calculus & modeling

summer camp @ constructor school, together with Shrajesh Thapa

July 19th, first class!
Name me one class that starts with linear functions and ends with {insert project title for project in projects}. I'll wait.
Left to right: Ali, Nuray, Mikhail (Max), Herman, Sven

a prelude

This class teaches mathematical frameworks to model and understand the world. There are two research foci:

  • differential equations as physical models,
  • neural networks1.

The class proceeds with a self-paced strategy. This means, you get the creative freedom to work on what you find both interesting and challenging! That being said, you will be working independently during class. We will be there in strategic moments to get you moving forward.

Based on your progress and interests, you will be assigned a project. The final deliverable is an article plus a presentation. All proceedings go to the Muffin seminar!

> the muffin seminar 🧁

projects

Below is a diverse set of projects. Each project contains a precise set of deliverables, accompanied with useful resources.

> the heat equation

This project explores how a simple conservation law, combined with an empirical observation about heat flow, leads to one of the most important partial differential equations in physics and engineering.

> the two, three-body problem

This project explores how gravitational attraction governs the motion of celestial bodies, using systems of differential equations to describe and analyze their dynamics. The focus is on deriving, solving, and explaining the resulting equations of motion. Clear communication, correct modeling, and insight into solution structure are prioritized.

> tsiolkovsky’s rocket equation

We launch into how conservation of momentum and calculus combine to derive the elegant Tsiolkovsky rocket equation. The focus is on careful modeling, a clean derivation, and a concrete real-world application.

> logistic regression

This project discusses the conceptual and practical aspects of credit scoring using logistic regression, gradually bridging to neural networks. The focus is on clarity of explanation and the fact that logistic regression is just a simple neural network.

gallery

With Shrajesh, cooking the coolest Muffin projects at 3am {insert guy with sunglasses emoji}
Have you ever seen this many students,
gathered around,
eager to hear about the general solution to \(x' + p(t)x = q(t)\)?
Well,
there you go!
Everybody locked in {insert guy with sunglasses emoji again}
Self-paced progress as it should be
Me, spending 30 minutes with Nuray just to tell her to consult the large langauge models...

bonus

How about a talk with two speakers?

Talk on Hilbert's Infinite hotel. Tablet decides to crash 5 minutes before the talk. What do we do?
We improvise!
Hilbert has promoted me to assistant hotel manager, and handed me this speaker. It can speak to an infinite number of guests. Is the infinite hotel really infinite, or is there an end to the story?

  1. See neural networks & ai for more projects. ↩