Undergrad trauma edition. Grad-level probability not included because that is no longer a course, that is a lifestyle disease.

🧮 1. Calculus I

Limits, derivatives, basic integrals.

The first boss of STEM. It feels scary because everyone tells you it is scary. Then you realize half the class is just learning how not to drop a minus sign.

Rating: $$ \boxed{\text{NPC with a graphing calculator}} $$

📊 2. Intro Statistics

Mean, variance, normal distribution, confidence intervals, p-values.

Mostly button-pressing, formula-matching, and pretending you know what a p-value means.

Rating: $$ \boxed{\text{cooked, but microwave cooked}} $$

📐 3. Linear Algebra

Matrices, determinants, eigenvalues, diagonalization.

At first it looks like arithmetic with rectangles. Then one day someone says “vector space” and the floor quietly disappears.

Rating: $$ \boxed{\text{NPC until it suddenly isn’t}} $$

🔄 4. Calculus II

Integration techniques, series, polar coordinates.

This is where many pre-meds meet the reaper. Not because it is the deepest course, but because it is a bag of tricks wearing a trench coat.

Rating: $$ \boxed{\text{weed-out boss}} $$

🌪️ 5. Multivariable Calculus

Grad, div, curl, surface integrals, Stokes’ theorem.

Looks like Calculus I got a third dimension and started doing CrossFit.

Rating: $$ \boxed{\text{cooked in 3D}} $$

🧩 6. Discrete Math

Logic, sets, induction, graphs, combinatorics.

This is where computer science students discover that “obvious” is not a proof.

Rating: $$ \boxed{\text{proof tutorial hell}} $$

⚙️ 7. Differential Equations

Solve this equation. Now solve this system. Now solve this thing that models a spring, a circuit, a plague, or your GPA.

Bonus note:
$\text{ODE}$ = still human
$\text{PDE}$ = the room gets cold

Rating: $$ \boxed{\text{engineer boss fight}} $$

⚖️ 8. Real Analysis

Calculus, but the instructor removes all vibes and demands legal documentation for every sentence.

You thought limits were intuitive. Analysis says: prove it.

Rating: $$ \boxed{\text{canon event}} $$

🌀 9. Abstract Algebra

Groups, rings, fields, modules.

No numbers. No graphs. No mercy. Just structure staring back at you.

Rating: $$ \boxed{\text{major character development}} $$

🍩 10. Topology

Open sets, compactness, connectedness, quotient spaces.

The course where a coffee mug and a donut become relatives, and somehow that is your problem.

Rating: $$ \boxed{\text{geometry after taking psychedelics}} $$

🌌 11. Measure Theory / Functional Analysis

Measure theory asks: what even is size?
Functional analysis asks: what if linear algebra happened in infinite dimensions and all your instincts were illegal?

Rating: $$ \boxed{\text{eldritch DLC}} $$

☠️ 12. Measure-Theoretic Probability / Stochastic Analysis

This is not “probability and statistics.” This is probability after it joined a monastery, studied analysis for ten years, and came back speaking in filtrations.

Intro probability: $$ P(A\mid B)=\frac{P(A\cap B)}{P(B)} $$

Measure-theoretic probability: $$ \text{conditional expectation as an } L^2 \text{ projection modulo null sets} $$

Stochastic analysis: $$ dX_t=b(X_t)dt+\sigma(X_t)dW_t $$

Translation:
The Brownian motion is driving and you are in the trunk.

Rating: $$ \boxed{\text{Probably dead}} $$

[!NOTE] Easter Egg:

• Intro Probability: I know what a coin flip is.
• Annals of Probability: The coin flip lives in a Polish space and no longer answers your emails.