Limit (mathematics) by Ciro Santilli 35 Updated +Created
The fundamental concept of calculus!
The reason why the epsilon delta definition is so venerated is that it fits directly into well known methods of the formalization of mathematics, making the notion completely precise.
University by Ciro Santilli 35 Updated +Created
One major issue is that teachers don't have the right incentive to, nor are selected to, teach well. Thus the existence of Rate My Professors! But we can do better...
Which is why Ciro Santilli wants to destroy its current format with OurBigBook.com. He believes that we can find a more efficient organization to achieve both the social and research functions of university, by first doing as much as possible online
Ciro's university experiences are mentioned at: Ciro Santilli's formal education.
Intel by Ciro Santilli 35 Updated +Created
Git design rationale by Ciro Santilli 35 Updated +Created
The fundamental insight of Git design is: a SHA represents not only current state, but also the full history due to the Merkle tree implementation, see notably:
This makes it so that you will always notice if you are overwriting history on the remote, even if you are developing from two separate local computers (or more commonly, two people in two different local computers) and therefore will never lose any work accidentally.
It is very hard to achieve that without the Merkle tree.
Consider for example the most naive approach possible of marking versions with consecutive numbers:
  • Local 1:
    • 0: root commit
    • 1: commit 1
    • 2: commit 2 by local 1
  • Local 2:
    • 0: root commit
    • 1: commit 1
    • 2: commit 2 by local 2
    • 3: commit 3 by local 2
  • Remote
    • 0: root commit
    • 1: commit 1
If Local 1 were to push to Remote first, how could Local 2 notice that when it tries to push itself? The navie method of just checking: "does Remote have commit "2"" does not work, because Local 2 has a different version of commit 2 than local 1.
GNU screen by Ciro Santilli 35 Updated +Created
Most important things to know:
  • kill window: Ctrl + A K
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Video 1.
Intro to OurBigBook
. Source.
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
    Video 2.
    OurBigBook Web topics demo
    . Source.
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    • to OurBigBook.com to get awesome multi-user features like topics and likes
    • as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact