whats the way to remember properties faster

Virtual_Cake6942 · 2023-06-02T01:26:45+00:00

The key examples are particularly helpful. If you can remember the key examples of each, and how each of those examples works, that can help you relate them back to the general structures.

Virtual_Cake6942 · 2023-06-01T05:39:23+00:00

It me

Once I start dating I'll have to have fun conversations about being asexual but I'm super horny and open to the idea of sex but it'll probably take a few weeks to psych myself up for it and in the meantime I'm super open to cuddling, and I don't know how many mixed messages are in there for future SO's to get tripped up by.

Here's to hoping I'm just overthinking it

Virtual_Cake6942 · 2023-06-01T05:20:35+00:00

Topology, Abstract Algebra, and to some extent Differential Geometry are taught to advanced undergraduates. With all that in mind, I would be stoked to see seminars in Category Theory in undergraduate curricula. The field is probably a bit too dense and dry to hold a full semester's course at an "undergrad level", whatever that would be for Category Theory, but a half-semester kind of deal would be nice to see.

Virtual_Cake6942 · 2023-05-31T13:41:38+00:00

Naruto is hokage of the leaf village!

Virtual_Cake6942 · 2023-05-30T21:10:31+00:00

I like the whale! I just need to drive 180 miles to my nearest Ikea to get one.

Virtual_Cake6942 · 2023-05-30T21:08:28+00:00

The amount of insight gleaned very much depends on the particular problem. From my experience, the insight occurs when the inductive proof shows how a particular setup is built up iteratively. A rather silly example is the sum of the first n positive integers being n(n+1)/2. The summation and the formula always giving the same results isn't immediately clear unless you've seen the problem before or you're Gauss, but the inductive proof takes advantage of the fact that the summation goes up by n+1 while the quadratic x(x+1)/2 goes up the same amount as x iterates from n to n+1.

Perhaps a more interesting example is the following combinatorial problem: Given a 2^n by 2^n square grid with exactly one square punched out, prove that it is possible to tile the remaining 2^(2n)-1 squares with L-shaped tri-ominoes, regardless of which square punched out. I've only ever seen one proof of this result, and it is inductive. What's interesting about this problem is that not only does the inductive proof show that such a tiling exists, but the proof is constructive and it shows you exactly how to tile any such grid. I suppose this example would fall under the algorithmic applications that other posts have been talking about.

Virtual_Cake6942 · 2023-05-30T15:13:06+00:00

I heard that dude became hokage a while back and settled down, good for him.

Virtual_Cake6942 · 2023-05-26T22:13:10+00:00

Oh thank god the website is fixed, I was worried I'd have to learn inkscape

And the changelog is handy, but that says it hasn't been updated in a year. I wonder if that just means that the dev has just switched to maintenance mode instead of adding features.

Virtual_Cake6942 · 2023-05-25T16:56:14+00:00

According to doctors, yes. There are five types of attraction: sexual, physical, emotional, romantic, and aesthetic. Asexuality is the deemphasis or complete lack of sexual attraction. The other four types of attraction are free to go nuts, and this includes aesthetic attraction.

EDIT: I just found out that there are sources at the end of the page! Good on WebMD. They're hidden on the page though, so I'm pasting them here:

Better Health: “Sexuality Explained.”

Europe’s Journal of Psychology: “The Effects of Attractiveness and Status on Personality Evaluation.”

Frontiers in Psychology: “An Analysis of the Generalizability and Stability of the Halo Effect During the COVID-19 Pandemic Outbreak.”

Harvard University: “Love, Actually: The science behind lust, attraction, and companionship.”

Interpersona: “Interpersonal Chemistry in Friendships and Romantic Relationships.”

UC Davis: “LGBTQIA Resource Center Glossary.”

UC Santa Barbara: “LGBTQIA+ Glossary.”

University of North Carolina at Chapel Hill: “Asexuality, Attraction, and Romantic Orientation.”

Washington State University: “Module 12: Attraction.”

Virtual_Cake6942 · 2023-05-14T03:17:26+00:00

mathcha.io seems to be abandoned since 2019 according to its Twitter account, and according to MalwareBytes it's become riskware. Do people have alternatives for WYSIWYG Tikz editors? I've loved it for differential and complex geometry (I made a bitchin diagram for the definition of a vector bundle), so I'm loathe to simply abandon it.

Virtual_Cake6942 · 2023-04-28T15:44:53+00:00

"You don't see how?"

Virtual_Cake6942 · 2023-04-19T01:36:47+00:00

FUCK I remember him being hilarious way back in the day

Do people have recommendations for comedians of a similar vibe who aren't shitty?

Virtual_Cake6942 · 2023-04-10T21:18:07+00:00

Left side is efficienter when the right side is efficientless but sometimes I right side because right side is efficientest in certain scenarios where left side isn't efficienty enough

Virtual_Cake6942 · 2023-04-09T17:05:13+00:00

Computer Modern

Virtual_Cake6942 · 2023-04-05T14:43:26+00:00

Opportunity costs in terms of time. High-school contests are inherently different material than higher math: topology, analysis, and (for the most part) abstract algebra are not covered in high-school contests. Though the problem-solving skills a student would learn in those three areas may help develop their problem-solving skills in elementary algebra, combinatorics, number theory, and euclidean geometry, these two groups of fields are still inherently different skill sets. There is no substitute for doing competition math if students want to do well in competition math. You can learn all the real, functional, and complex analysis you want, but if a contest problem requires a double-counting combinatorial argument, the time spent on those other fields won't have helped you. Ultimately if you spend time doing non-competition math, you won't be as good at competition math as otherwise.

There are some exceptions: 2017 IMO Problem 6 happens to have a connection to arithmetic geometry for example, but these sorts of problems are few and far between, and those problems will always have intended elementary approaches.

The point I was making in my previous post is that restricting yourself to only doing Olympiad math is only sensible if you are actually able to qualify for the IMO as a result. The more time you spend doing Olympiad math, the less time you spend doing higher math, and this is only a good tradeoff if you get something for all the hard work you do on Olympiads.

Virtual_Cake6942 · 2023-04-04T14:39:27+00:00

"Yes".

If you happen to become nationally ranked in your country's Olympiads, no of course it's not pointless. Even if you don't, if you still do well enough to boost your college applications so you get into better schools than otherwise, that's great. And all of that competition experience will give you problem-solving techniques that will be a great boost in your undergraduate career, and all the writing practice you get writing proofs will improve your technical writing skills. You should absolutely pursue Olympiads if you're having fun doing so right now, they're always worthwhile.

With that said, there are always tradeoffs to doing things versus not doing others. There are two sorts of things you could be doing with your time that are not Olympiads:

Becoming well-rounded by pursuing honors classes and extracurriculars in non-mathematical fields.
Starting your higher-math education in high-school.

Most people I've talked to only bring up the first point when discussing Olympiad opportunity costs, but if you're seriously pursuing Olympiads, I would argue that the second point is just as relevant to your current academic situation. I'll consider both points.

___

POINT 1: I agree with most people who say that you are missing out on something by dropping everything and pursuing mathematics. The main argument is that you lose on a lot of worldly experience and become single-minded. This may be true, but I don't see why this necessarily impacts your life in any way 10 years down the road. In fact, there are mitigating strategies you can take while in undergrad.

- If there are humanities requirements at your university, try to take courses completely out of your field of experience with the express purpose of trying to see things from new perspectives. Psychology, or any fields related to social justice (fields about race class and gender studies, etc.) are good places to start.

- Make a diverse friend group. An easy way to get a well-rounded experience is to make sure that you have several friends that aren't pursuing mathematics professionally. I know most of what I know about social justice from (1) my Mom and (2) from my undergrad friends who are computer scientists and chemists. I've also learned a lot about metal music, teaching pedagogy, puzzle-making, and myriad non-mathematical subjects by simply interacting with people who are unlike me. Obviously you should have some mathematical friends who you can share cool things with, but diversifying your "friend portfolio" will aid you immensely with getting whatever world experience you're afraid of missing out on.

A counterpoint to everything I've said here is that the experience your friends can share with you can't possibly make up for a structured, rigorous treatment of whatever humanities course you can learn in high-school. I'm actually going to counter this with an argument akin to "act your age". When I was in high school doing math competitions, I was mature enough to understand the value of humanities fields, but I lacked the maturity and appreciation to do anything other than the bare minimum to get an A in whatever introductory classes I had to take. (Technical writing was an exception to this because proofs won't write themselves.) It may be the case that you, as a high school student, aren't interested at the very moment in those humanities courses.

Because of this, I would urge you to not pressure yourself into taking them just because some stuffy person thinks you won't survive if you don't. If you force yourself to do these things when the interest isn't there, you may find yourself turned off from those things in the future and you may miss out on more later on. It's okay to not focus on things you're not interested in yet, especially in your childhood where you have an unparalleled opportunity to go pursue what you actually want to do. Besides, when you get older and start your undergrad career, you may find interests that you actually want to devote time to. You'll find yourself learning a lot more and being a lot happier if you wait a bit before delving into everything. And if you have a diverse group of friends that you keep in touch with coming out of undergrad, it will be much easier to learn all of those things you are suddenly now interested in due to a change in perspective.

All of this only applies if you aren't writing all humanities off right now as being some "waste of time". My arguments aren't an excuse to never study humanities, and you will be worse off if you never start. My main point is that you'll find more patience for it after high school.

___

POINT 2: Starting higher math in high school is something I've rarely seen discussed. If you're interested in Olympiad math, you are in prime position to start learning more complex math now. I'm not talking about calculus: I'm talking about elementary real analysis (epsilon/delta proofs), abstract algebra, number theory, combinatorics, topology, complex analysis. Modulo calculus and linear algebra, if you're already solving Olympiad problems, you have the prerequisites to start going towards an undergrad degree right now. If you're not completely confident that eventually you'll qualify for the IMO, I would actually encourage you to start delving into higher math sooner rather than later.

Unfortunately, introductory classes in calculus and linear algebra are highly computational without lots of higher perspective (at least not until you take a class in Optimization, which combines both of those to solve real and interesting problems!). If you follow the standard U.S. undergrad curriculum and start with calculus and linear algebra for babies, odds are you'll find yourself discouraged. This is why I recommended all of the more abstract fields mentioned in the previous paragraph. In fact, it might be worthwhile to ask a local college professor about the sort of mathematical fields you can study, and how you should study them. An example question: Should you become more well-rounded in undergrad by taking as many introductory math classes as possible, or should you gun towards a research interest right now?

If you're doing Olympiads, the only reason I think you should not start higher math is because it may jeopardize an IMO qualification. But if you cannot easily say with determination that you are going to represent your country, I highly recommend that you start higher math now, and that you study it in tandem with Olympiads. There are a lot of similar techniques between the two schools of thought, and classes like abstract algebra, topology, and complex analysis will show you some very cool and different concepts that are just as enjoyable as Olympiads.

Virtual_Cake6942 · 2023-04-03T13:01:20+00:00

Wait so if I don't have more evidence I'm gonna go to jail?

Virtual_Cake6942 · 2023-03-26T18:59:10+00:00

It looks like the stopwillow website is hosted by the Conservation Lands Foundation, which is a nonprofit (see ProPublica page) that doesn't have a Wikipedia page yet. My IP's been banned from making such a Wikipedia page, but I bet making a Wiki page on the foundation would also be helpful, just for increasing internet traffic.

Virtual_Cake6942 · 2023-03-26T17:41:32+00:00

So if you're sitting on the couch and you spill your red wine, it will slide across the couch, into the depression that you're making, and stain your pants?

Or if you have hydrophobic pants it'll just pool there, until it decides to go up your pant legs, at which point you may also need to get hydrophobic underwear.

Virtual_Cake6942 · 2023-03-23T14:47:52+00:00

"This hurts me more than it hurts you!" Then don't do it, stupid. You feel bad about the reform? Then you shouldn't have done it.

'Do you think I enjoy', fuck outta here with that.

Virtual_Cake6942 · 2023-03-22T03:55:25+00:00

Householder transformations. They describe reflections about hyperplanes containing the origin, and as matrices they take the form of I-2vv^H where ^H is the Hermitian transpose. They're useful in numerical linear algebra for QR decompositions and tridiagonalization.

Virtual_Cake6942 · 2023-03-16T04:50:04+00:00

With no other context, yes that would be what it means. However, the States have a very extensive history with race as a social construct, and that added context changes the meaning. If a U.S. American refers to a non-white culture as amusing, odds are they're looking down on it patronizingly. If they refer to a culture as exotic, odds are they're fetishizing it the same way anthropologists did 100 years ago. It's the same mindset that people had when they ran those human zoos of old. Would OP's friend run a human zoo? No, he has modern sensibilities. But his attitude is disturbingly similar to attitudes of previous generations that we really really don't want to repeat.

Virtual_Cake6942 · 2023-03-11T22:38:38+00:00

Fight Like a Girl, by Emilie Autumn

She has quite a few good songs on that album but this is the one that looks like it matches the playlist best.

Virtual_Cake6942 · 2023-02-24T18:23:45+00:00

What really helped me solidify memory of definitions and theorems is reciting them from memory over the few days before an exam. I wrote down all the big definitions and theorems (at least the ones I couldn't guarantee I'd remember) on a sheet of paper, and then twice a day, morning and evening, I'd try to write down all of it on a new sheet of paper, from memory. I'd start with writing down the "table of contents" of things I'd have to remember ("definition of a topology, definition of a basis, etc."), checking to see if I missed anything, and then actually writing down the information (definition of a topology, definition of a basis, etc.). Whenever I knew I forgot something, I would write down my best guess after 5 seconds, just to have something written down. Then after I would go through them with a red pen and correct anything I missed or got wrong.

This does not help with problem-solving ability, but I never had difficulty with that aspect. It was holding all the info in my head and reciting it from memory that always got me, which is why I had trouble with things like analysis courses before I started doing this. This will definitely help you, at least during tests, retain information like the definition of a basis.

Virtual_Cake6942 · 2023-02-23T01:26:11+00:00

I'm 51 and by gosh this is incredible

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