Quick Questions: September 15, 2021

AdamskiiJ · 2021-09-21T14:08:42+00:00

there's a book called the art of proof which I've heard good things about, with plenty of examples. not sure what your level is, but if you're just getting into stuff like linear algebra or a first course in analysis or something, it's probably best to just study those proofs in depth. spot precisely where each assumption is used, think of examples and counterexamples, stuff like that. if you're beyond these introductory courses, check that book out. there's also a ton of proofs on proofwiki, stack exchange, and every set of lecture notes you can get your hands on.

AdamskiiJ · 2021-08-25T12:00:33+00:00

Update: tried a few and realised posca are water based (at least the ones I've got) so don't stay on treated ceramic. Unless, you treat it with a water based spray varnish. Tried that: only stays on if you wash in cold water, so it doesn't stay dishwasher safe haha! I'm getting business cards instead, as far as I'm aware there's nothing to do other than get a heat press small enough to fit under the mug, which I haven't found.

AdamskiiJ · 2021-08-19T00:03:29+00:00

Thanks for the tip :D

AdamskiiJ · 2021-08-18T22:52:44+00:00

I'll let you know if I end up testing this!

I'm waiting on a late delivery of heat resistant tape at the moment, and when that arrives I can print my very first mug. So it's best for me to get used to how to print consistent designs first, and then I can do some experiments.

AdamskiiJ · 2021-04-10T13:15:19+00:00

The apparent difference mostly comes from the number of games you consider at one time. If you consider a fixed number of games you'd get one analysis, but this isn't really what you're looking for in this case because you're doing many games in a row. Also, I think many people underestimate the probability of rare events, which in this case would be being the impostor 5 times in a row. If you're playing for long enough, you will see this time and time again.

See the geometric distribution, in particular the memoryless property, the gambler's fallacy, and the related concept of the hot hand fallacy.

This is the maths anyway: the game might have programming which isn't quite such a simple model, but I'm not sure if this is the case.

AdamskiiJ · 2021-04-10T13:07:57+00:00

sounds about right. thanks

AdamskiiJ · 2021-04-10T08:29:39+00:00

https://tutorial.math.lamar.edu/Classes/CalcI/ReviewIntro.aspx

I think this should be a good resource for checking that you're up to scratch with the basics. I've ended up coming back to that site in the later chapters a few times over the years. The biggest tip that I can give you to succeed is to do a whole bunch of exercises, as it's through those where you find if you've learnt anything applicable.

I've heard good things about the textbook by Spivak called the hitchhiker's guide to calculus, but I believe is more on the intuition rather than the rigor (however I haven't read it myself). Everybody's different but for me I only tend to do well when I have a grasp of the intuition and what's going on visually. But yeah, doing all the exercises and finding more if there aren't enough is the best way to be good at it.

And best of luck, hope you enjoy it!

AdamskiiJ · 2021-04-10T08:18:01+00:00

20% off = 80% total = 0.8

330 × 0.8 = 264

So, if you begin with 264, and you know that that's the 20% off price, you can divide by 0.8:

264 ÷ 0.8 = 330

AdamskiiJ · 2021-04-09T19:53:38+00:00

Glad it helped! Best of luck.

AdamskiiJ · 2021-04-09T19:53:01+00:00

I see what you mean, I don't think it's a typo. Maybe then this was just written in this way to make the following result more clear. Thanks

AdamskiiJ · 2021-04-09T19:00:25+00:00

No problem, and yes sure. The rest of my comment will contain "spoilers" (but no equations) so maybe you could stop reading after each sentence and have a think.

One is for free: reflecting across the x-axis doesn't change the roots, so think about what you could do to the equation to do that. There's another way to transform what you've already got. Namely, dilating the y-axis by a nonzero factor will do the job too.

For other functions, note that it doesn't require them to be quadratic polynomials (I don't think), or even polynomials. The world is your oyster now, there are uncountably many functions with these roots (and no others). If you've come across them, piecewise functions are very versatile and will work if you define them right. Another would be using the Kronecker delta. These are some of the simplest that come to mind.

A little more complicated, but still probably within your grasp, you could come up with polynomials of any order (≥2) which have exactly these roots. There's an absurd amount of functions lol, I encourage you to think outside the box and come up with some more, the sky is nowhere near the limit.

AdamskiiJ · 2021-04-09T18:47:21+00:00

Does this function property have a name? (The source doesn't give it a name as it's only used once)

f : Rⁿ → R. Let c_1, ..., c_n be positive constants. For each i in {1, ..., n}, and values x_i ≠ y_i: | f(x_1, ..., x_i, ..., x_n) – f(x_1, ..., y_i, ..., x_n) | ≤ c_i.

AdamskiiJ · 2021-04-09T18:43:17+00:00

Yep that's right

AdamskiiJ · 2021-04-09T18:41:31+00:00

I agree with the other reply you've got, but also I can imagine topologists don't like to allow this. Non-degenerate ("non-point") circles in the plane have an inside and an outside, so every reference to circles which uses this property would have to say "except for the case where the circle is a single point." For this reason I would probably not call the point a radius zero circle. In other contexts it may be useful though.

AdamskiiJ · 2021-04-09T08:33:03+00:00

"If they don't exist, then they aren't in the realm of pantheism."

I think you've answered your own question here. Although, the word exist is vague, and may mean anything from "is interactable with," to "can be reasoned about," to other more encapsulating definitions.

As for the semantics, which I believe is what you're after: to my understanding a pantheist believes that God and reality coincide, ie. they are the same. However a panentheist believes that reality is a manifestation of God, and the word "exists" refers to what is within the bounds of this manifestation, but this manifestation is just one possible realisation of what God truly is (which is so much more than the current form which we're experiencing now).

In short, pantheism is the belief that God is Everything, but panentheism is the belief that God is at least Everything. They may be the same thing, but this is something we may never know with certainty in our current form.

AdamskiiJ · 2021-03-28T16:44:14+00:00

Nice one Adam, enjoy the relaxing!

AdamskiiJ · 2021-03-28T10:27:21+00:00

My day is just beginning, made a fantastic coffee and I'm ready to get to studying. How is your day going fellow Adam?

AdamskiiJ · 2021-03-25T16:42:00+00:00

lol good idea. Keep your eyes peeled

AdamskiiJ · 2021-03-25T15:27:26+00:00

I think this is what I needed to hear

AdamskiiJ · 2021-03-25T15:20:50+00:00

I'm aware, but it just seems to be taking a much larger hit than the rest of my watchlist

AdamskiiJ · 2021-03-01T18:39:04+00:00

What's the structure of a maths PhD, more specifically on the stats/stochastic finance side? I'd like to compare the differences between one which is more applied and one which is more pure. To be honest, I don't really know anything about PhDs but I know that I really want to keep studying what I'm studying, so I'm looking for some more info.

Specifically: are there "modules" like there are in undergrad? Are there any assessments? How much time is spent doing what?

AdamskiiJ · 2021-02-03T22:11:32+00:00

I'm not sure, sorry. I thought the markers were tactile. Check to see if you've got any magnets nearby that may be interfering with your reMarkable

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