What I learned from every class I took so far
This is my 6th semester in college. I’ve taken quite a few classes at this point, so I thought it would be a useful exercise to reflect on what I learned from each one. I may keep updating this throughout my life.
Fall 2023
PHIL 4770 · Philosophy of Math
How the hell we get a line, which has length, from points, which don’t. Basically the philosophy department’s intro to measure theory.
MATH 3140 · Advanced Linear Algebra
Got the intuition for the idea of a canonical object, though really understanding what it means would come later.
CIS 1200 · Programming Languages and Techniques I
How to fold things, both from the left and the right.
WRIT 0730 · Writing Seminar
AI is pretty racist. Also, white paper can be written on a yellow paper. Chew on that.
Spring 2024
CIS 1600 · Mathematical Foundations of Computer Science
If you have 1601 pigeons and 1600 pigeonholes, you have way too many pigeons and pigeonholes.
HIST 0877 · History of Modern Biology and Social Implications
Pokémon evolutions are actually Lamarckian evolutions.
LING 0600 · Intro to Sociolinguistics
For some people, “Mary”, “merry”, and “marry” are pronounced all differently. Also: people sometimes don’t get housing because of their accent.
MATH 4100 · Complex Analysis
If you wanna integrate over a complex plane, just look at the holes.
MATH 4990 · Directed Reading Program
If a theory is -categorical for one uncountable , then it is for all . Also, strongly minimal categories behave really nicely. My mentor told me about this sick website.
Summer 2024
AFRC 1510 · Music of Africa
People of the DRC miss Lumumba, and music is a powerful way to keep that going.
CIS 2620 · Automata, Computability, and Complexity
DFA and NFA describe the same set. Not obvious at all.
Fall 2024
CIS 1210 · Programming Languages and Techniques II
Mergesort is .
CIS 4210 · Introduction to HCI
Wikipedia kind of sucks for highlighting links in blue, because blue is harder for our eyes to perceive.
MATH 3700 · Algebra I
I “learned” what universal properties are.
CIS 4600 · Interactive Computer Graphics
How to generate Minecraft terrains via noise functions.
MATH 4990 · Directed Reading Program
Types are propositions and terms are proofs. Maybe the biggest thing I learned in college.
Spring 2025
HIST 1788 · The United States and the Middle East
Iran is the only country to have ever banned veils.
PHIL 3800 · Topics in Philosophy of Science
Church-Turing thesis is a nontrivial assumption.
CIS 5610 . Advanced Computer Graphics
If our reality was a simulation, computers must be crazy because computing all that BRDFs is not cheap.
MATH 3710 . Algebra II
Yes, modules are vectorspaces over a ring instead of a field, but that’s not really the best intuition. God, that one assumption that nonzero elements are invertible does a lot for this world.
CIS 6700 . Advanced Topics in Programming Languages
The subtyping relation in is undecidable (and that’s the professor’s result).
Fall 2025
CIS 5000 . Software Foundations
Making notations look nice in Rocq is hard.
CIS 7000 . Programming Language Semantics
CPS-style is classical logic. Crazy.
MATH 5200 . Category Theory
I learned what universal properties are.
LGIC 3100 . Logic and Computability I
We compare primitive recursive arithmetic (PRA) functions to r.e. functions, but PRA functions aren’t that canonical.
LING 3740 . Neurolinguistics
Chomsky Hierarchy is stupid and just not how language works in our brain.
THAR 0171 . Movement for the Actor
We should be sillier with our bodies, really.
Spring 2026
MATH 3410 . Discrete Math II
“When there is a gap between math and a real world problem, this calls for more math.” - Dr. Andre Scedrov
MATH 8100 . Homotopy Type Theory
In HOTT, you can’t actually write a discontinuous function.
LING 2170 . Evolution of Language
Sign language may have come before spoken language.
URBS 2020 . Urban Education
Before blaming a student, first consider everything else in the environment.
THAR 0140 . Introduction to Dance
Physical knowledge is undervalued but it’s very real.