://github.com/cirosantilli[GitHub] |
https://stackoverflow.com/users/895245[Stack Overflow] |
https://www.linkedin.com/in/cirosantilli[LinkedIn] |
https://www.youtube.com/c/CiroSantilli[YouTube] |
https://twitter.com/cirosantilli[Twitter] |
https://en.wikipedia.org/wiki/User:Cirosantilli2[Wikipedia] |
https://www.zhihu.com/people/cirosantilli/activities[Zhihu 知乎] |
https://www.weibo.com/p/1005055601627311[Weibo 微博] |
<accounts>[Other accounts]

\image[https://raw.githubusercontent.com/cirosantilli/media/master/ID_photo_of_Ciro_Santilli_taken_in_2013.jpg]{height=300}
\image[https://raw.githubusercontent.com/cirosantilli/media/master/Ciro_Santilli's_learn_teach_apply_logo.png]{height=300}

Besides that, I'm also a <Ciro Santilli's campaign for freedom of speech in China>[freedom of speech] <slacktivist> and <Ciro Santilli's cycling>[recreational cyclist]. Opinions are my own, but they could be yours too.

Let's <the ideal university>[create an educational system] with:
* no distinction between <university> and <high school>, <students must have a flexible choice of what to learn>[students just go as fast as they can to what they really want] without stupid <university entry exams>
* <OurBigBook.com>[fully open source learning material]
* <exam as a service>[on-demand examinations that anyone can easily take without prerequisites]
* <the only reason for universities to exist should be the laboratories>[granular entry selection only for space in specific laboratories] or participation in specific <novel research> projects

\b[I offer]:
* online private tutoring for:
  * any <STEM> university course
  * passionate younger <STEM> students (any age) who want to learn university level material and beyond. Can your kid be the next <Fields Medalist> or <Nobel Prize> winner? I'm here to help, especially if you are filthy rich! I focus <Students must be allowed to progress as fast as they want>[moving students forward as fast as they want] on and on <how to teach/Projects must aim for novelty>[producing useful novel tutorials and results]
* educational consulting for institutions looking to improve their <STEM> courses
  * do you know \i[that] course or teacher that consistently gets bad reviews every year? I'll work with the teacher to turn the problem around!
  * are you looking to create a consistent <open educational resources> offering to increase your institutions internationally visibility? I can help with that too.
Let <Emile, or On Education>[your child be my Emile], and let's see how far they can go!

My approach is to:
* propose interesting research projects. The starting point is always deciding the end goal: <backward design>{full}
* learn what is needed to do the project together with the student(s)
* publish any novel results or tutorials/tools produced <freely licensed> online, and encourage the student to do the same (<how to teach/Let students learn by teaching>{full}, <digital garden>)
For minors, parents are welcome to join video calls, and all interactions with the student will be recorded and made available to parents.

I have <articles>[a proven track of explaining complex concepts in an interesting and useful way]. I work for the learner. Teaching statement at: <How to teach>{full}. Pricing to be discussed. Contact details at: <How to contact Ciro Santilli>{full}.

I am particularly excited about pointing people to the potential <next big things>, my top picks these days are:
* <quantum computing>
* <AGI research>
* assorted <molecular biology technologies>

\Image[https://stackoverflow.com/users/flair/895245.png?theme=dark]
{disambiguate=home}
{height=150}
{title=<Ciro Santilli>'s amazing <Stack Overflow> profile}
{description=Ciro contributes almost exclusively by answering question he <Googles> into out of his own need, and never by refreshing the newest question of big tags for low hanging fruit! More information at: <Ciro Santilli's Stack Overflow contributions>{full}.}
{link=https://stackoverflow.com/users/895245}

\Video[https://www.youtube.com/watch?v=7JOJYx0mmhg]
{disambiguate=home}
{height=500}
{title=Introduction to the <OurBigBook Project>}

\Video[https://www.youtube.com/watch?v=54nxjC9BWTg]
{disambiguate=home}
{height=700}
{width=700}
{title=<OurBigBook Web> topics demo}
{description=The <OurBigBook topic feature> allows users to "merge their minds" in a "sort by upvote"-stack overflow-like manner for each subject. This is the killer feature of <OurBigBook Web>. More information at: https://docs.ourbigbook.com/ourbigbook-web-topics[].}

\Video[https://www.youtube.com/watch?v=sX_D_5tCQgg]
{height=700}
{width=700}
{title=<OurBigBook> dynamic article tree demo}
{description=The <OurBigBook dynamic tree> feature allows any of your headers to be the toplevel `h1` header of a page, while still displaying its descendants. <SEO> loves this, and it also allows users to always get their content on the correct granularity. More information at: https://docs.ourbigbook.com/ourbigbook-web-dynamic-article-tree[].}

\Video[https://www.youtube.com/watch?v=Ghvlztiu6rI]
{height=720}
{width=720}
{title=<OurBigBook> local editing and publishing demo}
{description=With <OurBigBook> you can store your content as plaintext files in a <Lightweight markup>, and then publish that to either <OurBigBook.com>  to get awesome multi-user features, or as a <static website> where you are in full control. More information at: https://docs.ourbigbook.com/publish-your-content[].}

\Video[https://youtube.com/watch?v=j_fl4xoGTKU]
{disambiguate=home}
{height=500}
{title=Top Down <2D continuous game> with <Urho3D> <C++> <SDL> and <Box2D> for <Reinforcement learning> by <Ciro Santilli> (2018)}
{description=More information: <Ciro's 2D reinforcement learning games>{full}. This is Ciro's underwhelming stab at the fundamental question: <Can AGI be trained in simulations?>. This project <todo>[could be taken much further].}

\Video[https://www.youtube.com/watch?v=P7-OYQatYvA]
{disambiguate=home}
{height=500}
{title=<Water Margin> tribute to <Chinese> dissidents by <Ciro Santilli> (2022)}
{description=Part of <Ciro Santilli's campaign for freedom of speech in China>, see also: https://cirosantilli.com/china-dictatorship/water-margin[].}

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/lenovo-thinkpad-t430-bios-hello-world.jpg]
{height=500}
{title=<Lenovo> <ThinkPad> T430 running a <BIOS> <hello world>}
{description=Source code: https://github.com/cirosantilli/x86-bare-metal-examples[]. Ciro's <Linux Kernel Module Cheat> is a closely related and much more important project that covers the <Linux kernel> and <assembly language>.}

``
 -------------------------------------
|  Force of Will               3 U U  |
|  ---------------------------------  |
| |                  ////////////   | |
| |                ////() ()\////\  | |
| |               ///_\ (--) \///\  | |
| |        )      ////  \_____///\\ | |
| |       ) \      /   /   /    /   | |
| |    ) /   \     |   |  /   _/    | |
| |   ) \  (  (   /   / /   / \     | |
| |  / ) ( )  / (    )/(    )  \    | |
| |  \(_)/(_)/  /UUUU \  \\\/   |   | |
| .---------------------------------. |
| Interrupt                           |
| ,---------------------------------, |
| | You may pay 1 life and remove a | |
| | blue card in your hand from the | |
| | game instead of paying Force of | |
| | Will's casting cost.  Effects   | |
| | that prevent or redirect damage | |
| | cannot be used to counter this  | |
| | loss of life.                   | |
| | Counter target spell.           | |
| `---------------------------------` |
|                                     l
| Illus.  Terese Nelsen               |
 -------------------------------------
``
{title=<ASCII art> of https://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=413591[Force of Will] <Magic: The Gathering> card <inscribed (Blockchain)> in the <Bitcoin blockchain>}
{description=
Artist unknown, uploaded December 2014. Part of <Cool data embedded in the Bitcoin blockchain>{full} where <Ciro Santilli> maintains a curated list of such interesting inscriptions.

This was a small project done by Ciro for <artistic> purposes that received some attention due to the incredible hype surrounding <cryptocurrencies> at the time. <Ciro Santilli>'s views on  <cryptocurrencies> are summarized at: <Are cryptocurrencies useful?>{full}.
}

\Image[https://web.archive.org/web/20220102092623im_/http://bitfossil.org/4cbb32cd27b5b5edc12d3559bdffc1355ac2a210463d5cfaadc7ce9b06675b2b/YellowRobot.jpg]
{disambiguate=index}
{height=600}
{title=`YellowRobot.jpg`}
{description=
<JPG> image fully embedded in the <Bitcoin blockchain> depicting some kind of cut material art depicting a yellow robot, <inscription (Blockchain)>[inscribed] on https://www.blockchain.com/explorer/transactions/btc/4cbb32cd27b5b5edc12d3559bdffc1355ac2a210463d5cfaadc7ce9b06675b2b[January 29, 2017].

<Ciro Santilli> found this image and others during his research for <Cool data embedded in the Bitcoin blockchain>{full} by searching for image fingerprints on every transaction payload of the blockchain with a script.

The image was uploaded by <EMBII>, co-creator of the <cool data embedded in the bitcoin blockchain/AtomSea & EMBII> upload mechanism, which was responsible for a large part of the image <inscription (Blockchain)>[inscriptions] in the <Bitcoin blockchain>.

The associated message reads:
\Q[Chiharu \[<EMBII>'s Japanese wife\] and I found this little yellow robot while exploring Chicago. It will be covered by tar or eventually removed but this tribute will remain. N 41.880778 E -87.629210]
This is one of <Ciro Santilli>'s favorite AtomSea & EMBII uploads, as it perfectly encapsules the "medium as an artform" approach to blockchain art, where even non-novel works can be recontextualized into something interesting, here depicting an opposition between the ephemeral and the immutable.

At https://twitter.com/EMBII4U/status/1615389973343268871 <EMBII> announced that he would be giving off shares of that image on <Sup!? (Bitcoin-based social media)>, a <Bitcoin>-backed <NFT> system he was; making. In December 2023, he gave some shares of the robot to <Ciro Santilli>.
}
{source=http://bitfossil.org/4cbb32cd27b5b5edc12d3559bdffc1355ac2a210463d5cfaadc7ce9b06675b2b/index.htm}

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/cia-2010-covert-communication-websites/screenshots/starwarsweb.net.jpg]
{disambiguate=index}
{height=1400}
{title=2010 <Wayback Machine> archive of https://web.archive.org/web/20101230033220/http://starwarsweb.net/[starwarsweb.net]}
{description=
This website was used as one of the <CIA 2010 covert communication websites>, a covert system the <CIA> used to communicate with its assets. More details at: <CIA 2010 covert communication websites>{full}.

<Ciro Santilli> had some <Ciro Santilli's naughty projects>[naughty OSINT fun] finding some of the websites of this defunct network in 2023 after he heard about https://www.reuters.com/investigates/special-report/usa-spies-iran/[the 2022 Reuters report on the matter], which for the first time gave away 7 concrete websites out of a claimed 885 total found. As of November 2023, Ciro had found about 350 of them.
}

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/cia-2010-covert-communication-websites/screenshots/noticiasmusica.net.jpg]
{disambiguate=index}
{height=1400}
{title=2010 <Wayback Machine> archive of https://web.archive.org/web/20101230165001/http://noticiasmusica.net/[noticiasmusica.net]}
{description=
This is another website that was used as one of the <CIA 2010 covert communication websites>. This website is written in <Brazilian Portuguese>, and therefore suggests that the <CIA> had assets in <Brazil> at the time, and thus was spying on a "fellow democracy".

Although <Snowden>'s revelations made it extremely obvious to the world that the USA spies upon everyone outside of the <Five Eyes>, including fellow democracies, it is rare to have such a direct a concrete proof of it visible live right on the <Wayback Machine>. Other targeted democracies include <France>, <Germany>, <Italy> and <Spain>. More details at: <cia 2010 covert communication websites/USA spying on its own allies>.
}

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/Diagram_of_the_fundamental_theorem_on_homomorphisms_with_subtitles.svg]
{disambiguate=index}
{height=800}
{title=Diagram of the <fundamental theorem on homomorphisms> by <Ciro Santilli> (2020)}
{description=
Shows the relationship between <group homomorphisms> and <normal subgroups>.

Used in the <Stack Exchange> answer to https://math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426\#3732426[What is the intuition behind normal subgroups?] One of <articles>{full}.
}

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/Faster_than_light_implies_time_travel_diagram.svg]
{disambiguate=articles}
{height=600}
{title=<Spacetime diagram> illustrating how <faster-than-light> travel implies time travel by <Ciro Santilli> (2021)}
{description=Used in the <Stack Exchange> ansewr to https://physics.stackexchange.com/questions/13001/does-superluminal-travel-imply-travelling-back-in-time/615079\#615079[Does faster than light travel imply travelling back in time?]. One of <articles>{full}.}

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/C++_Heap_vs_BST_vs_hash_map_insert_time.png]
{height=1000}
{title=Average insertion time into heaps, <binary search tree> and <hash maps> of the <#C++ standard library> by <Ciro Santilli> (2015)}
{description=Used in the <Stack Overflow> answer to https://stackoverflow.com/questions/6147242/heap-vs-binary-search-tree-bst/29548834\#29548834[Heap vs Binary Search Tree (BST)]. One of <articles>{full}.}
{{source=https://stackoverflow.com/questions/6147242/heap-vs-binary-search-tree-bst/29548834#29548834}}

\Video[https://www.youtube.com/watch?v=84ig5cih4kI]
{height=600}
{title=<Birch and Swinnerton-Dyer conjecture in two minutes by Ciro Santilli>}
{description=Quick and direct explanation of the statement of the <BSD Conjecture> for people who know basic university mathematics. This is one of the <Millennium Prize Problems>, and you will get a million dollars if you can solve it! This therefore falls in the <Simple to state but hard to prove> of <Ciro Santilli>'s <the beauty of mathematics> aesthetics.}

\Image[https://upload.wikimedia.org/wikipedia/commons/thumb/5/57/Oxford_Nanopore_MinION_top_cropped.jpg/392px-Oxford_Nanopore_MinION_top_cropped.jpg]
{disambiguate=index}
{height=600}
{title=Top view of an open <Oxford Nanopore MinION>}
{description=This is <Ciro Santilli>'s hand on the <Wikipedia> article: https://en.wikipedia.org/wiki/Oxford_Nanopore_Technologies[]. He put it there after working a bit on <Oxford nanopore river bacteria>{full} :-) And he would love to document more experiments like that one <Videos of all key physics experiments>{full}, but opportunities are extremelly rare.}

A quick <2D continuous AI game> prototype for <reinforcement learning> written in <Matter.js>, you can view it on a separate page at https://cirosantilli.com/_raw/js/matterjs/examples.html\#top-down-asdw-fixed-viewport[]. This is a for-fun-only prototype for <Ciro's 2D reinforcement learning games>, <C++> or maybe <Python> (for the <deep learning> ecosystem) seems inevitable for a serious version of such a project. But it is cute how much you can do with a few lines of <Matter.js>!

\passthrough[[<iframe src="_raw/js/matterjs/examples.html#top-down-asdw-fixed-viewport" width="1000" height="850"></iframe>]]


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