nicf

11 ms·

31.
by nicf 2y ago
I'm a private tutor who works with adults on proof-based math. I've often had a similar thought to the one you're expressing here --- I also found proofs pretty revelatory when I first exposed to them and wondered where this
32.
by nicf 2y ago
You're welcome! There's actually one more point that I thought of after sending that reply, which since you mentioned it again I should maybe flag. Totally apart from physics, it may seem intuitively plausible that if you have a f
33.
by nicf 2y ago
I'm not sure if this will make you feel any better, but there's an interesting mathematical corner case at work with Norton's Dome that's responsible for the breakdown in the intuition you're expressing in (1). You
34.
by nicf 2y ago
I work as a private tutor for proof-based math, and I have a lot of students who've spent some time self-studying before coming to me. The comment by godelski matches my experience: the biggest obstacle seems to be the fact that it&#x2
35.
by nicf 2y ago
Nope. Many important results have names that are familiar to everyone in the subfield, so you might say "by So-and-So's Lemma, this module is finitely generated". Failing that, you could maybe cite a paper or a book where t
36.
by nicf 2y ago
That sounds like a fun and satisfying process! I realize my comment could be taken as denigrating all the people who write about this stuff, but that's certainly not my intention; I've also enjoyed a lot of the visualizations and
37.
by nicf 2y ago
I'm not the OP, I'm not a part of this community, and I don't know if the thing I'm about to complain about is what the author was thinking of with this comment, but as someone who was trained as a mathematician and who
38.
by nicf 2y ago
Good question! No, I don't usually work with college students. Most of my students are actual grown-ups with jobs. I've found quite a few people who just wish they'd been able to study this stuff in college but didn't ge
39.
by nicf 2y ago
Motivations vary a bit, but most of them are just in it for personal enrichment, and the people who are in it for personal enrichment tend to be the most likely to stick with it. There are definitely jobs that require more math than the thi
40.
by nicf 2y ago
I'm a tutor, mainly working with adults who want to learn proof-based math, and the message behind this post definitely lines up well with my experience! If you're the sort of person who's animated by the idea of learning mat
41.
by nicf 2y ago
Lots of good answers here already, but I can also add my own perspective. Fundamentally, you're right that there isn't really anything "special" about radicals. The reason I personally find the unsolvability of the quint
42.
by nicf 2y ago
I've been doing something similar, and it looks like you've managed to solve a problem I've been unable to: how did you get theorem and section numbering to work right?
43.
by nicf 3y ago
I assume you're talking about an algebra book for self-study? Gallian's "Contemporary Abstract Algebra" is a common suggestion for a more accessible algebra book, and people also sometimes suggest Fraleigh's "A
44.
by nicf 3y ago
I agree that this is not within the reach of most high school students, and if I had to guess, I think that either these Moscow kids were very carefully selected to be in this group or most of them didn't follow it. But I do think some
45.
by nicf 3y ago
I'm a mathematician, currently working as a private tutor for adults who want to learn proof-based math. I had a quick glance through this book and it seems to me like a pretty nice version of this "intro to proofs" sort of b
46.
by nicf 3y ago
Sure, but I think we're just talking about two slightly different things here: I was trying to describe the "sociological" reasons why math notation might end up in a state that you don't like rather than trying to list
47.
by nicf 3y ago
For what it's worth, I am a mathematician, and I'll say that there is definitely a lot of awkward notation out there in math, and some of it I would agree is even fair to describe as just bad. But I'm pretty confident in sayi
48.
by nicf 3y ago
This is the Spectral Theorem. It says (in the version for real matrices, which are what we have here) that any symmetric matrix has an orthonormal basis of eigenvectors, or equivalently that any symmetric matrix can be diagonalized via an o
49.
by nicf 3y ago
I do appreciate the feedback. (And I should mention that there is a supplement to the thermodynamics article that this post is about which goes through some numerical experiments; you can see it here: https://nicf.net/articl
50.
by nicf 3y ago
That's very lovely to hear! Thanks for sharing that.
51.
by nicf 3y ago
(This is the author of the article.) I agree! One of my favorite things about this topic is that you can prove the polyhedron version using very simple tools, so it's possible to get a feel for the concept of curvature (at least for su
52.
by nicf 3y ago
Hi, this is the author. It's been really fun to see these articles getting a little more attention. I wanted to repeat something I said when my website was posted here a couple of weeks ago, which is that I'm a private math tutor.
53.
by nicf 3y ago
I do! Thanks for the kind words. I'm happy to hear someone enjoyed the linear algebra article --- after I finished that one and heard from some people who tried to read it I ended up with the impression that I'd pitched it too har
54.
by nicf 3y ago
I'm a mathematician, although I'm too young to have been around for this. I feel like I might be able to add a little cultural perspective, though. My impression is that most of the people who were "upset" didn't th
55.
by nicf 3y ago
(Looks like I can no longer edit my last message, so including this as a separate reply.) You've successfully nudged me into making a PayPal donation link, which you can find right here: https://nicf.net/donate/ .
56.
by nicf 3y ago
What a sweet idea! I don't have a Patreon at the moment but if I get around to making one I'll definitely post it on the website. I appreciate the heads up about the typesetting --- it looks like it's due to some macros that
57.
by nicf 3y ago
This is actually on the agenda for this series! (At least for some value of "rigorous".) The question of why gravity isn't renormalizable was one of the questions that made me want to dig into this project in the first place.
58.
by nicf 3y ago
I own a copy of that book, and I also highly recommend it! (The full title is "Physics for Mathematicians: Mechanics I", but sadly we're now never going to get a "Mechanics II".) It has a different goal than my note
59.
by nicf 3y ago
> I have never heard this terminology, I have only heard Schrodinger's picture vs. Heisenberg's picture. I wrote the QM article a very long time ago at this point, and I actually can't reconstruct at the moment why I used
60.
by nicf 3y ago
Hi, this is the author. I've been coming back to this project off and on over the past few years but I often think of these articles as mostly something I'm writing for myself, so I'm really happy to see that some other peopl

More ›