It’s time to get our hands dirty with some topology! Instead of studying spaces directly, we’re going to study a way of building topological spaces. In particular, we’re going to view a space as a collection of analogous subspaces appropriately glued together satisfying a few restrictions.

Continue reading## The Arithmetic of Polynomial Rings over Finite Fields

We’re going to discuss the arithmetic of polynomial rings over finite fields and its similarity to the arithmetic of the integers. We’ll first run though some preliminary observations about the arithmetic of polynomial rings which will suggest that it behaves similar to the arithmetic of the integers.

Continue reading## An Introduction to Topological Groups

We’re going to talk about an interesting merger of abstract algebra and topology, namely topological groups.

Continue reading## Directed Reading Programs

Today I have something wonderful to talk about for budding mathematicians: directed readings.

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