#diff eq and probability

[becquerelian]

Easiest and hardest exams both done, we are in the home stretch now boys

[femslashspuffy]

It's really funny that most people in my math department are very algebra focused (because everyone who's staying wants to work with this one specific guy in algebra) but even after they've shown me the entire world of math I'm holding strong to my principles (diff eq supremacy)

[transgenderer]

Summer if you have recently discovered that you no longer think language is ill-ordered (which of course I agree with), you may change your mind upon studying french. Not because of anything to do with french itself, but because french is grammatically similar enough to english that french as taught to english speakers is basically uh. it's like undergrad diff eq, right, it's a bag of random bullshit and not a coherent system. Of course spoken french or written french as taught to an alien or something *is* a coherent system. But you will likely be taught a hodge podge of the two, with everything that is grammatically similar to english simply left unexplained, that what you will get is basically a bunch of nonsense. Probably. I mean maybe you have a really good french teacher. But this is how it is with pedagogy of european languages.

You should go. You should like dabble in greenlandic or some shit. There used to be a guy on here who was learning greenlandic. Or whatever.

i actually am finding it weirdly charming! i was very annoyed by the grammar of french when i was in high school. but idk now i feel like im seeing the patterns. heres a boring post i thought of about french grammar (i have a posts text doc and many die on the threshing floor):

my knowledge of french grammar was very classroomy before and i feel like actual french grammar (at least that represented in le petit prince. so maybe he talks weird) is much stranger. like, this/that words, ce (and forms), ca, -la are very prevalent. also "that" in the other sense, que (which also seems to fill a certain grammatical role of "than" in english). like i mostly get what they mean but there seems to be an important element of redundancy that's not clicking. like. i think its less redundant than it seems. but still somewhat redundant. this also follows with double negatives i guess

i think one of these days the way they use que is gonna click and make sense to me. instead of seeming weird and random. but it feels much less pointless and random when im trying to read an actual book. it feels kinda right. we read books in high school but it wasnt the same. it was school-french.

oh also, ive been reading "essential french grammar" by resnick which explains it pretty well

[elipsi]

matlab is kicking my ass, it keeps crashing bc of an error in the diff eq library and i have no idea what it is or how to solve it and i'll probably have to mess around with env variables again

[jingyuanyuan]

i forgor... all of linalg... its been 3 years... and now i have to do stability analysis... i barely remember what an eigenvalue is its so embarrassing i've only been doing computational modeling with diff eqs for the last 3 years

the physics grad students in this class are probably having a great time

[1d1195]

I think the interview went well! They said I’ll hear from them next week or the week after. At the beginning, the interviewers said they filled the full-time position (which is what I applied for🙄) so they interviewed me for the part-time. If I get that, I might work both labs! I had a meeting with my kind-of-supervisor at my current lab earlier about a few things, and they basically said “yeah just work your hours here around the hours there” lol they want my ass to stay here 🤣

Also, regarding school… I did kinda booty on my third exam last week and got an 80 :( then I felt AWFUL about the final yesterday, but I got an 87 so I didn’t do as poorly as I thought! Literally spent probably 50 minutes on a problem bc FUCK Bernoulli eqs💀 in my defense, I looked up the solution after, and it was (2*sqrt(5)e^2x)/(sqrt(10e^(10x)x-e^(10x)+c1)). Like??? On a FINAL?? I feel like an asshole for complaining about exam scores of 92, 98.5, 80, and 87, but when you’re good at math, anything below a 95 kinda stings 🙃 an exam average of 89 isn’t too bad though! All that said…BESTIE I GOT AN A IN DIFF EQ!!!!😭😭😭 damn near shit myself honestly lmao but I don’t have like, *any* support in terms of STEM, so your encouragement has meant so much to me🥹

-👩🏻‍🔬

I feel like there should be research done on that phenomenon. I would imagine it's even worse because women in STEM is almost like "I'm proving a point while also being a badass" if that makes sense. That's what it felt like to me in my undergrad anyway and even in my grad classes. But yes, not a lot of encouragement which is tragic. (Although one time my advisor called me a "good girl" for having good grades and taking a bunch of classes one semester and I swear to god I think about it once a week (also will def be making an appearance in a piece I'll be writing 😍)) If you ever need a pep talk I'm happy to help! 💕

I vaguely remember the Bernoulli equations. Probs blocked it out along with LaPlace Transform. Mathematicians really be doing the most sometimes. Anyway. That equation made me want to cry a little bit. I SO know what you mean about the 95 thing! It's like an expectation. I got an 80 on my first calculus quiz in high school and I wanted to CRY. My friends wouldn't stop hounding me about it and making fun of me (I was a 90 or better kinda girl) so it was traumatizing. I never announce grades to my classes and stuff. Don't feel bad for complaining. I totally know what you mean. You should def be proud of your grades but it's not a bad thing to strive for higher--especially when you're putting in the hard work. Not surprised you got an A but I love that for you! Congratulations! One less thing to worry about 💕

That's good news about the job I think! At least you can keep the job you wanted! How does that work for benefits though? That would be my only concern. Sorry to be all mom about it, but I know you mentioned that before 😂

xoxo

[realtalk-princeton]

what are common paths to get to quant trading? any recommendations for courses to take, programs to look out for, etc? thank you!

Response from Heisenberg:

There's not really a linear or common path to being a quant. Quants are good at math (specifically probability, stats, linear algebra) and coding. They take a good amount of statistics classes too.

If your profile fits this, then you're on the path to being a quant. No finance knowledge is required since firms figured that they can just take a smart person and teach them finance in a few weeks. As for programs, there are too many to list but there are things like Jane Street's FOCUS program, Akuna Capital's Options 101/201 course, and Optiver's Ready Trader Go.

Here are a few courses that I think are highly relevant to a quant career. Call it the RTP quant minor/certificate, I guess:

ORF 309 (probability)

MAT 321 (numerical methods)

MAT 322 (diff eqs)

ORF 335 (options)

ORF 405 (time series)

ORF 445 (HFT)

ORF 504 (financial econometrics)

ORF 531 (financial C++)

FIN 580 (financial ML)

COS 226 (algorithms, data structures)

COS 326 (ocaml, take as freshman so you can do JS interviews in ocaml /s)

With that said, know that classes aren't the most important thing. For example, ORF 309 teaches all concepts you'll need for probability questions. After that, there's not really any point in taking more probability classes. Just practice brainteasers and expectation questions that you'd expect to see during interviews, all of which are super easy compared to 309 pset problems. You could also take stuff like combinatorics, game theory, and stochastic calculus too, but that's kind of overkill and offers diminishing returns at that point. What's more impressive on a resume, the fact that you PDF'd ORF 527 or that you made an algorithmic trading bot in C++ that has an annualized Sharpe ratio of 7? (answer: the latter)

[gaykuvira]

leo might be more technically inclined but annabeth is able to think big picture and conceptualize large scale projects. both require intensely analytical mindsets. it doesnt mean leo’s smarter than annabeth or vice versa

[lithnin]

I'm probably in the 90th percentile of math ability among non-mathematicians – in college I got through calculus and diff-eq and stat mech without too much difficulty, and survived graph theory with some more effort. The problem I had was how to actually write a proof in the first place. Given an existing one I could generally follow along and understand it, but if I had to create a new one from scratch, I never received any more instruction on how to do so than "*shrug* idk, figure it out?"

The post on that reading comprehension study is good (and reminded me of some of my complaints about GPT a couple years ago, although the LLMs have gotten much better since then).

But the thing that really stood out to me is that I feel much this same way about math instruction:

i have seen this repeatedly, too - actually i was particularly taken with how similar this is to the behavior of struggling readers at much younger ages - and would summarize the hypothesis i have forged over time as: struggling readers do not expect what they read to make sense. my hypothesis for why this is the case is that their reading deficits were not attended to or remediated adequately early enough, and so, in their formative years - the early to mid elementary grades - they spent a lot of time "reading" things that did not make sense to them - in fact they spent much more time doing this than they ever did reading things that did make sense to them - and so they did not internalize a meaningful subjective sense of what it feels like to actually read things.

One of the big problems I have primarily in Calculus 1 (which is the lowest-level course I've taught) is that students just don't expect math to make sense. There's a bunch of rules to follow, which you have to memorize, and then you look at an expression and use some rule that seems like you could use it.

But that's not how competent mathematicians (and I use that word in the broadest possible sense) interact with mathematics. Mathematical formulas mean things. They have syntax, and semantics, and you can break apart a computation and talk about what individual terms mean and are doing, and what manipulation you're doing and what that corresponds to.

(Sometimes, of course, that's easier than others. Calc 2, in particular, involves a lot of "tricks" where it's hard to explain the logic in the middle of using them. But that's why I'm focusing on Calc 1 here, which is mostly not like that but does have a lot of application-y problems where this semantic understanding is important.)

But if you've never worked through a math problem and felt like everything was meaningful, you don't expect meaning in what you're doing, and you don't expect your own work to make sense. And then, well, it won't, and you'll struggle and get lost in the middle of every problem.

[1d1195]

Oo oo oo!! Which calc?? Or like… ALL of the differential, integral, vector, etc? I hated vector unfortunately. I thought I’d love it bc, ya know…physics is my thing😂 but then we got into triple integrals and changing the variables of them, and I did not feel very hypnotic fully fresh anymore. I think derivatives were my favorite, but in integral, I figured out I could do IBP in my head 💀 so that was fun☺️

Also, I think I told you I decided to retake diff eq this summer(?) bc my instructor last year decided to hate me, but this term I got a 92 on my first exam and a 98.5 on my second one😭 We have two more exams before the term is out, so hopefully those go okay. like??? Fair grading goes so far! My instructor last year, if I lost a sign or fucked up a constant, they would take points off for every step after. I remember one problem I did that on like, step two, and it was graded a 1/15. Hello?? All my work is correct, I just made a tiny algebraic error, so what is this for😭 This instructor tho, they just write like “-.25” for that one part and call it good😂 BC I KNOW THE CONCEPTS!!!! I JUST CAN’T ADD FOUR AND SEVEN ANYMORE!! Got to far into math and now I have to check on my calculator three separate times that five and five is indeed ten 🤣 you think after four calcs, linear algebra, stats, diff eq, and a year of calc based physics that I can do simple arithmetic?? Absolutely not lmao

I’ve been looking for a new job because my current lab position doesn’t receive benefits, and where I live, you can only stay on your parents insurance until you’re 26. And I’ll be that old on the 26th😂 I have too many health issues to NOT have insurance.

I applied for a position at another lab, and they emailed me yesterday for the next step! It sucks that I have to leave my current lab since I’ve been there for over five and a half years, and I LOVE what I do, but there’s also been a lot of shit going down so it’s probably for the best lmao

-👩🏻‍🔬

Honestly, haven't even looked at the curriculum. I'm pretty sure it's Calc I for most college level courses. I actually took AP Calc ages ago and I remember we covered derivatives, limits, implicit differentiation (MY FAVORITE 😍😍), some integrals, optimization maybe? I forget. I'm pretty nervous about teaching it so I really SHOULD start looking at it, but I'm on fumes of remembering how much I LOVED it when I took it and I'm just so excited. IBP is actually terrifying to me. Idk if I could do that I really need to study 🤭

LOVE that for you! I knew you would do well! I'm happy to report that as a teacher I'm a very fair grader the way you described. If you mess up a sign anywhere on the problem I take at most 1 point away. (Algebra doesn't have like 15 steps for me to take away additional points). I want them to know the process more than the little arithmetic (but also they get a calculator that they REFUSE to use when I offer it so I like to take points off for that too). So 3/4 for an otherwise flawless problem is what I do.

I'M THE SAME WAY. All my friends ask me to split checks and do the tip when we go out to eat and I'm like "lol, give me a piece of paper be, I can't subtract anymore."

I hope you get the new job! Benefits are so important. Your golden birthday! How lovely! Do you have any fun plans? I'm going to do my best to remember but that's around when I go back to work!

Thanks for checking in! I hope you're having a great week! 💕

xoxo

[mass-convergence]

I remember a common “trope” among meteorologists is to post something along the lines of:

And I get it … we get tired of being shit on all the time. Of people saying “your job is so easy! You get to be wrong all the time and still get paid! Haha!!”

And like … we def struggled through several semesters of calc and diff eq to get where we are. But the other thing is … the people that disparage us aren’t going to respect us any more because we do hard math. They have their joke and they’re going to keep driving it into the ground.

But the people who *are* actually going to look at this fucking shit are people who are interested in meteorology. And maybe they’re like me - not the best at math (or have a diagnosed or undiagnosed learning disorder) - and get intimidated by this. And the thing is we NEED people in our field who are effective communicators, creative folks, people who may not quite have the best math skills.

I can tell you those equations helped me understand the chaotic system that is our atmosphere and the relationships between different variables (like temp, wind speed, etc) slightly more

But I can tell you in my relatively young career as a meteorologist I’ve never had to derive an equation. But you know what I’ve had to do? Figure out how to make accessible graphics to communicate risk. How to word things correctly to communicate our confidence in a forecast. How to change my language for each group I talk to - I’ll talk to a group of emergency managers a lot differently than I talk to a group of kids or even my own coworkers. You don’t need to be good at math for that. So never think that you can’t get into science because you struggle with a derivation that probably will only come up once or twice more in your career (and that’s probably when you get bored one afternoon and just doodle on the whiteboard in the break room and try to remember anything from your junior year of college).

[adhdo5]

If I retake Calc III on the down low next semester but ALSO take diff eqs and I really finesse my schedule then I can probably avoid my parents finding out 🤔

[gothicprep]

I should probably delete facebook because I’ve seen multiple incidents of people in the “of course they’re from pennsy” group post the incredibly humiliating tinder profiles of present or former classmates. I don’t consent to this information. I don’t want to see these assholes I sat next to in diff eq posing with deer they shot. Get me out of here.

[borisfenestra]

Riri Williams is probably the most relatable character in the MCU, because when she was told her life was in danger, her immediate reaction was "Yeah but I can't be late for Diff EQ"

[yearningwitherrors]

Honestly, I remember it being a bit dull. Kind of like a bag of tricks with no greater theory emerging. And the prof being like: "Well, we know only how to solve these limited types of differential equations. And if people want to solve them in real life, they use numerical methods anyway, lol." It felt kinda ad-hoc-y, I guess. There were some other bag-of-tricks courses but there the tricks felt, idk, more widely applicable? I remember talking to an older friend about it who said: "If it consoles you, that is how they teach diff-eq in all the universities in the world, that's kinda how it it is." Although, I guess, in the end it will boil probably down to a matter of taste.

i got a giant fuckinf diff eq textbook for $6

so im gonna try and learn some differential equations stuff over winter break. never actually had to take a class on it so i wanna try and learn it now.

so hey uhh mathblr, how was ur diff eq class? what parts were super cool, what sucked ass, what was tricky to wrap ur head around, i wanna know!!!!!!!!!