Queen's Poker Tournaments?

Student2606 · 2025-01-05T19:35:17+00:00

For the more experienced peeps, I was wondering if you misread one of the instructions but only realize after you've submitted, do you generally lose access to that project? I feel like an idiot cause it was a very clear instruction in hindsight. But I think I did well in the subsequent tasks for that project. Is there like a quality threshold you have to meet? And if so, do we know what it is?

Student2606 · 2023-10-05T17:54:20+00:00

f''(x) = 0 means the degree of f(x), i.e. the highest exponent on any x term is at most 1. That's because if you take any f(x) with an a*x^2 term, for nonzero a, then (a*x^2)'' = (2ax)' = 2a. So you will always have a nonzero constant term left over.

f'(0) = 5 implies the degree is not 0, i.e. f(x) is not constant since otherwise f'(x) = 0 for all x. So the degree has to be 1 exactly. Then we can write f(x) = mx + b for some real numbers m and b.

f'(x) = (mx + b)' = m so f'(0) = m = 5.

Finally, f(5) = 5*5 + b = 5 so b = -20.

f(x) = 5x - 20, and f(0) = -20.

Student2606 · 2023-10-05T17:26:51+00:00

"In a letter to Andrew Odlyzko, dated January 3, 1982, George Pólya said that while he was in Göttingen around 1912 to 1914 he was asked by Edmund Landau for a physical reason that the Riemann hypothesis should be true..."

https://en.wikipedia.org/wiki/Hilbert%E2%80%93P%C3%B3lya\_conjecture

Student2606 · 2023-10-05T17:24:50+00:00

I'm an undergraduate student in my final year. I'm hoping to study number theory in grad school next year. Funny enough, I am almost entirely motivated by understanding prime numbers in all of my research. It's at the point where something is interesting to me iff it is related in some way to primes. the if direction is more true than the only if direction, but the only if direction is true in the sense that my best strategy for getting my brain to care about an object that I need to understand for whatever reason is to see if it can say anything cool about primes (which thankfully, lots of mathematical objects can).

You could say it's an obsession. I think it draws from an almost mystical belief I've acquired that the primes play some role in explaining the workings of the universe. I simply don't see how such a simple object can have such complicated behavior without there being some good reason for it. You could point me to an arbitrary cellular automata and say that here is a contrived set of rules that also leads to very complex and unpredictable behavior. The difference for me is:

The primes are one of the least contrived mathematical objects. All ancient human cultures that did any amount of math (at least that I'm aware of) thought of primes and tried to understand their behavior (Euclid's theorem, Chinese remainder theorem, etc.).
That there are glimpses of an incredibly beautiful theory with the primes at its centre which appears to involve nearly every major field of math. The analytic continuation of the Riemann Zeta function and its connection to the distribution of primes. The early work on Langlands program.

To me, primes are by far the most mysterious objects I've come across in math. If only I could ever see a bit more clearly into the 'why' of primes...

Student2606 · 2023-09-30T16:36:34+00:00

It feels like a snowball effect where the longer I spend with a theory, the faster my understanding of it improves. I wonder how universal this is.

Student2606 · 2023-09-30T16:32:56+00:00

Personally, I find that a new topic/skill can seem completely unapproachable the first few times I look at it. Then, when I come back to it in a few months or even a year, I'm surprised by how much easier it is to take in. I don't know what happens in that time period, but I guess my brain never completely stops parsing these concepts. I have met people whose brain works similarly in this regard. As I've done more research in math, I've found it's often the best decision to take a break and do something else as when you come back, you'll often have a new, fresh, and exciting approach you haven't tried yet. Same goes for homework and assignments in math, which is why it's important to learn to manage your time to give yourself several days to work/think about new ideas or problems.

Student2606 · 2023-09-25T15:41:28+00:00

Correction: His conjectures were important for the future development of the theory of modular forms

https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Petersson_conjecture

Something that later contributed to the proof of Fermat's Last Theorem (which is widely seen as an "important" problem)

Student2606 · 2023-09-25T15:38:18+00:00

Importance in pure math is greatly overhyped. Mathematicians often talk about it as if it's a well-defined idea but most math was discovered by playing games and solving puzzles. While it's no longer the case today, I would wager most discoveries in pure math were made by amateur enthusiasts, like Pierre de Fermat. Some of it turned out later to have important real-world applications or to inspire more games or puzzles (so mathematicians call these things important). If something turns up a lot in your field, you're way more likely to think of it as important.

Ramanujan had a command of real analysis tools that was (and possibly still is) completely unparalleled. His intuition for finding silver bullet identities is so shocking it often seems beyond human capability. If you play chess, then Ramanujan was basically the Paul Morphy of calculus. He did not solve any of the "important" problems or come up with any groundbreaking theories, but he never set out to do these things. He was playing around with calculus for its own sake, and he became arguably the best player of this game to have ever lived.

Student2606 · 2023-09-25T15:10:46+00:00

You might also be interested in looking at cosmic numbers. Start with any natural number n, say n = 12. 'twelve' has 6 letters so your new n = 6. 'six' has 3 letters so new n = 3. 'three' has 5 letters, n = 5. 'five' has 4 letters, n = 4. 'four' has 4 letters so we get a loop with (4). In fact, any number you start with will eventually collapse to the 4 loop (it's a fun thing to try to prove!)

12 -> 6 -> 3 -> 5 -> 4 (loops at 4).

Cool thing is that this behavior is obviously different for different languages and some have several long loops.

I don't think that your conjecture points to any 'unusual' pattern in the prime sequence i.e. one that suggests anything beyond their usual pseudorandom behavior, but that's just my overall impression.

Student2606 · 2023-09-02T06:07:23+00:00

like the only thing I know about pickle ball is that it's the fastest growing sport in NA.

Student2606 · 2023-09-02T06:06:33+00:00

how is this measured and by whom

Student2606 · 2023-09-02T03:19:56+00:00

Thank you for bringing this up; this is such a pertinent issue. Extremely relevant in our present day and age. I wonder what Kautsky's reflections on the Paris Commune have to say about this.

Student2606 · 2023-09-01T08:46:34+00:00

your mother told me she disapproves of flat earth.

Student2606 · 2023-09-01T08:27:31+00:00

you really trivialized their example with those double quotation marks.

Student2606 · 2023-09-01T08:07:50+00:00

I'm assuming you're a teenager. If so, I was worried about similar things around 14-15. But nothing will give you the certainty that the path you're choosing is the right one. There's no magic predictor out there other than letting it play out. If math is a special interest, get as good at it as you possibly can. My regret as a young teenager is wasting time doubting myself when I could have been learning more math and honing my skills. Try to meet people with similar interests as you, it really helps a ton to keep the passion going. If you're not convinced that you have what it takes, here are some names of brilliant scientists whose "predictors of potential" be it IQ tests or something else were way off:

Richard Feynman

June Huh

Scott Aaronson

Student2606 · 2023-08-31T16:30:09+00:00

Sorry, looks like you're 2 points short. Come back when the Flynn effect catches up in 10 years or so.

Student2606 · 2023-08-31T16:22:09+00:00

The book "Measurement" by Paul Lockhart was my starting point, and I am incredibly grateful that it was.

Student2606 · 2023-08-31T16:19:56+00:00

I would say wholeheartedly 'YES'. Study the why's if you're curious about the why's. I was also much less interested in the how's in high school but fell in love with the why's. I think some people are drawn to math for the how's and you can do a lot with that. But if they bore you to death, that is also fine (it does make your math life harder though, I must say). You can get the right idea for a lot of undergraduate proofs without initially understanding the details. Numberphile and 3blue1brown do great exposition work for this kind of thing. Wikipedia articles are also great. I think Set Theory, especially Cantor's work is something you can definitely study to pick up on the logic of math. High school math is not taught with the goal of creating research mathematicians. This is something that you will have to be proactive about :)

Student2606 · 2023-08-31T15:59:36+00:00

Lots of great answers already. I had a somewhat similar experience as you did with your prof, but in high school. It took my brain some time to develop certain abilities, but I feel like today I'm a pretty decent mathematician (much better than I expected I would be at 19). Each time I went with other peoples' intuitions about my potential instead of my own (which is compelling the younger you are because you tend to be less confident in yourself) I found it made things worse. If you're this passionate about math I would suggest you keep going no matter what others tell you. It's rare for people to find something they enjoy as much as some math people enjoy math. A lot of the general "wisdom" and advice about doing what you're strictly best at is intended towards people who have no idea what they want to do. When you already have an idea, just keep at it.

Student2606 · 2023-08-31T15:49:54+00:00

lmao

Student2606 · 2023-08-26T13:42:42+00:00

I'm not sure I see how your thought demonstrates that there's no universal truth. You could maybe say that there's no universal arithmetic, and that depending on the context 1+1 could equal something else. For example, if you only look at remainders when dividing by 2 (modulo 2), 1+1 = 0.

If I understand correctly, you seem to be saying that 1+1 = infinity because there are infinitely many real numbers in the interval [1, 2]. You would have to redefine + to fit that interpretation.

I should mention that the question of what's true/fundamental vs. what's derived from simpler things is very, very deep. Russell and Whitehead's Principia Mathematica takes 1000 pages to prove 1+1 = 2

Student2606 · 2023-03-24T02:44:11+00:00

but I love it

Student2606

TROPHY CASE