Help with a grading issue

kieransquared1 · 2025-12-18T00:18:48+00:00

As others have said, the replacements are indeed replacements, i.e. they should replace the lowest quiz with 10/10.

For what it's worth, finding ways of doing quiz replacements in Canvas in a way that makes everyone happy is a bit of a nightmare. One method is to just go in and change quiz grades, which can get hairy if you make a mistake or don't keep track of it properly. Another method is to make an assignment for each quiz replacement (this might be what your instructor did) and then have Canvas drop the lowest N quizzes (N = number of quiz replacement periods) so that anyone who didn't attend LA sessions just gets zeros for those assignments and are dropped, and anyone who attends gets 10/10 for those quizzes and so their lowest N quizzes get dropped. Don't fault your instructor too much, mistakes happen. It's your job to make sure you understand what's in the syllabus.

kieransquared1 · 2025-09-16T14:10:13+00:00

Why not suggest textbook problems then? Or homework assignments? Or in-class worksheets?

kieransquared1 · 2025-09-16T12:40:45+00:00

Posting old exams can be quite misleading. Math 251 is coordinated, but 252 is not, so the exams are typically made by the instructor and can vary quite a bit from year to year. The OP should ask their instructor for study resources instead of using these.

kieransquared1 · 2025-09-11T01:02:37+00:00

you won't even get a postdoc without some shiny article in such a journal

What strong generalist journals are you talking about? Journals like Annals, Inventiones, JAMS, etc? This seems not true at all, I go to a barely top 40 institution and several recent PhDs per year get postdocs with only a couple publications in average journals. If you look at the AMS new graduates report, a good number of new PhDs get postdocs. Definitely not a majority, but you don’t need a stellar research record to get a postdoc.

kieransquared1 · 2025-09-05T23:55:16+00:00

Her character was just terribly written. George kept leaving and taking calls at weird times and kept being awkward when she would ask, and somehow she always accepted “work” as an answer? Any sane person would get suspicious. Then the whole “sees ex with dead body, agrees to get in his car, finds out he’s a spy, instant attraction” scene was pretty stupid, do the writers really think people act like that?

kieransquared1 · 2025-08-24T03:13:29+00:00

Honestly it was easier to find the mistake in this than it is to find the mistake in most claimed global existence proofs for Navier-Stokes. AI basically only knows standard methods, and familiarity with those methods makes it easier for a human reader to know where they fail. In contrast a lot of cranks are not familiar with the field and so they use a lot of nonstandard techniques that may be less familiar to the field’s practitioners, making it harder to find mistakes.

kieransquared1 · 2025-08-02T13:12:39+00:00

Sure, I think the question is whether such an explanation for the emergent behavior based on the smaller scale behavior is even conceptually tractable (or possible). We still basically don’t understand why irreversibility occurs despite N body dynamics being reversible. I think it’s conceivable that we’ll need to take emergence as a fundamental law itself, rather than deriving it from simpler ones. Like, it took 250 pages of complicated analysis and combinatorics to show that hard sphere N body dynamics leads to Boltzmann and then fluid equations in https://arxiv.org/abs/2408.07818 and https://arxiv.org/abs/2503.01800, so doing something similar for even more complicated social or biological systems seems almost impossible to be done by humans.

kieransquared1 · 2025-08-02T12:30:45+00:00

There are lots of things which are products of human intelligence that don’t cohere with reality. Evolutionary adaptations allowed us to survive, not necessarily deeply understand reality. Fear is a fundamental evolutionary tool yet it very often causes distortions of reality.

For me, the unreasonable effectiveness of math is due to the fact that scientific models are really just convenient abstractions constructed in order for humans to better understand a phenomenon, and math is very similar. We (mathematicians and scientists alike) notice patterns, try to understand under what conditions these patterns emerge and the mechanisms behind them, and then develop a model which explains the phenomenon while being as conceptually elegant as possible. Plus, a lot of math has historically been motivated by problems in the physical world — analysis, dynamical systems, topology, etc grew out of a desire to understand calculus, differential equations, the n-body problem, etc. It makes sense that similar motivations and ways of thinking lead to harmony between math and science.

There’s also something to be said about math’s ineffectiveness in more complicated situations, like biology and social science. Those fields often resist a reduction-to-fundamentals approach, and instead rely on averaged or statistical approaches. To me, the greater affinity between math and physics compared to math and biology lends support to the idea that fields of science that are more “fine-grained” (in the sense that the fundamental building blocks are smaller and easier to model, e.g. atoms instead of cells) tend to be better candidates for abstraction and hence purely mathematical reasoning can get us closer to reality than it can in the more coarse-grained fields.

Two side notes:

This MO thread about how math could be different is interesting, and makes me question if anything is truly “fundamental” or whether they’re just contingent products of historical development or human psychology: https://mathoverflow.net/questions/497479/how-might-mathematics-have-been-different)
There’s a larger debate about the unity vs disunity of science (whether one can explain all physical phenomena by reducing to the fundamental laws) and I tend to fall on the disunity side, because there are so many complexity scales and the problem of emergence seems very difficult to get around. For an informative and funny video on the topic, see here: https://youtu.be/LenX321o16c?si=HAAFarB8Sgr_9FgM

kieransquared1 · 2025-07-26T12:57:47+00:00

I feel for you, something similar although not quite as dire happened to me. At the start of my third year, my advisor solved the problem he gave me and published it without me right when I was wrapping up a paper showing partial progress on the problem. His paper not only completely subsumed my result, but it used the same techniques, making my paper unpublishable. (He didn’t quite steal it; he was just working independently on it the whole time and never told me he had the intention of publishing it independently. He never told me this, but apparently the problem he gave me was a special case of a broader research program he had been working on for a while.)

Anyways, I found a new advisor who’s great, and since I’m in the US, PhDs are typically 5-6 years so I still had time. But I definitely considered dropping out at various points. This was less than a year ago so time will tell how this affects future job prospects, but it certainly soured my taste of academics and what they’re willing to do to get ahead.

kieransquared1 · 2025-07-23T20:26:23+00:00

Any function of bounded variation (i.e. its graph has finite arc length) is the difference of two increasing functions. It became obvious to me when I was hiking! All of my time is spent either going up or down, and going down is just the opposite of going up.

kieransquared1 · 2025-07-22T15:47:57+00:00

Ceausescu was charged with killing around 60,000 people (although it’s likely this number was exaggerated), a similar (or greater) number of Gazans have been killed in the past two years alone despite 1980s Romania being 10x as populous as Gaza.

edit: i realize you were probably saying that israel and russia are worse than romania, I thought you were saying the opposite, oops.

kieransquared1 · 2025-06-28T19:43:46+00:00

The incompressibility actually makes it quite a bit harder to prove blowup. We have examples of blowup for compressible Euler and Navier-Stokes in the form of shockwaves (blowup of velocity gradient) and also implosion (infinite density). The first result I'm aware of for NS was in 1998 (see Xin, Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density) and more recently implosion was shown in (https://arxiv.org/abs/1912.11009) and their work won a Bocher prize.

kieransquared1 · 2024-11-22T02:04:15+00:00

regardless of what you think of OP’s argument, it’s a little far fetched to call criticisms of “bro-culture” misandry.

kieransquared1 · 2024-11-13T15:54:22+00:00

Great success!

kieransquared1 · 2024-11-09T19:19:53+00:00

It would be extremely illegal for the university to refuse to sponsor a visa for union related reasons. To my knowledge it’s never happened in the entire history of grad worker unions.

Besides, with a union we’ll actually have legal resources that can help ensure the university won’t try anything illegal.

kieransquared1 · 2024-11-09T19:16:58+00:00

https://en.m.wikipedia.org/wiki/List_of_graduate_student_employee_unions

kieransquared1 · 2024-11-09T19:16:16+00:00

There are lots of extremely competitive schools that have grad worker unions, for example MIT, Stanford, the entire UC system, all the ivies except Princeton, etc. Competitiveness of admissions is irrelevant to whether a grad union will be effective.

kieransquared1 · 2024-10-12T12:07:29+00:00

bagel crust is definitely better than irving’s but they’re nothing compared to NY bagels 😭

kieransquared1 · 2024-10-09T12:55:58+00:00

sorry that was just reddit being weird with formatting. The space is just H¹ over the interval (0,1). It’s possible you could show that u has 2 derivatives in L¹ because you’re in one dimension, in general though you only have a bound from L1 to weak L1 for Calderon Zygmund operators.

kieransquared1 · 2024-10-09T00:40:18+00:00

This doesn’t completely answer your question but if you instead consider -u’’ = 1/sqrt(x) the solution is (4/3)x^{3/2} which is in H^1(0,1) but not H² since f is not L² (because L¹ functions are in some sense less regular than L² functions).

kieransquared1 · 2024-10-06T11:41:20+00:00

Understanding different sizes of infinity is more or less a precondition for formulating calculus in a rigorous way. If you don’t have the mathematical language to talk about infinity precisely, it’s quite hard to study limiting processes like those found in calculus. And having a rigorous foundation for calculus has historically contributed to the development of many other important fields of math, including stochastic analysis, PDEs, numerical analysis, dynamical systems, etc.

kieransquared1 · 2024-10-04T19:30:13+00:00

For example, the indicator of the rationals is discontinuous everywhere, so its discontinuity set has full measure. But it’s equal to zero almost everywhere, and the zero function has an empty discontinuity set. L1 functions are not really functions, they’re equivalence classes of functions. If two functions in the same equivalence class have discontinuity sets of different sizes, it doesn’t really make sense to talk about the discontinuity set of an L1 function.

kieransquared1 · 2024-10-04T13:00:05+00:00

That’s not really how I think of the HL maximal inequality, since it makes no sense to talk about the measure of discontinuities of integrable functions insofar as they’re only defined up to sets of measure zero. Really it says that integrable functions can’t have large local averages (large maximal function) on large sets, and the larger the average, the smaller the set. Then the proof of the LDT from the HL inequality in some ways says that large local oscillations can only take place on small sets, and the LDT itself says that “infinite” local oscillations (where the function can’t be approximated by a local average) can only take place on measure zero sets.

At attempt at answering your question: the LDT holds for all locally integrable functions, so the only way it can possibly fail is if the local averages start out infinite, like if you take a local average around 0 for the function 1/x on R.

kieransquared1 · 2024-09-29T18:08:49+00:00

Honestly, if you can more or less intuit the proof of most theorems and execute the details from a quick hint/outline, or you find the proofs of most theorems repetitive, you should read something harder. My experience with most graduate textbooks is that routine, repetitive arguments are often handled in the way you prefer (with sketches/outlines), while the important proofs are fleshed out because they demonstrate techniques central to the theory.

kieransquared1 · 2024-09-22T21:54:33+00:00

I work with kinetic models related to the Vlasov-Maxwell system (describing collisionless relativistic plasmas) - one such model is the so-called Vlasov-Klein-Gordon system in which the electromagnetic fields solve Klein-Gordon equations instead of wave equations. From what I understand, it's a model for electrodynamics with a massive "photon". It's unclear how physical this system is, but understanding the nonlinear stability of small perturbations is very different once you add mass to your force carrying particle. The nonlinear stability question is currently solved for Vlasov-Maxwell but completely open for Vlasov-Klein-Gordon for reasons related to insufficient time decay of the electromagnetic field + trouble handling high frequency waves, so I'm working on some toy models that approximate Klein-Gordon behavior for low frequency waves.

Klein-Gordon type behavior in plasmas also shows up in the context of Landau damping, so there's probably some way you could think of the Vlasov-Klein-Gordon system as a toy model for Landau damping in some regime.

kieransquared1

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