A long-standing annual tradition, dating back to 2024, we get together on the week of 3/14 and run algorithms to calculate π, some on the computer, and some manual. We conclude the activity by (you guessed it!) eating pie!

RSA is a very famous cryptosystem. WE spent a fair bit of time on the necessary mathematical background: modular arithmetic, prime numbers, Euclid's Algorithm, Euler's Theorem... by the end of the semester, each student was able to design their own RSA system, and we sued it to send them a personalized message the gave the first hint to start their scavenger hunt!

Have you ever wandered how many primes numbers there are? Over 2,000 years ago, Euclid proved that there are infinitely many. But the story only starts there! After we proves this theorem (and we saw a few proofs!), we constructed long lists of primes by hand (and even longer using a computer), using the nifty Sieve of Eratosthenes. As the story developed, we studied complex analysis (calculus over the complex numbers) and discussed the Prime Number Theorem, a theorem the counts the number of primes less than a given number.

In 3D computer graphics and game design, we learned about how geometric objects are represented inside of computer software. We used a tool called p5js to code up our own 2D, and then 3D graphics renderer in JavaScript, encoded polyhedra as lists of points in a vector space, and worked out the equations for a perspective projection from 3 dimensions onto 2. We then simulated basic physics using Euler’s method for approximating differential equations after using facts about linear algebra to deduce when two polygons intersect. This programming-heavy semester focused on both the practical aspects of implementing mathematically motivated models and on the interplay between geometry and algebra.

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Until recently, quantum computers (an idea first discussed by Manin and by Feynman around '81) seemed like science fiction. Today, amazingly, we have quantum computers that are up and running. What is a quantum computer? How do we write a quantum program? In this course we will explain these concepts and learn the basic quantum algorithms. Students will implement these algorithms on simulators as well as actual quantum hardware (if free access is still available).

There are no prerequisites and no programming experience is needed. 

Topology is sometimes called "rubber sheet geometry", a world in which we can deform, strech, and contract. It is a world in which the basic concepts of geometry (lengths, areas, and angles) have no meaning. Still, not all shapes were created equal. In this course we will focus in surfaces and learn how to tell when two surfaces are the same and, more importatly, when they are distinct. Amusingly, one tool that can be used for this, and in a very elegant way, is geometry!