BEAM Courses

Pigeons & Partitions

Are there two people in LA who have the exact same number of hairs on their head? Can we find two BEAM students who were born on the same day? How many pigeons will it take before we find at least two begrudging roommates? 

We’ll begin by exploring mathematical ways to answer these types of questions, and even come up with some of our own! Along the way, we will learn how to actually prove that our crazy statements are correct. 

We will then realize that our questions fall into a broader category of problems about distribution, which will lead us into the exciting world of integer partitions. Here, we will spend a lot of time collecting mathematical data, drawing diagrams, and searching for patterns. We will learn how to “count without counting” to prove why our patterns appear — and then use our results to find shortcut (i.e. magic!) ways to add up sums like 1 + 3 + 5 + 7 + 9 + …. + 99.

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Operation Operations

An Intro to Group Theory

If I asked you what the four operations are, you might immediately say (or scratch your head for a second, and then say), “Addition, subtraction, multiplication, and division!” 

Are these the only operations? What if we lived in a different world where instead of numbers we had socks? Or shapes? Or dance moves? Or light switches? Or mazes? What would our “operations'' be, then? Would our “numbers” have opposites? Would any of them act like the number 1? 

We will explore these questions in class with lots of examples, some of which you will create on your own. Together, we will decide what we think should be true about our operations. Should two dance moves make another, or can they make a sock? Are shapes ever dance moves, or light switches socks?

Along the way, we’ll realize that many of our examples form what is called a group in mathematics. A group is a set of objects with an operation that follows certain rules. While for us groups will be mostly fun and games, they are actually far more — groups have provided the tools to solve problems that stumped mathematicians for centuries, and have predicted the existence of elementary particles before scientists found them experimentally. But first we’ll talk about socks!

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Puzzles & Permutations

You and 2 of your friends from BEAM are in line to get lunch at the dining hall. If you swap spots with one of your friends, the 3 of you are now in a different order. 

That seems like an obvious statement, but in math, we have a word to describe a rearrangement of some objects (or people!) — a permutation. It may seem like a simple concept, but understanding permutations has helped mathematicians describe symmetries, crack codes, understand molecular vibrations, and study the universe! 

In this class, we will explore permutations from a number of different lenses. We’ll think about the question involving you and your friends at lunch, but then we’ll go even further. We’ll draw diagrams like the ones below to discover more about permutations. We’ll play the game Swap!  and see how permutations can tell us when these puzzles are solvable — without having to actually solve them! We’ll use permutations to encode secret messages, and learn how drawing taxi routes gives us shortcuts for finding patterns in permutations.