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I haven't heard one media outlet claiming e.g. Dylann Roof was influenced by video games, and I think they would have a stronger case nowadays with games like Hatred on the market.

I do.

I'm pushing 30, have a well-paying job, and a long-term significant other, but I never plan on "becoming an adult" if it means religious affiliation, griping about the talking heads like my father, or giving up video games and hangovers.

I totally agree. IMO it doesn't even have to be a CS course; my experience TAing calculus helped immensely with whiteboard interviews.

I think it's the process of pacing yourself through the problem. If I see some fancy integral, I might be able to solve it in one or two lines. But if I want the students to understand, I'm not allowed to skip steps so it'll take more like 15 lines, and I'll have to verbally explain each line as I write it. It's getting used to switching back and forth between dictation and logical process.

Usually with caps like this the break is phased out. So if you make between e.g. $20k and $25k, maybe only x% of your rent is paid for, where x is between 0 and 20.

Unfortunately, she was not American.

The purpose of the SAT is to be a unbiased barometer; say what you will about it, but everyone takes the same test. Unfortunately, a 4.0 GPA from an obscure high school may tell you very little about a candidate.

I don't know how much admissions officers care about 96th versus 99th percentile, but if someone has an otherwise amazing resume yet ranks in the 40th percentile on their SAT, that's a bit of a red flag.

From Rounders: "Why do you think the same five guys make it to the final table of the World Series of Poker EVERY YEAR? What, are they the luckiest guys in Las Vegas?"

The bar is lower or higher for MS/Amazon?

Yes.

Not a normally distributed example, but:

(1,1), (0,0), (1,-1)

X and Y are uncorrelated but not independent.

FWIW I regularly got destroyed by the homeschooled kids in math competitions in high school. That said, they were a weird bunch.

To bolster your point, I averaged about $25k/year at UCLA math in the 2010's, and I had a car by the time I graduated (granted I tutored to Beverly Hills high school students on the side).

I would even say there's a substantial difference between a typical grad student from a top-10-and-not-top-5 university and a typical grad student from Harvard; this is not at all meant to disparage the former schools, but basically every student I met from Harvard REALLY knew their stuff.

By the way, to those saying the system is not a meritocracy, I got into UCLA coming from an undergraduate institution that's not even top-100 because I was bright and I worked my tail off. Would it have been easier if my parents were buddies with the president of Harvard? Sure, but life's not fair.

Because grad schools produce more (graduating students) than they consume (hiring faculty).

I was just thinking today about how cool a modern open world version of SimAnt would be. Oh well.

Edit: Someone posted a link to this but then it got deleted: http://www.formicarium.org/

This kind of thing happens in math a lot. Any time you use the axiom of choice to prove something exists, it's non-constructive. It exists, but you can't get your hands on it.

I wrote a comment down below about how one could in principle determine a number which is probably BB(n), but you could never be sure. But I just had the crazy thought that if a human brain is really just an N-state Turing machine for some giant N, then any human would either wait forever or give up before finding the true BB(n) for some n. Time for bed!

I think it is possible, in principle, to find a number which you can be pretty sure is BB(n). The problem I think is being sure that this number really is BB(n).

Like you run all n-state Turing Machines for a super long time, and take the max of the output of all the ones that have halted. Now this might give you BB(n), but you can't be sure because you don't know whether the ones that haven't halted are ever going to halt.

In mathematics, we can just say "Well consider the set of all the ones that do halt, and take their max." In real life, it's not so easy to "consider the set".

Maybe in applied math. In pure math that question would immediately reveal you as an outsider.

I probably should've thrown in combinatorics, which certainly existed before calculus or linear algebra, and certainly plays a role in applied math.

I would say graph theory is part of combinatorics, and set theory is part of logic.

Category theory was born out of trying to abstract the relationships between different objects in abstract algebra, so is kind of the child of abstract algebra and logic. I think it's fair to say the parents of abstract algebra are combinatorics and linear algebra.

Number theory at an elementary level is combinatorics, but at higher levels branches into analytic number theory (Calculus) and algebraic number theory ((Linear) Algebra).

Re: 4). As a pure mathematician, I would argue Calculus and Linear Algebra are the father and mother of pure math as well (okay maybe not logic).

Pretty sure if a taxi driver was accused of rape in India, no one would bat an eye.

dual tap is kind of like clicking twice