In this class we will discuss the basics of algorithms. How can you efficiently search through and sort a large amount of data? How can you find the shortest path between two points on a weighted graph? How can you test if a large number is a prime? We will answer these problems, and many more!

The "Theorem of Sandwich Awesomeness" says that sandwiches cut into triangles taste better than square sandwiches because each bite is different. However, have you ever tried dividing a sandwich into equal area triangles between three people? Or five people? Or any odd number of people? Is it possible? Come to class and figure out! Along the way, you will unexpectedly meet topics such as modular arithmetic and p-adic valuations.

Bertrand's Postulate states that there is always a prime between n and 2n. In this class, we will present a beautiful proof by Paul Erdos. In leading to the proof, we will cover methods such as induction and proof by contradiction, and expand on topics such as binomial coefficients, Legendre's Theorem, and estimations. If time permits, we will see how we may derive a weaker form of the Prime Number Theorem using the same methods, or see how Bertrand's Postulate may be used in interesting problems, depending on student interests.

You have a bag consisting of 100 balls, some red and others green. You pick 5 balls with replacement out of the bag, resulting in a sequence red, red, green, red, red. What is the probability the next ball you pick will be red? In another situation, you are given n cards, labelled 1 to n, and a random number generator. How can you shuffle the n cards so that each possible ordering has an equal probability? Uncle John has two children. At least one of them is a boy. What is the probability the other child is also a boy? What if I told you the boy was born on a Wednesday? Think you have the answer? Come to class and see if you're right! Remember, the answer is probably not what you think.