Coding Theory

Ruby Kim Photo

Instructor: Ruby Kim

Have you ever listened to music on a vinyl record? Usually, you’ll hear some noise with the music—crackling, popping, clicking—caused by mere dust and fingerprints. On the other hand, you can scratch a digital CD and it’ll often play back noise-free. Music on a CD is translated into a series of bits (ones and zeros) where some of these bits are arranged in a clever way to locate errors and fix them before the information is translated back into music. These strategies, called error-correcting codes, were first developed about 70 years ago and have changed the way data is transmitted and stored. In this course, we will explore some of the mathematical building blocks of error control. We will discuss how Coding Theory is applicable not only to everyday devices like the telephone, CD, and computer, but also in fields ranging from cryptography to biology. No prerequisites required.

Squeezing Shapes

Aygul Galimova photo

Instructor: Aygul Galimova

We’ll explore the field of topology, the study of shapes up to stretching and squeezing, comes into play here. Topology studies the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, and bending, but no cutting. Topology comes up in the study of knots and objects, billiards and pool, and even breast cancer detection. This course will cover how to play tic-tac-toe on a donut, glue spaces to get new ones, orientation, knots, the rent-sharing problem, and a few applications. No prerequisites except curiosity.