A week in the life of a CMU math major

by greenturtle3141, Nov 11, 2021, 1:29 AM

Thursday

I barely get up at 8:00 AM because someone decided it was a good idea to have a class at 8:30 AM. It's just a gen ed (Evolution) but I try to attend class because it's a good idea for not doing poorly. Also the attendance literally halved since the beginning of the semester and I don't want the professors to feel bad.

Well, by "professors" I mean the TAs, because for some reason they're the ones teaching the class. Or, at least they've been teaching ever since the first module finished. I haven't actually seen the professor since then. I have no complaints though, the TAs are doing a fine job.

Unfortunately, Evolution was boring that day. For some reason we talked a lot about geology, which I didn't find particularly interesting.

Class finishes early at 9:45 AM and I'm left with nothing to do until 1:20 PM. Er, well, technically I have a Functional Programming class at 11:40 AM. But after the first three lectures (during each of which I almost fell asleep), I got convinced that it wasn't worth attending because I can just learn everything from the mandatory recitation anyways. Also it overlaps with my lunchtime, which I'm unwilling to move earlier because my stomach is suffering from some unknown medical condition. So that's why I don't go.

I spend the downtime trying to do my Measure Theory homework, which was due that night. I kinda feel like I'm screwed: Problem 4 seems impossible, and I haven't really thought about Problem 5 yet. I also haven't done some of the previous parts. Worst comes to worst, I can use the Homework Drop on this.

At 1:20 PM I'm in my Technological Ethics class. It's a surprisingly good class, even though the workload can get a bit heavy. The professor brought in a guest lecturer who talked about content regulation on social media.

At around 4:00 PM I'm home.

I'm kinda panicking on my Measure Theory homework. I'm really sure I have an answer for Problem 4, I just can't prove it... I give up and start trying to do damage control, sweeping some of the previous parts. Fortunately they fall apart pretty quickly. I then go look at Problem 5. The conversations I've been overhearing about this problem start to make sense... and it seems kinda silly. Can't I just do this via "brute force"? Turns out it works perfectly fine. I prove it cleanly with 3 lemmas.

And now the cursed Problem 4. It's a two-parter and I can't get either of them.

After analyzing a bunch of my previous failed attempts (which ended in horrible messes of inequalities that led nowhere), I stared a bit at the second part, and that gave me an idea for the first. I realized that even though my answer was probably correct, it would be so much better to write it in a totally different way. I work it out on paper, and it all clicks together!

I write up the proof quickly for the first part, and then I feel slightly strange because my construction just completely nukes the second part. I'm a bit paranoid that something's off, but I don't notice anything wrong. I think it works.

With 10 minutes left, I'm done. But I'm concerned that I did too much "handwaving". I very quickly type up the two lemmas I need to patch up any holes in rigor and submit with minutes to spare. That was a close call!

I relax by playing Genshin until like 5AM or something. I have more assignments due on Saturday, but I feel like I deserve a break.


Friday

No classes today! Because it's "community engagement day" or something. I wake up around 11:40 AM or something though, because some friends wanted to meet up at noon.

For Community Engagement Day, there's a ton of different food trucks giving free lunch to people... But all the lines are huge. Our plan was to get some free food and then do one of the activities, particularly an escape room. But every single line everywhere was like a zillion kilometers long, so we scrapped that part of the plan and went to an escape room.

I've done better escape rooms, but it certainly wasn't bad. Apparently we had the fastest time that day. My main contribution was figuring out the code to one of the locks by solving one of those "Mastermind" puzzles.

After the escape room, pretty much most of the food trucks were closing down, so some of us just bought food instead.

When I got home, I alternated between playing a Celeste mod and doing one of my reading assignments for Ethics. I accidentally fall asleep. It was a long day.


Saturday

I magically wake up at like 10 something, just in time to get a message from K telling me to join her and J to do work.

I didn't really get much done there, except start a little of my Ethics essay that was due by midnight. We managed to solve some puzzles though!

At around 6:30 I leave with S to go pick up a birthday cake for C. I really don't have time for birthday parties, especially considering that I should be trying to raise my grade in Ethics to preserve the 4.0, but sometimes we all just need some downtime. And for C's sake, some things are more important than academics.

We surprised C. It was fun. C's roommate ordered dinner too. C learned how to cut a cake, apparently for the first time. The night is filled with conversations about sadistic CMU professors and math jokes.

During the small party I manage to finish writing my essay on my phone and submit it with about half an hour to spare. I introduced C to Celeste and let her play a bit. We stayed around until 2 AM. It was a good night.


Sunday

This time it's (J')'s birthday. We don't really talk much anymore, which is probably for the best. But J' happens to have cake, and cake is good. And, everyone is entitled to some slack on their birthday too. So I don't mind offering my apartment as the birthday party location.

I wake up earlyish (by which I mean, before 1 PM) and order lunch delivery from Choolaah. Ordering food is pretty expensive, but I have an excuse: I'm cooking dinner! At 1 PM! And apparently it's going to take 12 hours!

I prep the "Tortellini ala Genovese" by cutting up a bunch of onions and carrots. I put them in the pot with the beef and I let it sit there. I don't have white wine because I'm still only 20, so I used water to deglaze instead. Unfortunately, I'm not entirely sure why, but despite following the instructions pretty closely the sauce started to burn pretty badly. With some quick thinking I salvage about 2/3 of the sauce and transfer it to a different pot. I pick out some burned bits, add some salt and sugar, and the taste was somewhat salvaged. It was pretty much done within like 5-7 hours, probably because I halved the recipe (and probably why it burned too).

I finish a bit of my functional programming homework before the party. Other than that, I didn't do much work :p

The party is fun, a bunch of good friends showed up.

Eventually everyone leaves to A's house to play some kind of board game. I wasn't that interested though. Also I have a Combinatorics midterm on Monday. In theory I really shouldn't be able to afford doing all these fun things, but I somehow make do anyway. I study a bit of Combinatorial Game Theory and Polya's counting theorem, before falling asleep.


Monday

I arrive about 3 minutes late for the 12:20 PM Combinatorics midterm. I destroy the midterm and go get lunch at Au Bon Pain.

At ABP I find L! She's apparently running late to one of her languages classes, but she's not in a rush because her professor is apparently chill. We talked about what she was learning about: How languages have evolved to become the way they are. For example, one of the original words for 5 was "penkwe". Due to some kind of split, one group of people started using the "pen" part and another group started using the "kwe" part, and that's why both penta- and quint- are both prefixes for 5 today. The more you know!

I go to my Measure Theory class at 2:20 PM. And... wow, what the heck are we even learning anymore? Sometimes lecture is just really hard to follow and understand. I guess today was just one of those days.

I stay after for a while and one of the other students starts teaching me about the Pizza Theorem. That's why I wrote about that a few days ago.

I go home. I take an accidental nap and wake up at dinnertime. I cooked some chicken thighs with sautéed mushrooms and cherry tomatoes, and tried to make a pan sauce. The pan sauce didn't really work, but it definitely tasted good.

I don't get any programming done. Oh well.


Tuesday

Another early Evolution day. The lecture this time was about a bunch of invertebrates. More interesting than last time, but I still found it a bit boring.

For lunch, I text A' to see if she'll be at Tepper. She says yes! I get a pizza and we talk about things while I try to finish my functional programming homework. One of the programming tasks is worth like 35 points, which I found strange because it... didn't seem that hard? I was pretty much done with it before Ethics. I was getting confident that I could finish this by the due date, which was... er, midnight.

In Ethics we talked about risk and uncertainty. Interesting lecture, as usual.

At home, I procrastinate my programming homework, though I get a little bit done. I feel a little bit stuck trying to figure out the solution to one of the problems, because the things I tried didn't seem to meet the time complexity requirements. But then I find out that some internet friends are playing One Word. How could I pass that up? I try to alternate playing One Word with doing my programming homework.

Eventually, I decided to give up on the programming homework and take a late day on it. Because hey, sometimes we all just need some downtime. And I really didn't want to think about the programming anymore.

One Word was really fun! In one of the rounds, I managed to guess the noun Click to reveal hidden text from only the clues TOMATO, JUICE, and STALK. The clue Click to reveal hidden text had a collision. I also managed to guess the noun Click to reveal hidden text from the one clue BODYCAM. That was funny.

During all that, I heated up the Genovese sauce for a quick dinner. The wonders of meal prep!

After that was over, I play some Genshin with no intention of turning in my programming assignment on time. Which is fine, because I still has two "late days" I could use.


Wednesday

Today's 10 AM Functional Programming recitation was a midterm review session. Did I ever mention that my Functional Programming TAs are really good? They're part of the reason as to why I can afford to ditch every lecture :p

Combinatorics had a guest lecturer today, because the professor was out of town. He talked about some Combinatorial Game Theory of Tic-Tac-Toe-like variants such as Gomoku. His accent was a bit rough, but I got used to it. A shame that the attendance rate for this class went down...

I learned that:
  • There's this "Erdos-Selfridge" theorem that gives a sufficient condition for determining whether a draw can be forced in a game or not. Whoa! It can be used to prove that the "$k$-in-a-row" game on an infinite board is a strong draw for $k=40$. That is, the second player can always force a draw.
  • Apparently, using some cute arguments, you can show that $k=8$ is a strong draw too.
  • $k=4$ is a strong win in that the first player can always win (Exercise: Prove this! Horizontal, vertical, and 45-degree-diagonal lines are all legal). However, $k=5,6,7$ are actually open problems!

I get lunch at the Exchange, which is basically everyone's favorite place for lunch. They make really good sandwiches.

In Measure Theory, we prove the Lebesgue Differentiation Theorem. Apparently, the Radon-Nikodym derivative $\frac{d\nu}{d\mathcal{L}^N}$ for $\mathcal{L}^N$ the Lebesgue measure on $\mathbb{R}^N$ and $\nu \ll \mathcal{L}^N$, i.e. the unique measurable function up to a.e. equivalence satisfying $\nu(E) = \int_E \frac{d\nu}{d\mathcal{L}^N}\,d\mathcal{L}^N$, is actually kinda a "derivative" in the sense that $\frac{d\nu}{d\mathcal{L}^N}(x) = \lim_{r \to 0^+} \frac{\nu(E_r)}{\mathcal{L}^N(E_r)}$ where $E_r$ is a set that "tends" or "shrinks" to $x$ in a "nice" way as $r \to 0^+$.

I get some ice cream because I crave sugar before I head home. Now that I was less burnt out from programming, I managed to finish my Functional Programming assignment, which ended up being not that bad.

After handing that in, I finished writing this blog post, and then made myself a steak and mashed potatoes dinner. And by that I mean, I will make some steak and mashed potatoes starting in 5 minutes. Hopefully that goes well.


Best of luck on the AMCs! If you're stressing over your score, go play games and/or have fun. Because remember, sometimes we all just need some downtime :)

Comment

12 Comments

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How do you have so much money to spend on food and college? Do you live in a dorm or apartment of house? You do so much fun stuff that it seems like you have no time for homework. Can I see problem 4? I want to see how complex this is, cause if you had trouble solving this I want to see it.

by Jwenslawski, Nov 11, 2021, 5:48 AM

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@Jwenslawski

Money for college: I'm fortunate to come from a well-off family that can support my academic endeavors. Though, not everyone that goes to CMU is necessarily in a good financial situation. If tuition is an issue, CMU tries to help via financial aid, and you could potentially obtain scholarships.

It's very true that CMU tuition is pretty expensive. Whether the high tuition is justified is... debatable. That can probably be said of many other prestigious schools too, including MIT, Princeton, etc.

Money for food: The most expensive way to feed myself, other than the ocassional special ocassion, is by ordering delivery. I try not to do this unless I'm really crunched for time or I'm just extremely burnt out and really don't feel like cooking. I try to make up for it by... cooking pretty often! It's really cheap, delicious, relaxing and fun, the only con being that it can be time consuming. I think cooking is such a great idea that I might make a blog post about it eventually.

Where I live:
  • Freshman year: Lived in a dorm. I think it was basically mandatory. Not cheap, unfortunately.
  • Sophomore year: Lived in a house with 3-4 friends. Pretty good price and great learning experience. It's how I learned to cook.
  • Junior year: I currently live in an apartment with two others. More expensive than the house I think, but it's reasonable.

How do I have time for fun things?

I talked about a lot of fun things in this blog post for two reasons: (1) I just happened to have more free time than usual this week, partly because Friday was a day off. (2) I wanted to emphasize that having fun is a good thing and is ok! We shouldn't be working ourselves to death, instead we should enjoy life while we still can.

To wit, I think it's totally ok to sometimes put off some academics in order to relax a bit. I hear that CMU has a reputation for work and work and work... and I think that's not very ideal.

As for how I actually have so much free time to do fun things... I'm not sure! Most people I talk to are shocked that I'm able to juggle 5 classes. To be perfectly blunt, part of it may be because I'm "smart", which is something that I'd hate to admit if true, but who knows...

Two of those five classes are basically trivialized due to easy homeworks (Evolution, Combinatorics). As for the other classes, they have pretty big workloads. I typically deal with one class (Functional Programming) by sacrificing the entire day of Saturday to do the homework, which can take up to 14 hours. Then I juggle the other two (Measure Theory, Ethics) throughout the week. In this view, I think having a bunch of free time is reasonable.

This work cycle isn't reflected in this blog post because relatively recent shenanigans (such as USAMTS grading) have broken the cycle.

What was Problem 4?

Keep in mind that I actually get stuck on homework problems relatively often. After all, college math is hard! Really hard! But if you're interested, here's the problem:

Let $\nu_1,\nu_2$ be finite signed measures. Prove that there exists a finite signed measure $\nu_1 \lor \nu_2$ such that $\nu_1 \lor \nu_2 \geq \max(\nu_1,\nu_2)$ and such that $\nu_1 \lor \nu_2$ is minimal in the sense that $\nu_1 \lor \nu_2 \geq \nu$ for any other finite signed measure $\nu$ satisfying $\nu \geq \max(\nu_1,\nu_2)$.

Prove moreover that if $|\nu_1|,|\nu_2| \ll \mu$ for some $\sigma$-finite measure $\mu$, then $\nu_1 \lor \nu_2 \ll \mu$. Then, find a formula for $\frac{d(\nu_1 \lor \nu_2)}{d\mu}$ in terms of $\frac{d\nu_1}{d\mu}$ and $\frac{d\nu_2}{d\mu}$.

Feel free to let me know if you have any more questions.
This post has been edited 1 time. Last edited by greenturtle3141, Nov 11, 2021, 8:01 AM

by greenturtle3141, Nov 11, 2021, 7:59 AM

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interesting

by v4913, Nov 11, 2021, 11:31 AM

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I don't even understand anything that math problem means. Are you trying to major in math? Or coding? I got to say your a genius, I don't think I could get that far in math and understand it. Have you considered working for AoPS? You could probably get a good job at AoPS to make more money. I mean your not in need of money right now but it could be a good temporary job. What math classes have you taken in college so far? Have you already taken linear algebra? Differential equations? What all have you taken?

by Jwenslawski, Nov 13, 2021, 6:22 PM

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@Jwenslawski

Of course you don't understand any of it! You're still young and have much to learn. College math is wildly different from anything you learn in school or in math competitions. I'm guessing that you wouldn't understand any homework problem from real analysis, abstract algebra, field theory, measure theory, functional analysis, differential geometry, topology, complex analysis, etc. all of which are classes that you can/will take in college.

Yes, I am a math major. In particular I am going for a Masters in math in 4 years as well as a CS minor.

I am not a genius. You don't need to be smart to understand college math. Being smart can help, but do not underestimate the value of hard work. Moreover, working hard can make you smarter.

I have not much interest in working for AoPS. In the past, I've worked as an AMC teacher for a local prep school, interned at Po Shen-Loh's Expii, and graded for the USAMTS. The main point of jobs at this level is to gain experience.

The classes I've taken in college, in order, are:

Summer 2018

21-127 Concepts of Mathematics (Sets, logic, functions, proofs, etc.)

Fall 2019

21-242 Matrix Theory (Linear algebra)

Spring 2020

21-228 Discrete Math (Counting, graphs, etc.)
21-261 Introduction to Ordinary Differential Equations (Solving diffeqs with proofs of existence and uniqueness)
21-269 Vector Analysis (Construction of real numbers, real analysis, multivar)

Summer 2020

21-325 Probability (from basics to proving the central limit theorem)

Fall 2020

21-235 Mathematical Studies Analysis I (Arzela domination, fixed point theorems, Jordan curve theorem, Ascoli-Arzela)
21-237 Mathematical Studies Algebra I (Groups, rings, modules, category theory)
15-251 Great Ideas in Theoretical Computer Science (Complexity classes, turing machines, etc.)

Spring 2021

21-236 Mathematical Studies Analysis II (Lebesgue measure, Lebesgue integral, absolute continuity and FTC, integration on curves, manifolds)
21-238 Mathematical Studies Algebra II (PID structure theorem, linear algebra on arbitrary fields, field theory, algebraic number theory)
21-623 Complex Analysis (from basics to proving the Prime Number Theorem)

Fall 2021

21-301 Combinatorics
21-720 Measure and Integration

by greenturtle3141, Nov 13, 2021, 8:53 PM

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What's the difference between real analysis and complex analysis? What gets taught in those classes? My dad said that the last Calculus he took was vector analysis. He is now a civil engineer.

by Jwenslawski, Nov 13, 2021, 11:11 PM

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@Jwenslawski

Good question. You can think of real analysis as "advanced calculus". Basically, a lot of what you learn in calculus is kinda wrong and "handwavy", meaning that they tell you a lot of things without actually saying why it's true (or, their explanations aren't rigorous).

For example, in calculus you learn something called "u substitution". In real analysis, this is not assumed. In fact, it's very difficult to prove that u substitution is a legal thing to do!

Another way to "interpret" the course of real analysis is taking the name literally: It is, literally, the study of real numbers. Real numbers is what allows us to take limits, derivatives, and integrals. So, real analysis can be thought of as studying the real numbers in order to understand properly how things like limits actually work.

In that perspective, complex analysis is the study of complex numbers. We can think of complex analysis as a careful study of complex numbers in order to extend the things you do in real analysis to the complex plane. This lets us take, for example, "complex derivatives", and integrals over complex numbers. As it turns out, combining complex numbers and "calculus"/real analysis leads to so many fantastic miracles. I highly recommend learning about it when you get the chance (though it may be quite some time before you have the required background to understand it fully).

by greenturtle3141, Nov 13, 2021, 11:27 PM

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Thanks! What is the last math you have to take to get a degree?

by Jwenslawski, Nov 14, 2021, 8:47 PM

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@Jwenslawski Math degree requirements will differ from college to college. For me, I basically have taken enough courses to be at the "level" of having a completed undergraduate degree. Right now I'm taking graduate courses in order to shoot for an additional Masters degree on top of my Bachelor's.

Also keep in mind that the courses aren't "linear". In middle/high school, you do algebra -> geometry -> algebra 2 -> precalc -> calc. There is no such progression in college. Arguably the progression looks more like a "skill tree".

For instance, after some preliminary courses (typically a proof-writing class) you can jump right into any of Real Analysis I, Abstract Algebra, Differential Equations, Discrete Math, or Probability. None of these classes depend on another, but in theory you should take all of them in some order before you graduate.

Some of these courses lead "deeper" into the "skill tree". Real Analysis I leads to Real II, leads to Measure and Integration, leading to Advanced Real Analysis. Abstract Algebra leads to courses like Linear Algebra (over arbitrary field) and Field Theory.

There are lots of graduation requirements at CMU MCS (which is unfortunate), but among the math classes you have to take:

The introductory proofs course
A Discrete Maths course
A linear algebra course
Probability
Multivariable calculus
Differential equations
A second linear algebra course
Two semesters of Real Analysis
Abstract algebra
5 math "electives" (basically whatever interests you; could be number theory, combinatorics, measure theory, more real analysis, etc.)

To get the extra masters degree, I have to take 5 additional graduate courses and write a master's thesis.

The last courses I need to take all fall into the 5 "electives" and the 5 graduate courses.

by greenturtle3141, Nov 14, 2021, 10:01 PM

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Are you trying to be a math professor? Other wise how are you able to apply math to the world?

by Jwenslawski, Nov 14, 2021, 10:45 PM

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@Jwenslawski

That is a good question. I have no idea.

Well, in terms of using my math, there's always a use. Some career options include:
Working as a trader/hedgefund at wall street (lots of math majors end up here), working in cryptography, applying math in other fields like in tech or 3D graphics, and others.

I do not yet know if working as a hedgefund will be fulfilling, even though it would certainly make me filthy rich. In the end, I want to be able to use my math so somehow help this world. As such, I'm not yet entirely sure what profession my ideal career will place me in.

I also like teaching, so becoming a math researcher + professor is an option. But again, doing nothing but researching math doesn't 100% appeal to me because it's not immediately clear if the work I do will be of benefit to people.

All in all, it's a tough question that I'm still working towards answering.

by greenturtle3141, Nov 14, 2021, 11:01 PM

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You could probably become a coder. I'm sorry, what is a hedgefund?

by Jwenslawski, Nov 15, 2021, 1:58 AM

Turtle math!

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  • Can you give some thought to dropping a guide to STS? Just like how you presented your research (in your paper), what your essays were about, etc. Also cool blog!

    by Shreyasharma, Mar 13, 2025, 7:03 PM

  • this is so good

    by purpledonutdragon, Mar 4, 2025, 2:05 PM

  • orz usamts grader

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  • Entertaining blog

    by eduD_looC, Dec 31, 2024, 8:57 PM

  • wow really cool stuff

    by kingu, Dec 4, 2024, 1:02 AM

  • Although I had a decent college essay, this isn't really my specialty so I don't really have anything useful to say that isn't already available online.

    by greenturtle3141, Nov 3, 2024, 7:25 PM

  • Could you also make a blog post about college essay writing :skull:

    by Shreyasharma, Nov 2, 2024, 9:04 PM

  • what gold

    by peace09, Oct 15, 2024, 3:39 PM

  • oh lmao, i was confused because of the title initially. thanks! great read

    by OlympusHero, Jul 20, 2024, 5:00 AM

  • It should be under August 2023

    by greenturtle3141, Jul 11, 2024, 11:44 PM

  • does this blog still have the post about your math journey? for some reason i can't find it

    by OlympusHero, Jul 10, 2024, 5:41 PM

  • imagine not tortoise math

    no but seriously really interesting blog

    by fruitmonster97, Apr 2, 2024, 12:39 AM

  • W blog man

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  • very nice blog greenturtle it is very descriptive and fascinating to pay attention to :-D

    by StarLex1, Jan 3, 2024, 3:12 PM

  • orz blog

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