Here are some mini-course descriptions taken from HCSSiM maxi-mini catalogs in recent years.
G'raffes: Spotted, Striped, and Coloring: (Taught by Amber Verser)
Have you ever wondered what the colorings are for a wild g'raffe? Or what the difference between a snark and a bridge is? And just what was the big huff in the 1970s about the first Appel computer? We will explore the world of assigning colors to graphs, visiting how to tell is a graph is planar by making it look pretty and the instructions Erdos gave about how to deal with visiting aliens. We'll create algorithms for coloring graphs, attempt to color the plane, and see how a number of problems can be solved with a small number of crayons.
Hyperfying: (Taught by Cynthia Vinzant)
Feeling too limited by the restrictions of graph theory? Ever wish edges could be sets of any number of vertices rather than just two? Well, just hyperfy your problems away. Learn about quirky kinds of hypergraphs, such as “linear spaces” and Steiner systems (like the Fano plane and the game SET). Learn how to properly color your very own hypergraph! “And what about Ramsey theory,” you ask? No, you won’t even need to give up Ramsey theory. Free yourself from the world of 2-uniform hypergraphs!
Really Really Really Really Big Things: (Taught by Max Levit)
Mathematicians really like sets. Everything from graphs and groups to probability and functional analysis is built out of sets of sets of sets of sets of... But what about these sets? What can you do with them all by themselves? How do we build them? And how big can we build them? REALLY REALLY REALLY REALLY REALLY BIG! In this mini we will talk about a few different types of really really really really big sets. We will prove theorems about order, and show the equivalence of three seemingly unrelated statements (one of which is the infamous Axiom of Choice).
You might like this mini if you like talking about definitions and abstractions without worrying about what they correspond to in real life or are interested in question such as: What's the biggest set we can make without getting into trouble a la the barber paradox (does the set containing exactly those that don't contain themselves contain itself?).
Peg Solitaire: (Taught by Paul Phillips)
A good career, wealth sufficient for your every need, and good friends can all be yours even if you take this mini. In the game of peg solitaire, the goal is (like golf) to get the lowest score possible; in particular, by making a series of "jumps" with the pegs, to remove all but one peg from the board. We will investigate the patterns and mathematics that underlie this seemingly simple game with its nearly endless variants. By the end of this mini, you should be able to solve many of the standard versions and have acquired some useful concepts that can be applied to your other mathematical studies.
Gal-Whaaaa?: (Taught by Amber Verser)
Ever wonder why Euclid couldn't trisect an angle, other than the fact that he was too old to have paper to fold? Or why he couldn't double a cube? Or perhaps why people claim that quintics are "unsolvable"? Wait no longer! We'll explore the magical world of polynomials, how their roots can answer those nagging questions in the back of your skull, explain why heptadecagons are but heptagons are not constructible, learn a lot about the hidden structure of groups (and just how much they can tell you about polynomials), and talk about the myth of the man who was killed in a duel at age 20 who is responsible for this math.
Disclaimer statement: This mini is "just algebra".