A broad overview of the progression of mathematics over history. We will briefly go over some mathematical concepts, in tandem with interesting anecdotes about mathematicians (mathematicians are weird people).

People act in selfish ways, and most of the time we should not fault them for this. However there are many situations when selfish behavior is detrimental to the group as a whole. Instead of trying to force people to not be selfish, this class explores the alternative: designing systems so that selfish behavior is benign. We will draw from many real world examples to demonstrate how systems can fail catastrophically and discuss what we can do to fix these problems.

P vs. NP is the central problem of theoretical computer science, providing the first formally articulated way of describing why some problems are hard to compute and some are easy. The problem is somewhat infamous for not only being unsolved and seemingly unsolvable, but for also being somewhat obvious in its answer. This course will spend time on explaining what the problem, why it is so important, and then demonstrating some evidence that P ≠ NP. Prior knowledge of P vs. NP is not required, however some background with computer science and physics is preferred, as we will draw from these areas.

$\mathbf P$ vs $\mathbf {NP}$ is the holy grail of unsolved problems in computability, dealing with what can and cannot be computed in any reasonable amount of time. In this course we will discuss evidence that $\mathbf P \neq \mathbf{NP}$ as it appears in the physical world. An understanding of $\mathbf P$ vs $\mathbf{NP}$ is NOT required for this course.

We will discuss the phenomena of Benford's Law and how it appears naturally and seemingly inexplicably arises across a large slew of data. We will discuss applications of Benford's Law and discuss some explanations of the phenomena.

Programming contests are quite fun but there is a bit of a barrier to getting started. This course will go over the general structure of programming contests, general tips for how to approach problems, and some basic topics that contests test.