PROMYS 2024 Review (incomplete but I'm too lazy to write the rest)

It is Thursday, July 25, and Week 4 of PROMYS 2024 is almost over. I've wanted to write this for a while, but I finally have time to do it today because my counselor is behind in grading, so that makes me feel a little better about taking breaks.

My Counselor:
My counselor, P, is a rising sophomore at Yale. Lots of the counselors are very close in age to the students, which makes them easy to talk to. P is very introverted and quiet, and most of our conversations are quite short. I've only had one meeting with him to go over the problems that lasted one entire hour. Maybe I should request meetings, but all my friends' counselors ask them to meet up first. Some of them even grab lunch together. I would love to have a counselor like that, because I want to discuss math. P got Covid the second week, so I saw even less of him. I usually communicate with him through Discord dms by bombarding him with questions. Half the time he replies with "that's a really good question! You should think about it more!" I think he's a good grader, though. He's definitely very smart. Somehow, another student in my group found his old Aops blog, and apparently he missed AMO by 1.5 points and made it the year after. I used to be scared of P because he seemed cold, but I think he's just very shy. The epitome of a math nerd. He said I did very well on the midterm writeup, so I think I'm in his good graces. Unfortunately I feel like lots of times I'm driven to do things to not disappoint people. That's why I'm always stressed because I don't want to disappoint P.

Sleeping:
My sleep schedule at PROMYS has gotten slowly worse and worse. I used to sleep at 1 am and recently I've slept at 3 am for two days in a row. It's a vicious cycle because if I sleep late, then I usually have to take naps during the day, which means that I get less work done, so I sleep late again. Last week there were 10 billion minicourses and because I have FOMO I went to almost all of them. I think I was also taking Graph Theory at the time. From Monday to Wednesday I was lowkey burnt out, but I think it's best to just take it slow and do the best you can. Tomorrow is Friday, aka the best day because there is no stress to finish the Pset. Today I'll try to pull through and not take any naps, so I can finish my Pset satisfactorily and sleep before 2 am. My body has adjusted to sleeping at 2am. I'm not sure if I've gotten used to it because I'm at PROMYS or that I've gotten used to it in general.

Social Life:
Somehow, there are already 5 couples at PROMYS. That is 15% of the population. I used to like this rising senior delusionally because we barely have had any conversations. I've had like 50x more conversations with his roommate, who's a giant teddy bear to say the least. I'm also friends with someone who goes to the same school as him, because she is roommates with my friend A. She is much cooler than him, in my personal opinion. I don't think that dating during this time is very productive because in 3 weeks you're never going to see each other again. Also, the math is lowkey much cooler.

The math:
You can probably find this on the PROMYS website, but all first-years have to take the NT lecture and do the Psets. There are a lot of different threads in the Psets. I won't get into too much detail in case some random person stumbles across this blog because they don't want too much to be out there in the Internet. But we've been focusing on:

• Z, the set of integers. Chain of reasoning: division algorithm, Bezout's, Fundamental Theorem of Arithmetic, Euclid's Lemma, Unique Prime Factorization. Most podasips in the first 3 weeks are from Z.
• Gaussian integers (Z[i]) and its properties (how do you effectively prove that some element is prime in Z[i]??)
• Order of an element
• Primitive roots/generators, logarithm tables and indices
• Units
• Quadratic residues, Legendre's, solving quadratic equations in mod m
• Continued fractions, Magic Box, Pell's equation
• Farey sequences (these are really cool, but my brain is a little too dumb to understand it)
• Arithmetic functions like phi, Mobius Inversion
• Diophantine equations
• Fields. Polynomials with integer coefficients in F[x]
• Miscellaneous like the Beatty sequence

I saw that my friend from Cali posted Fenway park on his Instagram story, which is crazy because I live 3 minutes away from there. So then I texted him to meet up and we had lunch together. My friends kept bugging me that he was my boyfriend and I told them that I set very clear boundaries with all my guy best friends.

Week 5:
It is Saturday, August 3, so week 5 of PROMYS is over. Yesterday we had a "scavenger hunt" when in reality it was a problem set of absurd questions that we needed to take videos of to answer. It was pretty fun, although I would have preferred to use the time to take a nap.
My exploration lab (or expo lab) presented on Friday, after a week of grinding. Not gonna lie, I kind of figured out what I was going to say on the day before presenting. I used a hint that a second-year gave me regarding diagonalization of fractional linear functions and it solved our main conjecture on cycle lengths. Somehow, our proofs involved linear algebra and Galois Theory. Luckily, four out of five people in my group take Galois, including me, but I'm not sure what we would do without it. Also, I don't think any of us had linear algebra background, so in summary I feel like my expo lab required a lot of background knowledge in order to derive meaningful results, which was frustrating in the first four weeks because we didn't know enough to prove anything significant.
I am making a spreadsheet to keep track of the problems I've missed. I really want to make the most out of this last week here so I'm going to try to do as many problems as possible. That might possibly mean that my sleep schedule will go a little wack, but I'm not going to pull a N trust. N is this guy at our camp who has completely sacrificed his health for the grindset.

All my expenses:

• Nud Pob. A Thai cuisine restaurant. I've gone there four times. It's pretty cheap $12-13 for a big plate, and it sells really good Asian drinks like Thai milk tea with boba, lychee drinks, guava juice, and grass jelly.
• City Convenience. I don't really buy things from here because it's lowkey kinda expensive. I've bought pencils, a pack of gum (not worth spending my money), a pack of cookies, and a bag of BBQ chips.
• The Warren Towers vending machine. I've expanded my taste in snacks due to these machines. Drinks I've tried: apple juice (twice), raspberry and lemon Pure Leaf tea. Snacks: Ruffles chips, Popcorners (2), weird BBQ spicy chips, Haribo gummy bears (3)
• Starbucks. Oh god, this has been robbing my bank account. I've probably gotten it 7 times. The deals don't help, either.
• Target. I only bought my binder and paper clips here.
• 7-Eleven. I bought two sandwiches here for dinner and a snack pack.
• Barnes and Noble. I bought Supercommunicators here, then realized it cost $30.
• Tea One boba. I bought Rose Milk Tea and Peach Hakult
• Ben and Jerry's on Newbury Street
• AMC Theators
• Skating rink

So yeah, I've kind of been spending a lot.

Other stuff worth noting:

• Stress/mental health at PROMYS
• going out
• Discipline
• Last week sadness/depression
• Imposter syndrome
• Shirt colors
• Fun activities: fish, assassins, frisbee
• Study spots