a similar observation turns up in the theory of vector bundles: disk bundle modulo sphere bundle is the one-point compactification of the total space (this is, of course, the Thom space)

@Koro the UCPD is a state law-enforcement agency. They have statewide jurisdiction within a mile of a UC campus.

it is one of my favorite cute facts that the Thom space of the tautological bundle over $\mathbb{CP}^n$ is $\mathbb{CP}^{n+1}$

(this is one method to recursively calculate their cohomology rings using the Thom iso)

@Koro UGA police could make arrests within 500 yards of campus.

Hmm..Georgia is a bit more restrictive.

@Thorgott Suppose I take X= $D^2,$ the unit disk in R^2, $A= D^2-\delta D^2$, then X/A should be $S^1\cup \{p\}$, but S^1 has no 1 pt. compactification.

@TedShifrin ohh😮😮

ah, you're semi-right, I do need closed

I would argue $S^1$ has a one-point compactification, namely disjoint union with a closed point

but this isn't that, so garbage

Munkres defines 1 pt. compactification only for locally compact Hausdorff non-compact spaces and I use that convention :-).

Because for compact Hausdorff, if we do the 1 pt. compactification as per the procedure for non compact case, it turns out that $\infty$ becomes an isolated point.

perhaps it's worth to make a distinction between the Alexandroff extension and a one-point compactification

I mean the former

I don't know who created that avatar. It was never my gravatar.

possibly the author of the article

Isn't this at least a decade-old news?

I'd rather step on LEGO than get a B in Math class

I got a B in the one math class on which one might say I'm most expert. shrug

I think it's fair to say that some of my professors gave me As that I would never, as a professor, have given. I can think of several.

i got a C in linear algebra

Like 53A?

54

Oh, well, it was the ODE stuff that you couldn't learn.

were you there when they were still dabbling with the quarter system?

Our marks are from 18 to 30

We were on quarters throughout my graduate career. I think the switch happened just after. (I left in 79.)

yes, the ODE stuff went in one ear and out the other

marina ratner, about 20 years after the switch, would still say "this is something you remember from 53A" and we were like "wtf"

Wu told me that Berkeley couldn't consider using my linear algebra book because there was hardly any ODE in it. I said I understood.

@TedShifrin is there a pdf online of your book?

Actually, no, when I was there it was 51. 53 I thought was the numbering under semesters after. I think Marin was actually on semesters with that. 51A was linearly algebra, 51B was multivariable, 51C was diff eq (which I TAed my very first quarter)!

i TA'ed lienar algebra/ODE once and made a mess of the ODE part

Not anything legal, Sine. There are two books with illegal pdfs various places. I'm talking about the just linear algebra book. There's also the Multivariable Math book that contains almost all of that plus all the multivariable calculus/analysis.

Actually, I had some wonderful students in that 51C class. One asked me for recommendations years later.

@TedShifrin I guess is not legal

The one book that is legally available for free is the differential geometry text. You can find it linked in my profile (or on the AMS Open Notes website).

I've gotten Bs and Cs in many non-math classes though

thank you, I'm thinking what to study during summer

I find that, generally, the more math a class has the better I perform

I've a lot of books that I'd like to study, but I don't have time

@TedShifrin I got a D- in Calc II.

The minus was the real kicker. Why not just give me an F?

I’ve never studented or taught at any school that gave D-‘s.

same

@TedShifrin I know, right?!

It is kind of an insult. :(

Does anyone know some lectures notes or some other text that discusses symbolic notation used in definitions, for example $\forall$, $\exists$, ...?

At UGA we finally added +- grades. No A+, no D- or F+-. One needed a C (not C-) for a course to count for the major. I gave some C- to be “generous” rather than giving D. Some students of course complained, to which my response was “Would you rather have the D you earned?”

@XanderHenderson So there is previous evidence of my Redemption Arc in the real world?

@D.C.theIII I mean, I was 16 when I started college. Like most 16 year olds, I was very much lacking in maturity. It took me a while to get my head out of my ass.

@TedShifrin U of T specialty...........got a D- in an "Intro to Real Analysis" course and I got it out of sheer pity because of my constantly going to office hrs.

@TedShifrin I have been pushing rather hard to implement +/- grades here (A-; B+/-; C+). But the most vocal faculty don't want to change the current system, so we have no plusses and minuses.

@XanderHenderson Well a 16yr old doing Calc II is not an ordinary thing.....I'll disregard this last piece of information and just add what fits my narrative. :)

@D.C.theIII I mean, most Americans don't start college until they are 18. I was the second youngest person in my cohort.

Though I was 17 by the time I was failing Calc II.

All my career I kept hidden +- in my records, anyhow. I think the nuance is not unreasonable, bit more hassle for faculty. Especially with students complaining …

That was second semester.

In any event, I think it is time for me to call it a day and go home.

Later.

Night!

Yea that's why I was saying. In a relative sense you may have been failing, but you also still developed your math maturity earlier than most

Enjoy your afternoon

i skipped a grade, and my grandfather always said i was making up for him, who had to repeat a grade. mostly for problems of discipline and not academics.

I skipped 4th grade. I missed the whole year of CA history.

i skipped 5th, when 5th was CA history.

we had a parent teacher conference today at day care. apparently munchkin is developmentally ahead of her friends, and refuses to do work at her developmental level because her friends aren't there. she also blows up at people who won't do what she tells them to do.

Gee, why does none of this surprise me? It sounds like she continues her abusive behavior toward her parents at school with her friends and teachers.

I wonder about refusing to work "because her friends aren't there." Is it a conscious decision not to seem different, so as better to fit in? I certainly had issues a bit older than that with conspicuously not fitting in.

@leslie @robjohn @copper If you haven't seen this, it should be good for a laugh or three.

@TedShifrin it appears that they might be trying to define a Dirac delta function, but there is not enough structure to determine for sure.

Suppose $p \mid |G|$ and let $H \leq G$ be a $p$-group. Show that the number of Sylow $p$-subgroups which contain $H$ is congruent to $1 \pmod{p}$.

I know that the number of Sylow $p$-subgroups are congruent to $1 \pmod{p}$. To show the result, it suffices to show that every $H \leq G$ $p$-group is contained in one and only one Sylow-$p$ subgroup. I am not sure how to prove the only one part for this. Any hints.

@TedShifrin Can you help me with this question?

I am not an algebra expert. I last taught this about 10 years ago. I’ll think about it, but there are other options of people to help.

@TedShifrin Thank you.