I just recently went to the exploratorium in SF and saw an exhibit there suggesting that the catenary made a good arch, so browsed that chapter and saw a bit of explanation here which helped. Was also interested to see that Jefferson played some part in the history here.
I own the original Exploring Mathematics with Your Computer(Turbo Pascal version).
It’s an excellent introduction to algorithms for people coming from a mathematics background.
Really happy to see it revived in Python.
Very nice. I was looking for something fun to work on over the break. Thank you for this.
> Unfortunately, after lengthy discussions with the MAA, my hopes of publishing this (rather large) expansion have proved impossible, and so I've decided to put it online, hopefully to be of use to others.
It is painful to imagine how these fantastic works will be not be read by humans in future, as AI would digest all this and provide just-in-time code for humans.
I plan to upload the entire book as a single PDF when I finish the next chapter (on the cycloid). That will probably be early next week.
I used the original book by Arthur Engel for many years. He was an inspirational teacher.
The MAA tried very hard to publish the book, but I kept adding new material, and a text consisting of math 'selections' rather than a single theme is a hard sell in today's publishing environment.
- No colors in PDF illustrations. Is it a deliberate choice?
- > The first six chapters (and Appendix A) are essentially that book, but with the programming language changed to Python, some rewording, reformatting in Latex, and a few additions.
Try [typst](https://typst.app/) as an alternative to Latex.
This is an excellent resource for building mathematical intuition through code. Python's combination of readable syntax and powerful libraries (NumPy, SymPy, Matplotlib) makes it ideal for exploring concepts like linear algebra, calculus, and discrete math interactively.
One approach I've found effective: start with a conjecture, visualize it with matplotlib, then prove it formally. The instant feedback loop helps develop both computational thinking and mathematical rigor. Tools like Jupyter notebooks make this workflow seamless.
For anyone interested in similar resources, "Mathematics for Machine Learning" by Deisenroth et al. and 3Blue1Brown's linear algebra series complement this beautifully by bridging theory and computation.
Math was always the stumbling block for me then I realized through work how easy it is with pure rational or reals except when you need to translate it to an algorithm now you are throwing out all the elegant linear algebra for a numerical representation and using obscure characteristic polynomial constructs just to run a program and now math sucks again I went back to the beginning.
A nice course for this is of course TAOCP volume 2 old testament or MITs math github https://github.com/mitmath/18335/tree/spring22 (change the yr to suit) like we can't even have nice things like gradient descent anymore because it zigzags and is too inefficient
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[ 24.2 ms ] story [ 2414 ms ] threadI just recently went to the exploratorium in SF and saw an exhibit there suggesting that the catenary made a good arch, so browsed that chapter and saw a bit of explanation here which helped. Was also interested to see that Jefferson played some part in the history here.
However, I don't see the entire book as a single pdf?
> Unfortunately, after lengthy discussions with the MAA, my hopes of publishing this (rather large) expansion have proved impossible, and so I've decided to put it online, hopefully to be of use to others.
Too bad
I plan to upload the entire book as a single PDF when I finish the next chapter (on the cycloid). That will probably be early next week.
I used the original book by Arthur Engel for many years. He was an inspirational teacher.
The MAA tried very hard to publish the book, but I kept adding new material, and a text consisting of math 'selections' rather than a single theme is a hard sell in today's publishing environment.
- Seems great. Added to the backlog :)
- No colors in PDF illustrations. Is it a deliberate choice?
- > The first six chapters (and Appendix A) are essentially that book, but with the programming language changed to Python, some rewording, reformatting in Latex, and a few additions.
One approach I've found effective: start with a conjecture, visualize it with matplotlib, then prove it formally. The instant feedback loop helps develop both computational thinking and mathematical rigor. Tools like Jupyter notebooks make this workflow seamless.
For anyone interested in similar resources, "Mathematics for Machine Learning" by Deisenroth et al. and 3Blue1Brown's linear algebra series complement this beautifully by bridging theory and computation.
A nice course for this is of course TAOCP volume 2 old testament or MITs math github https://github.com/mitmath/18335/tree/spring22 (change the yr to suit) like we can't even have nice things like gradient descent anymore because it zigzags and is too inefficient
I will read it when it's available
Leaving a comment here so I can come back to this
<3