stacks-project
OpenLogic
stacks-project | OpenLogic | |
---|---|---|
14 | 3 | |
799 | 984 | |
4.1% | 0.6% | |
9.1 | 7.4 | |
15 days ago | 7 days ago | |
TeX | TeX | |
GNU General Public License v3.0 or later | Creative Commons Attribution 4.0 |
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stacks-project
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Wikipedia of Algebraic Geometry Will Forever Be Incomplete. (2022)
The Stacks project is meant to be a comprehensive Bourbaki-style textbook, not an encyclopedic survey, so the Wikipedia comparison is a miss. (The WP has a textbook level of detail on some topics, with proofs and examples, but these are few and far between and come from enthusiastic editors going above and beyond the WP's declared goals.)
Stacks is not finished, however -- still a lot of "Proof. Omitted.". From what I understand, the goal is to fill them all in (otherwise there would be references to the literature in their stead), but ultimately it is still mostly a one-person project (see https://github.com/stacks/stacks-project/graphs/contributors ).
I once filled in one of those missing proofs, only to see Johan replace it by a much better one that I would never have thought of. And this was (for him) a technical lemma, not one of the crown jewels of the project. His dedication to the project is truly incomparable to anything except Bourbaki and Serre. And the usefulness of the work extends far beyond algebraic stacks.
- I don't always use LaTeX, but when I do, I compile to HTML (2013)
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Ask HN: What are some well-designed websites?
Personally, I love the Stacks Project webpage (https://stacks.math.columbia.edu/); they way it is laid out, the font, the seamless integration of LaTeX in the test (https://stacks.math.columbia.edu/tag/0A2U) has made me rethink mathematical text for the web.
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Tree linking all math concepts together?
For algebraic geometry, there is the Stacks project online, which builds up all mathematics needed to understand algebraic stacks, from foundations. This time, foundations truly mean its basic axioms. Everything is proven except maybe with a few exceptions in the introduction, and everything has links. As such, it is a monstrously large project (the pdf-version is around 7500 pages iirc). This one is I think among my suggestions closest to what you had in mind. The only thing is that it again only focuses on one area of math.
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LaTeX for books?
Some famous collaborative books: * https://github.com/HoTT/book * https://github.com/OpenLogicProject/OpenLogic * https://github.com/stacks/stacks-project * http://math.uchicago.edu/~amathew/cr.html
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What are the subfields of algebraic geometry?
There is not really one good reference for algebraic geometry (even the EGA, SGA, FGA series, and that's assuming you can even plough through them all), but the Stacks Project (https://stacks.math.columbia.edu/) is at least very good for CAG.
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Comprehensive math education
The Stacks Project is a massive project covering algebraic geometry. The nLab is a wiki that covers a staggering amount of material from its own, rather specific, point of view.
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I finished Hartshorne… now what?
Well, I talked to a friend who knows a lot of AG. He recommended "learning some things in topology like model categories" and discouraged learning about infinity categories without other stuff. Also, if you're interested in stacks, try the Stacks Project?
- The Stacks project: open-source textbook and reference on algebraic geometry
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Found a little gem online. Do you know other gems that are worth mentioning?
For more specialized and advanced interests, The Stacks Project is mindboggling how in-depth it is. Once you know how to read it, it can be pretty useful. The LMFDB is also good for stuff regarding elliptic curves, L-functions, and modular forms.
OpenLogic
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I want to learn Logic. How should I proceed?
There are a number of open-access logic textbooks, https://github.com/OpenLogicProject/OpenLogic/wiki/Other-Logic-Textbooks. Depending on where you are aiming, I would either look at For All X or the Open Logic Project.
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LaTeX for books?
Some famous collaborative books: * https://github.com/HoTT/book * https://github.com/OpenLogicProject/OpenLogic * https://github.com/stacks/stacks-project * http://math.uchicago.edu/~amathew/cr.html
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Proposing a Stacks Project for real analysis
Can we try something similar to OpenLogic? They are using the original TeX engine to produce PDFs as far as I understand. I have some experience managing a similar repository (on a smaller scale) and it seems doable. The main benefits would be publicity and collaboration tools on GitHub (and even GitHub Actions for builds, but I've had some quirks with some luaTeX actions lately so I'm not sure how reliable are they). A single git repository can be used to produce multiple related PDFs on different topics.
What are some alternatives?
tectonic - A modernized, complete, self-contained TeX/LaTeX engine, powered by XeTeX and TeXLive.
latex - The LaTeX files used for Clopen Analysis.
numerical-linear-algebra - Free online textbook of Jupyter notebooks for fast.ai Computational Linear Algebra course
book - A textbook on informal homotopy type theory
maths_book - Planning for an entire maths LaTeX book
microMathematics - microMathematics Plus - Extended visual calculator
csswg-drafts - CSS Working Group Editor Drafts
lila - ♞ lichess.org: the forever free, adless and open source chess server ♞
cms - The core Laravel CMS Composer package
github-orgmode-tests - This is a test project where you can explore how github interprets Org-mode files