Tom M. Apostol's Project Mathematics videos circa 1988-2000 are wonderful:
https://en.wikipedia.org/wiki/Project_Mathematics!
https://www.youtube.com/watch?v=vpxWyJg4_1A&list=PL8_xPU5epJ...
Visual explanations of mathematics (2020)
21–28 of 28 posts
Re: Visual explanations of mathematics (2020)
#22Tom M. Apostol's Project Mathematics videos circa 1988-2000 are wonderful: https://en.wikipedia.org/wiki/Project_Mathematics ! https://www.youtube.com/watch?v=vpxWyJg4_1A&list=PL8_xPU5epJ...
I remember seeing these videos on youtube long time ago, but couldn't remember the sources. Thanks for sharing!
Re: Visual explanations of mathematics (2020)
#23I've seen physical-sciences research talks by people from Caltech, where the format is putting up a single equation, and then walking through it piece by piece. That's the entire talk, all the slides, and how the talk is organized. I've never seen that from elsewhere, and so think of it as a "caltech style". Does this have a real name? Can anyone flesh this out?
I can't speak to Caltech, but it sounds like what you're describing is a perfect example of a "worked example". The idea is that you are walking through an algorithm, piece by piece even to the most basic levels.
Its the style I use for my AI classes, though I've never been to Caltech; barely even to the west coast. I think its just something educators realized should get highlighted because all those symbols get complicated quickly like what the heck do η and τ mean for Ant Colony Optimization[1]?
[1] They mean desirability and # of ants that picked a path
Re: Visual explanations of mathematics (2020)
#24I am teaching intro stats and would love to have a textbook that introduces equations in this manner. I have been trying to incorporate this style into my slides but it is not as easy as it looks. (Same issue with syntax highlighting in PowerPoint/Google Slides.)
You might be interested in the work of Andrew Head, in particular his team's Formula Formatting Language: https://andrewhead.info/assets/pdf/ffl.pdf - I have not tried it myself though.
Re: Visual explanations of mathematics (2020)
#25If you are the owner of the website, could you please add a page where I can browse all the articles easily without scrolling 10 kms on every single page. It is a very interesting blog with a tonne of seismic machine learning articles that I would like to read but I have to keep hitting next and next browsing through every page. Can I just see an index or all the titles somewhere?
That's me, sorry it's frustrating. I don't maintain the site anymore, but I just added some new views to this page, in case they help at all > https://agilescientific.com/index
Re: Visual explanations of mathematics (2020)
#26I don’t think visual explanation should be about writing colored versions of formulas or adding notes, it’s providing a visual that immediately unlocks the core idea. Many examples are given here: https://math.stackexchange.com/questions/733754/visually-stu...
I agree that you can't beat a good visual. Sometimes, or for some people, the symbolic representations unlock other insights though, and I think adding them helps develop new scientists too. For me, code also helps a lot. I guess the main point is: add modalities.
Re: Visual explanations of mathematics (2020)
#27If you are the owner of the website, could you please add a page where I can browse all the articles easily without scrolling 10 kms on every single page. It is a very interesting blog with a tonne of seismic machine learning articles that I would like to read but I have to keep hitting next and next browsing through every page. Can I just see an index or all the titles somewhere?
That's me, sorry it's frustrating. I don't maintain the site anymore, but I just added some new views to this page, in case they help at all > https://agilescientific.com/index
i am a full stack dev, i can help create an index for that page if you want
Re: Visual explanations of mathematics (2020)
#28> We have lots of tools to write better mathematics: LaTeX, markdown, Jupyter Notebooks, and so on. But it feels like nothing has really converged yet. Technology that seamlessly mixes symbolic equations, illustrative-and-explicative annotation, and runnable code is, I am sure, not far off. [2020; emphasis added] Back in the 1990's, we had lots of tools to write better mathematics: LaTeX, HTML, Mathematica notebooks,…
Do you believe that existing open source symbolic kernels are the limitation here, given that we can now easily (for some value of n) render the notation and the notes/annotations? I mean, there are a ton of math libraries available for most programming languages, but symbolic solving is pretty important here, because presumably people would want to (for example) show the integral or summation symbols and use algebra…
> Do you believe [...] are the limitation here
[a late reply, but...] I strikes me as having a flavor I associate with PIMs, rich text formats (eg markdown etc, and their assorted extensions), literate programming, and book writing systems. A high-dimensional sparse space of possibilities and taste and needs and nopes, which scatters effort and users, avoids critical mass, and thus discourages use and convergence. LaTeX and github-flavored markdown and pandoc and Jupyter are all achievements of convergence within multi-decade slogs. Ongoing slogs (how do you edit that LaTeX, make a book using pandoc, wrap a development process around Jupyter, etc). So yes, symbolic math is another slog. With 1970's macsyma stalling on licensing, Mathematica suing to prevent open-source implementations, and more. But I'm not sure that's a critical bottleneck here. I'm guess I'm suggesting that these wins of convergence often have long slogs not just behind, but ahead too, making it easy to overestimate the pace of future progress when looking at a collection of recent wins. Sometimes not - rust as C successor. But until time, or some famous app, creates user expectations for notes/annotations, their future looks a slog?