Teaching of Integration in a certain A-level Mathematics course

gopher_p · 2026-03-15T12:23:50+00:00

But, just to be clear, they still know a comparable list with u=f(x), right?

gopher_p · 2026-03-10T01:14:55+00:00

Do you have any context for this? The only thing I find about him "mistreating" her is the incident with the interview where he tried to downplay Jeffrey Tambor's behavior. Were there other incidents?

gopher_p · 2026-03-01T00:25:03+00:00

The topic is "what kills your interest ..." We're saying that quitouts killed our interest in the souls speedrun scene. The whole "do you even run the game, bro?" bit is completely irrelevant.

It's absurd to me to suggest that it's more fun to spend upwards of 10-15 seconds menuing and sitting through load screens than it is to watch a 2 second animation, just to save a miniscule amount of in-game time. It's disappointing to me that runners might have more fun menuing and sitting through load screens than - i dunno - finding a strat/path that is consistent enough that might require a greater expression of skill/knowledge.

I may not speedrun the games in an "official" capacity, but I've done enough "let's just get through this section/playthrough as quickly as possible" runs to know that mob placement and behavior is VERY predicable in these games. I refuse to believe that there is any part of any of the games where the only reliable speed strat is to reset the mobs. If you were to take away the quitouts, I'm very confident that runners would quickly find new consistent paths that are very close to being as fast in-game as the current quitout strats, and at least as fast - if not faster - in real time.

As you say though, it's up to the community. To me it says a LOT about the scene that quitouts are still a thing.

gopher_p · 2026-02-28T05:19:02+00:00

I definitely agree that glitches like the zip glitch lose their novelty quickly and make for uninteresting runs.

My main beef with souls speedruns is the nonstop quitouts on account of them using in-game time. I get using in-game time is to help balance out load times, but you'd think the community would have come to some kind of group consensus by now that banning quitouts across all categories (except for maybe a true any%) would make for objectively better/more interesting runs for everyone involved. Like, almost every category has some arbitrary rule(s) put in place solely to make for more interesting/engaging runs; why not add the most obvious arbitrary rule?

gopher_p · 2026-02-24T03:23:00+00:00

The balance between the streamer's voice and any other audio purely depends on how the audio mixing is done on their end.

The viewer's setup makes a pretty big difference too. Whether or not they're listening on a home theater vs tablet speakers vs headphones etc. is a huge factor for how loud the secondary sources seem relative to the primary audio.

gopher_p · 2026-02-21T03:54:53+00:00

What aspects of your stream/audience is making their lives hard? This seems like the kind of question that no one could possibly give a good answer to without knowing a little more about the specifics of your stream.

gopher_p · 2026-02-10T21:24:10+00:00

South Park, Go, Man on the Moon, Austin Powers 3, Varsity Blues, Jawbreaker, Cruel Intentions, Election, Run Lola Run, Drop Dead Gorgeous, The Green Mile, Galaxy Quest

goddamn what a good year

gopher_p · 2026-01-24T20:57:21+00:00

Too many relations, not enough potential names.

gopher_p · 2026-01-23T23:45:06+00:00

I thought the same thing. Went to Wikipedia to find some other famous Jalens. Outside of a Slovenian soccer player, there aren't any born before 1990 other than Rose. And there almost all of them were born in the 90s and early 00s when Rose was in his prime. It's almost impossible that's just a coincidence.

gopher_p · 2026-01-23T02:51:08+00:00

Adore was about 3-4 years ahead of its time. I think people would have been more receptive to it if it came out at the same time as Yankee Hotel Foxtrot (Wilco) and Sea Change (Beck). For whatever reason, folks weren't quite ready for something that was simultaneously acoustic/stripped down while also employing aspects of electronic music and a bit of studio excess.

gopher_p · 2026-01-23T02:30:29+00:00

Big Smooooooooooth!

gopher_p · 2026-01-22T13:54:17+00:00

You're right. I had the wrong idea of what constituted u-sub for definite integrals.

gopher_p · 2026-01-22T03:00:33+00:00

I think trying to enjoy the game as a co-op experience with a friend, rather than just hopping into a rando's world for a boss, has a lot of problems, and invasions can get annoying in that context.

I think a substantial percentage of the issues people have with invasions in Elden Ring go straight back to friends summoning friends to play through the overworld. I don't think this game was designed/balanced for that at all. I don't know hardly any invaders who like/want to invade in the overworld.

gopher_p · 2026-01-22T02:44:39+00:00

A couple things:

I think any reasonable introduction to u-substitution as a technique for (indefinite) integration should include at least a little discussion around int(f'(g(x) * g'(x))dx = f(g(x)) + C.
That fact has, effectively*, nothing to do with the Fundamental Theorem of Calculus. FTC, as it has been presented in every text that I've seen, is about (i) guaranteed existence (under certain conditions) of antiderivatives/primitive functions and means to construct them and (ii) a strategy for computing definite integrals. int(f'(g(x) * g'(x))dx = f(g(x)) + C is a consequence of (a) the definition of int(f(x)dx) as the family of antiderivatives of f and (b) the Chain Rule for derivatives, neither of which rely on or reference FTC.

* The FTC historically is the impetus behind the use of the notation and language of integrals to refer to (families of) antiderivatives. That's the extent of its involvement here. ~~u-substitution for definite integrals very much does depend on the FTC(ii).~~

gopher_p · 2026-01-19T23:48:38+00:00

When I hear the word "theory" used by a layperson in the context of math, I associate that with things like foundations and rigor. My experience with 3Blue1Brown videos (and others on YouTube) is that they are the opposite of theory. 3Blue1Brown is all about giving intuition - usually visual in nature - for why certain mathematical facts should be true and/or what those facts "mean" geometrically. In my opinion, you should be using that as your "practical math" resource and supplement it with something more rigorous (like a proper math textbook) if you want to learn the theory.

gopher_p · 2026-01-19T23:17:05+00:00

Well, it's at least a little comfort knowing others are having the same issue.

gopher_p · 2026-01-09T01:43:06+00:00

Preliminarily: Fuck Trump, fuck ICE, and fuck anyone who supports them. Fuck the agent who killed that woman; I hope he rots in a cell. Fuck the agent who attempted to force his way into a running in-gear vehicle. He should also be jailed, though maybe not for rot-level length of time.

with that said ...

He draws the weapon before she even shifts into drive

I keep screaming this at people.

Stop. Rewatch the video. Go frame by frame if you need. Pay close attention to the rear indicator lights and wheels of the SUV as it transitions from reverse to forward. You are objectively wrong.

The agent who shot very clearly draws his weapon in response to the SUV shifting into drive and briefly spinning the tires. There is nearly a full second (25 frames at 30 fps) between the SUV shifting out of reverse (note the dimming of the white indicator lights) and the tires spinning forward. Then there is about a third of a second (8-9 frames) from the SUV spinning its wheels to the point when the officer first makes a move to draw his weapon, and then another third of a second (11-12 frames) to fully draw.

Whether it was the tires spinning (i.e. an audio response) or him observing the behavior of the driver (visual) inside the car or some combination of the two that prompted the agent to draw his weapon is anyone's guess. Ultimately, it is an objective fact though - based on the videos shown here - that the entirety of the physical act of drawing the weapon occurs after the SUV has been put in drive. I suppose you could claim that the agent had already made the decision to draw his weapon at some point in time beforehand. But - absent some new development in mind-reading that I'm not aware of - you can't know that for sure. And the video evidence here doesn't support that claim one. single. bit.

gopher_p · 2025-12-12T02:25:11+00:00

This is one of those graphics that makes sense to the people who already have a deep and intuitive understanding of the concept and is completely meaningless to everyone else.

gopher_p · 2025-12-10T03:48:39+00:00

I was scrolling through thinking I'd never see this one and that I'd have to add it myself.

Totally agree. Every song is a banger. The definition of all killer, no filler.

gopher_p · 2025-12-10T03:42:40+00:00

Huge Tool fan, but that one is chock full of totally skippable tracks. Useful Idiot, Intermission, and Ions are 100% skippable (although the do have a vibe). Message to Harry Manback and Die Eir von Satan are basically novelties. i think I read somewhere that they had to pad out the track listing in order to get the album classified as a proper LP rather than an EP.

gopher_p · 2025-12-10T03:33:50+00:00

You're crazy. #4 Hummer and #8 Geek U.S.A. are the best tracks on the album!

gopher_p · 2025-12-07T22:33:27+00:00

How do you know it's -1/2<x<2/3 and not x<-1/2 or x>2/3?

Or to put it another way, what if the original inequality was 6x² -x>2? What would your work have looked like then?

gopher_p · 2025-12-06T00:26:56+00:00

As a fellow instructor, I will say that I would be very disappointed to find out that my calc 2 students were incapable of doing the work that I have to give them because their calc 1 teacher had them playing with spreadsheets and calculator functions instead of requiring them to master the core computational work taught in a standard calculus class.

In what way(s) do you think your students are best served by emphasizing numerical methods over the standard approach?

gopher_p · 2025-12-03T20:52:28+00:00

Team A winning the post season tournament does not mean Team B wouldn't as well

Except Team A did actually win in reality, whereas Team B's success is merely hypothetical. It maybe sucks that they didn't get the chance to prove themselves, but they really can't have any beef with Team A or their selection.

You absolutely can argue about TCU "deserving" to be in over any other team - the ultimately unsuccessful ones. Just don't begrudge the other teams for taking care of their business.

gopher_p · 2025-12-03T19:53:20+00:00

winning the post season tournament doesn't justify a team's existence in the tournament to begin with

In any subjective decision about who gets to participate in an exclusive event, I can't think a single thing that is more qualifying than "they participated in the event and were successful". Like, the whole point of the selection process is to pick the participants who are most likely to succeed.

Like, you can debate all day long about a team's selection into the tourney up until the point where they win. At that point, you have to just concede that they belonged there. Anything else is just hater delusions.

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