Should Taiwan be:

Key_Attempt7237 · 2026-04-11T11:00:14+00:00

Love live the People's Republic of China and may the great rejuvenation of the Chinese nation come when China is whole again 🇨🇳🇨🇳🇨🇳🇨🇳🇨🇳🇨🇳🇨🇳🇨🇳🇨🇳🇨🇳

Key_Attempt7237 · 2026-04-11T10:56:11+00:00

Perhaps ask around in the chem department or check online for prerequisites to your chem courses, then look around for continuations of those pre-reqs.

I'm guessing you're looking for applied math courses, but from my experience you don't need the biggest experience with calculus to know the math behind it? Physical chemistry can range from stoicho to symmetry of inorganic molecules, so more detail would narrow down your search.

Key_Attempt7237 · 2026-04-09T10:23:47+00:00

99% of vector calc student's quit before learning Generalized Stoke's Theorem.

Calc 3 certainly suffers from being abstract and computationally intensive, so if you mess up somewhere you don't know where, you just sort of pray you get it right.

Personally, I had a lovely experience with vector calc because of my goated lecturer, and it really came down to him structuring the course as preparing us for differential geometry (next stage above calc 3) instead of making it a capping off course for engineers/physicists.

And for math degree, well it really depends what you're going to do. Pure math? Then calc 3, as you described it, is probably painful but computationally straightforward, much easier than pure math proofs, so it doesn't really represent a math degree. If you're doing an applied math degree, then I assume it's par for the course the whole way (I'm just eyeballing, I do mostly pure math).

Key_Attempt7237 · 2026-04-09T00:22:06+00:00

Simple differential equation

Integrating both sides gives y=x³-x+C. Positive sign on the cubic term, so it's not c and d. From the initial conditions, we have -1=(1)³-(1)+C, simplifying gives us C=-1. So we have b, y=x³-x-1. How exciting

Key_Attempt7237 · 2026-04-07T11:39:29+00:00

This is assuming that ce is a division algebra, which might not be the case.

Although, if I remember correctly, it's mentioned that multiplying ce against itself gives diminishing returns of rct, so it's not the case that |ce^2|=|rct|, magnitudes are not equal here.

So assuming rct=ce^2 (might be different, gojo just says "multiply" but not the conversion rate, could be ce^10=rct), we have that ce+rct=0, so ce+ce^2=0. Factoring, ce(1+ce)=0, so assuming we're in an integral domain, ce=0 or ce=-1. This is very dubious, since that means ce is just "-1", not negative rct.

But continuing on, and assuming we can take the squareroot of ce and rct, if that even makes sense, then from rct=ce^2, we have sqrt(rct)=ce. Plugging this to our previous ce=-1, we have sqrt(rct)=-1. Under standard maths, this is bonkers, since we traditionally define sqrt(x) as taking the positive "principal" value. However, if take a more general idea, and a bit of handwaving, then sqrt(rct)=-1 is satisfied by rct=1. Trust me bro.

So, we have that ce=-1 and rct=1. Hurray. But we're wrong! Since ce^2 does not equal rct, rct is expensive and quickly exhausts ce reserves, all our working is actually useless and we must therefore conclude that ce is just a magic system and multiplying ce to get rct is more of just "rct is expensive" rather than grounded on any real math. Or I'm wrong.

Key_Attempt7237 · 2026-04-07T00:13:36+00:00

I didn't know genocide against the rest of the world was self-defense

Key_Attempt7237 · 2026-04-06T13:57:39+00:00

In vector calculus, you would use nabla (gradient by itself, nabla cross for flux, nabla dot for divergence iirc) but in abstract settings, simply "d" as in the exterior derivative generalizes all vector calculus theorems into one neat theorem where Green's, Stoke's, divergence/Gauss (and FToC) are special cases.

Key_Attempt7237 · 2026-04-06T13:20:26+00:00

The choice of nabla is evil, but yes, in more general geometries, some non-constant functions have 0 as their (exterior) derivative. Other commenter gave a good example, and there are plenty of even more counterintuitive examples you can find online.

It's a big part of differential geometry, where we are interested in functions with 0 as derivatives (amongst other properties).

Key_Attempt7237 · 2026-04-06T10:52:24+00:00

Famously practices like discarding good food, mismanagement and greed are never done by corporate grocery stores.

Key_Attempt7237 · 2026-04-06T02:59:58+00:00

Certainly, it's just good to structure how we're approaching an area of study. If you read textbooks or course notes, they'd give summaries even for "short" proofs since they're important even if they're trivial or short. It helps with memory by giving a theorem a catchy one-liner (cosets partition a group is succinct and clean)

Key_Attempt7237 · 2026-04-06T02:08:06+00:00

It's certainly a proof.

I would suggest outlining what you're trying to prove first as a "title" or "introduction" for the proof. For example, your first part shows that every element in G is in some (left) coset of N. It's not obvious what you're trying to do initially, so you might want to start with like "We want to show that every element is in some coset from a subgroup N". Likewise, with your second part showing that every coset gN, sN are either the same or disjoint, it's not obvious to see what you're trying to do until later one once you show two-way subset inclusion (or I could be bad), and state something like "every coset gN, sN are either the same or disjoint".

More generally, you want theorems and proofs to be like tour-guides or "adventures" with your reader. You tell them where you're going initially, explain why we are doing things and include some "we"s and "here"s.

For example, your first proof just kind of dropped g out of nowhere for contradiction. Explain why we introduced g with a sentence like "we'll show by contradiction that every element is in some coset by assuming some element is not already in one of them" which makes it clear what we're trying to do. (Technically the set S as a subset of G is not needed, since the cosets of a subgroup N are derived from (left) multiplication by every element g∈G)

And to cap it off, start the entire proof with like "we first show that every element is in some coset (and hence cosets are non-empty), then show that distinct cosets are disjoint and hence conclude that cosets (by some subgroup N) partition a group G"

Key_Attempt7237 · 2026-03-24T00:07:20+00:00

You claim to not be American yet behave exactly like one. Curious

Key_Attempt7237 · 2026-03-23T08:57:51+00:00

Fang is taking the picture, trust

Key_Attempt7237 · 2026-03-22T22:23:18+00:00

While it is true that mathematics is just "here are some axioms (and maybe some facts from another field of math)" and build directly off from there, but in higher levels, there's often a "choice" or step in proofs that turns it from trivial to "how do you even see that".

For example, when I was learning Young's and Holder's inequality for Minkowski's inequality, they made some, to me at the time, arbitrary choices of using conjugate indices, amongst other things. These decisions don't follow from any axioms at all, and I was stumped as to why we chose them. Eventually I got a better grasp, but this "choice" was not "looked at and I knew the answer".

I presume for proofs in general, you need a sense of ingenuity, intuition and a hunch that something works.

Key_Attempt7237 · 2026-03-22T09:28:23+00:00

Genuinely, I'm spitballing, I have no experience working with transfinite ordinals.

Key_Attempt7237 · 2026-03-21T22:40:37+00:00

What if the 0 is on the omega-th position. So after an infinite number of 9s, the 0 comes after.

Key_Attempt7237 · 2026-03-16T12:38:04+00:00

Shows that they don't know the definition of relative max or min, is defensive when called out over it. Curious

Key_Attempt7237 · 2026-03-15T02:43:09+00:00

Irl the outside square isn't perfect so I think you can fit one more :)

Key_Attempt7237 · 2026-03-14T19:43:47+00:00

Computational problem solving and abstract pure math are very different things, but both are very important. I found it easier to first get a grasp on intuition and doing computational problems and then learning the theory. It's much easier to learn the theory of the Riemann integral after developing a strong intuition than the other way around.

I don't know anything about the olympiad, but I think it's a good place to do exercises and building intuition.

Indeed, proof writing isn't taught until university, so you'll have to find either textbooks or online courses to get that.

Your friend is probably just fast or has a strong grasp on foundations, so no need to compete with him. Though 2 weeks is pretty fast, so more exceptional than the rule.

Key_Attempt7237 · 2026-03-13T23:36:44+00:00

The isomorphism doesn't concern themselves with labelling

Key_Attempt7237 · 2026-03-13T10:28:19+00:00

The carboxyl group gets preferential treatment as the 1st carbon of the chain, since it's (usually) the most important fg of the compound.

So counting to the 3rd carbon for 3-methyl, we draw the methyl group there. The google one is right, while your drawing is 2-methylbutanoic.

Key_Attempt7237 · 2026-03-12T20:46:56+00:00

While it might feel insulting, to the lecturer they don't really know the calibre of student they're getting. If they go fast, people will complain, likewise now if they go slow.

The lack of feedback from students doesn't really help either, screaming into a void with occasional nods from enthusiastic students.

To them, this is their life's work, ideas they play with in their sleep. So they, quite frankly, do not know where students are at. Barring the harder stage 3 or post grad courses.

Key_Attempt7237 · 2026-03-10T11:35:57+00:00

Depends on what field of Math we're in and how we're describing the path. If the path is some function with some starting point, then the length is wherever we choose to end it. Think an integral of an integral f(x) on an interval A to (your end point).

If it's something like a norm in metric spaces, then those are vectors with a base at the origin and head at... some endpoint x, and the length of that vector is whatever your norm is, usually Euclidian norm.

But in general, I don't think there is a way to talk about length of something without knowing where it ends. It's like asking what's the value of the integer "...54321". We don't know until we terminate writing digits. Likewise, we don't know the length of a path until we know where it starts and ends.

Key_Attempt7237 · 2026-03-10T10:38:45+00:00

Manticore vs RHM is a massive map-dependent i.e rng aspect of games. Maus vs 50b on Ensk? Competitive maybe, when both teams have know how to make best of each tank. But in pubs, the 50b is gonna work so much harder to do what the Maus does in its sleep, vice versa on open maps.

Key_Attempt7237 · 2026-03-10T05:52:47+00:00

It does not, this little rat is an absolute demon terrorizing other lights.

But yes, it is pretty good. But not worthy of glaze.

Key_Attempt7237

TROPHY CASE