i had an MIT interview. it was underwhelming. in-person, maybe 6 or 7 p.m. at the interviewer's obviously failing computer business in vallejo. he mostly talked about how unpleasant it was at MIT.
when applying for grad school, i made the mistake of translating my (non curved) grades literally and got a polite refusal. I only applied to one other which was a bit short sighted of me (and a reflection of impecunity).
i'm of two minds about that stuff. one, don't ask me for s---. two, if people like me say no, the only people doing it will be the people who have way too much free time, which is its own kind of hell.
i learned this attending city council meetings as a child. the new england ideal of this process is that it's democracy at its purest. the true town hall meeting. in reality it's just the people with the most free time holding their representative hostage for the duration of public comment time.
as we see more and more these days.
i do like that berkeley doesn't ask its alumni to do anything. i mean, the odd junk mail, sure. other than that.
i did interview for a scholarship at berkeley. that was another disaster. at the time it felt like a personal failing, in retrospect i think the guy just had no time for doing what he'd been asked to do.
copper three friends if you count jameson and beamish.
i mean, a lot of american vodka is made from corn. if they say 'distilled from grain' or something that means corn. they would say if it didn't. but this was 100% iowa corn.
that's how we lost our last honda civic. rear-ended on an on-ramp and an uninsured driver.
uninsured and who knows what else. the driver got out of the car and ran down and embankment into the darkness, rather than stay and exchange information.
definitely not. but i love driving it. she was out of town last week and i drove it instead of my own car.
got a lot of attention from the ladies.
i should clarify that. from the ladies dropping their children off at the same day care i was dropping my daughter off at. they would say things like "hi leslie's daughter!"
i don't even know my neighbors names. i was trying to describe the location of something to my wife, and i said "it was in front of, uh, joe's house? david's house? mike's house? bob's house?" i was just listing common names because i knew some of our neighbors had them.
it turns out we have neighbors named both bob and david, and the thing i was talking about was in front of david's house. so, right on the second try.
the program to generate the coefficients is easy, it is proving a bound on teh magnitude of the bezout coefficients for the following problem that has consumed my morning.
showing multiples of the gcd > ab lies in the positive span of a,b
I answered a simple Bezout coefficient question a few days ago (not a PSQ), without bothering to do a dupe search. Bad mistake. I got 2 downvotes fairly quickly. Several hours later, I got a comment politely requesting not to answer common dupes.
PM: i have mixed feelings about that sometime. sometimes, an answer responsive to the particulars of someone's attempt is not a dupe, even if the overall question is a dupe and there are answers elsewhere that would, at least formally, answer the question.
@TedShifrin the sad part is that i must at this stage know all the relevant tricks and certainly have the machinery but it escapes me for now. brain rot :-).
I don't know about induction on the euclidean algorithm. Just go from $kd = ma+nb$ with $m,n\ge 0$ to $(k+1)d$ using the "Bezout" formula. Can you make both coefficients nonnegative by exchanging $a$'s and $b$'s as required?
@leslietownes Yeah. I've seen plenty of questions closed as dupes where the dupe target does tell you how to calculate / show the thing the new OP wants, but doesn't actually clarify the misunderstanding that the OP has. Sometimes, that can be addressed in a comment, but not always.
I never liked these sorts of problems before, but teaching and writing this algebra book I became a believer in these sorts of baby number theory problems as good for teaching investigation and proof.
Have you looked at Pascal's triangle mod different primes? That is quite fascinating. That was a problem at the end of the first section.
I just did a sloppy induction answer. I did a half-hearted dupe search, but there are hundreds of questions involving marbles and probabilities. math.stackexchange.com/q/4299305/207316 At least it hasn't scored any downvotes yet...
probability questions are a particularly acute example of this. depending on how you model a situation, it might be 'clear' formally that one situation gives the same result as something else. which is not to say that a result applicable to one situation would immediately be understandable as applicable to something else.
@TedShifrin With many problems I have an idea where to go, but with a lot of discrete problems I get them eventually, but I certainly am not GRE material in speed...
Someone posted a question with definitions of vector/fiber bundles and then, when I commented to ask "have you thought about cylinders and Möbius strips mapping to the circle?" the person said — what does this have to do with my question. AGH.
With a lot of questions, the OP can do the required maths. But their main problem is in seeing the important mathematical structure hiding under the word problem.
Eg, there was a question a few days ago that's easy to solve using the CRT. A few of us were trying to gauge the OP's knowledge & dropping helpful hints in the comments. Then all of a sudden it got closed as a dupe of a generic CRT question. The OP knew how to solve a CRT system, so that dupe wasn't helpful for them. But they just didn't realise that their question was a CRT question.
there are a lot of social determinants of what math matters, but when you mix math with politics, you get politics. i can't enter that discussion.
bear in mind that almost every legislator and school board member has never studied anything resembling mathematics other than whatever was required to qualify them for a job. and yet they periodically acquire sudden interest in this area.
i think everyone who wants to enter a debate about math policy in any official capacity should be required to take the math SAT and post their score in public.
or sign onto something about abolishing standardized exams.
I expect people who've finished school to have some rudimentary understanding of arithmetic, but I don't expect them to know / understand much beyond that.
My theory is that a large proportion of people get bewildered somewhere around learning fractions in primary school, and never recover. They only manage to make it through school maths by memorising stuff that they don't actually understand. I suspect that most students who desperately ask "Is this going to be on the test?" are in that situation.
what was even more unbelievable was that himself & martin mcguinness got along very well, so much so they were known as the chuckle brothers,
can you imagine trump and biden being called the chuckle brothers?
@PM2Ring i think part of the problem with teaching is that many concepts evolved over a long time and when the end result is presented without any lead in it is often bewildering. and this is compounded by delivery mechanisms that do not understand what is being delivered.
why pemdos occupies some much of the early brain math development is beyond me.
of 3 ways to do multiplication.
more time on motivating would be well spent, i think.
reminds me of wandering around boots chemist in ireland a few months ago with my whatsapp on videoing the feminine products section for my offspring to make choices for me to purchase.
other patrons were amused (meaning they thought i was some sort of old pervert)
my kids spent hours on mind numbing pemdas problems with zero learning.
i can see why some folks see a need for a social agenda in maths, but it is because they are blaming the subject instead of poor teaching or poor teaching methods.
a lot of legislators and legislation adjacent people majored in very political fields, which is understandable. but they can't understand how you can teach something without the teachers/profs/whoever's beliefs entering into it.
a lot of ed reform is some weird psychological projection of people who intentionally subjected themselves to politicized environments and then want to somehow deal with that without therapy.
OTOH, there is probably room for improvement in the syllabus. So much school maths is part of the track leading to calculus, which is not necessarily very useful to those kids who never go on to study calculus.
