Splash Biography

There's a good chance that you've seen Pascal's triangle before in your Math classes. If not, you can find a picture of it on wikipedia here: (http://en.wikipedia.org/wiki/Pascal%27s_triangle). What you probably haven't seen is just how much math is hidden in this strange creature. Why is it that reading across the first five rows gives the numbers 1, 11, 121, 1331, 14641 -- the first five powers of 11? Did you notice that every row sums to a power of 2? And what are the triangular numbers (http://en.wikipedia.org/wiki/Triangular_number) doing on the third diagonal (1, 3, 6, 10, ...)? We can answer all of these questions by learning how to count in a mad clever way.

Here are two questions for you to think about: #1) How much information is there in an average sentence in the English language? #2) What do we even mean by the word "information" anyway? (This is actually a really fun question to think about -- "information" is incredibly difficult to define in English.) In this class, we'll find the surprising answer to #1 (hint: it's a lot less than you'd expect), and we'll see how we can use math to create the only reasonable definition of information. These two questions create the foundation of Information Theory. Any time that you download a file on the Internet, listen to your portable music player, or save a compressed file, you're using Information Theory. Information Theory tells us how to make our communication more efficient or more reliable, and it has been said that computers run on Information Theory as surely as they run on electricity. Come find out about this surprising and highly useful branch of mathematics.

You might have heard that every one of your computer's actions, both simple and complicated, can be boiled down to moving around bunches of 0s and 1s. In this class, we will look at some of the ways that a list of 0s and 1s can be interpreted as a letter, an image, or even a movie, and how these encodings can be used to do sneaky things like send secret messages. Topics that we will probably cover include: The binary number system, ASCII, basic image encoding and steganography, and, if we have time, we will try to give an actual definition of information. It should be possible to understand most of the big ideas from this course without any exceptional Mathematics or Computer Science background, but having completed a second year of Algebra will make things much easier to follow. Note that we will not actually be using computers in this class, but rather looking at the "language" that makes computing possible.

You might have seen Pascal's triangle at some point in your math classes. If not, you can find a picture of it here: http://commons.wikimedia.org/wiki/Image:Pascal%27s_Triangle_rows_0-16.svg. The triangle is built by placing 1's along the edges of the triangle, and then adding together adjacent pairs of numbers and placing their sum beneath them in the next row. So what. This gives us a pile of numbers. Big deal. Well yes, this is a pile of numbers. But this is also a very interesting pile of numbers. Try adding up the digits in each row -- you'll always get a power of 2. Try reading each of the first 5 rows as a single number -- you'll get a power of 11 every time. And what's with the triangular numbers running down the third diagonals? These are just a few of the many patterns you can uncover in the triangle. In this class, we'll figure out why all of these unexpected patterns occur by answering a single question: "In how many ways can I choose k objects from a set of n objects?"