Retrograde analysis chess problems are a type of chess logic puzzle. You are given a position, and asked to deduce something about it, such as: What were the last several moves played? Is there a game leading to this position? What is the shortest game leading to this position? We only assume that games are legal, not well-played, so no chess skill is required. If you are a chess player of any skill level that likes logic puzzles, you should find these problems enjoyable.

You've probably heard that it takes 7 shuffles to completely randomize a deck of cards. But did you know that 8 perfect shuffles will restore a (52-card) deck to its original state? In this class, we'll discuss the mathematics behind card shuffling, and take a look at some card tricks based on shuffling.

Symmetry is all around us, both in natural and man-made objects. A starfish has fivefold rotational symmetry, while a brick wall has translational symmetry. In this course, we'll discuss how mathematics helps us classify symmetries, and why there are 7 types of one-dimensional symmetries and 17 types of two-dimensional symmetries.

Let's play a game! In this course, we'll explore how a number system called the Surreal Numbers can help us understand many different games. Games that, at first glance, look very different turn out to be equivalent because they correspond to the same surreal number. We'll study a variety of games such as Nim, Hackenbush, Domineering, Amazons, and possibly others!

Dots and Boxes is a deceptively simple game you've probably played before. Starting with a grid of dots, two players take turns connecting two adjacent dots. A player that completes a box scores a point (by placing his or her initials in the box) and immediately takes another turn. When there are no more moves left, the player with more boxes wins. However, despite its simple rules, the game turns out to be quite rich in strategy. After playing several games, we will uncover several levels of strategies for the game. We will later relate the strategy of Dots and Boxes to the game of nim.