A lot of people like Sudoku, and they're fun puzzles, but there's a problem with them: they're all the same. Once you learn some basic strategies, you're mostly doing the same thing over and over again. In this class, each puzzle will be new and different. You'll have to keep coming up with new strategies, developing your thinking and learning to tackle new situations. You'll learn to stretch your mind and be more creative when faced with a new problem. Join us for a fun time, solving at your own pace and going over all kinds of different challenges!

Maybe you've heard that a continuous function is one you can draw without lifting your pencil off the paper. Do you really think that's the kind of definition a mathematician uses? It's all right for intuition, but it doesn't let you do any actual math with it. As a math major, the first real definition of a continuous function that you'd see is called the epsilon-delta definition, and it's much more sophisticated. This class is meant as an introduction to what deeper mathematics is really like. We'll see how to really define continuous functions, what exactly they can and can't do, and how to prove a lot about what's going on underneath the hood. We'll even see what continuous functions would look like if we go to strange spaces that are not like the Euclidean plane at all.

First, you get a circle. Go up a dimension and you get a "normal" sphere. Go up another dimension and you get the 3-sphere. This is a really interesting object: it has to sit inside four dimensions, because it doesn't fit in three-dimensional space, and it has a number of really interesting properties. We're going to study those properties, first by figuring out exactly what this 3-sphere thing is, and then by analyzing it by taking a "foliation." If that doesn't make sense, don't worry about it --- we'll go over it in class. But if you want to start to visualize things in four dimensions, this is a great class to do so. The main portion of this class will take about an hour and fifteen minutes; the rest of the time will be used for any questions you have about higher-dimensional geometry or topology.

Can there be different sizes of infinity? "Of course not!" says a friend. "Infinity is infinity. It means something goes on without end. There can't be different sizes of that." "Sure!" says another. "Say that you take the integers. They're infinite. Now take the positive integers. There must be more integers, because they have all the negatives!" You might think that it makes no sense to talk about different sizes of infinity. But mathematics has found a precise way to understand infinity and to measure its size. Come find out who above is right --- if anyone --- and to discover the power of a good mathematical definition.