# Tutor profile: Kody A.

## Questions

### Subject: Linear Algebra

What is a Banach space?

Simply put, a Banach space is a vector space where distances and angle measures have meaning. For example, consider the 1-dimensional vector space $Q$ with either the traditional norm, or even better yet, the p-adic metric, since these metrics are not complete.

### Subject: Set Theory

Anyone who says a set is a collection of objects is setting you up for failure, once you reach Russell's Paradox. What is Russell's Paradox?

Russell's Paradox demonstrates that if you define a set as a collection of objects, then you end up at a logical contradiction. Consider the set of all sets that don't contain themselves and call that set R.The set R is not in R, and so, by definition, R contains all sets that don't contain themselves. We just showed that R does not contain itself, which therefore means that R contains itself (according to the definition of R). This is a logical contradiction. This is not HOW I would teach this topic, but it is certainly a demonstration that I am very familiar with the topic. I also taught Discrete Math at a university, which is basically the same class, but much harder.

### Subject: Discrete Math

People "say" they teach discrete math, but what makes you different and special?

I have constructed an entire discrete math online video-lecture course on YouTube, which I highly recommend you watch to get a better understanding of how I teach. There might be a chance that you don't even need tutoring, after watching those videos.