# Lab 5: A second adventure

Once again, you will choose your own adventure for this lab. But this time your final product will be a group presentation instead of a formal article. The presentations will be graded in the same way as the articles, except that the “exposition” category will be replaced with a “presentation” category. Follow the jump for the fine print. Continue reading

This lab is quite different from the previous ones: your final product will be a series of posts on this web site instead of a formal article. So what exactly do you have to do? Continue reading

# Lab 3: graph coloring (chapter 5)

In combinatorics, a “graph” is just a fancy name for a collection of dots (vertices) and lines (edges) joining them. In this lab we will explore the coloring of graphs— a huge area of research with numerous real world applications. The main question we will be attacking is: how many ways are there to color a given graph so that no two joined vertices get the same color? Continue reading

# Lab 2: Euclidean algorithm (chapter 3)

In this lab, we will explore Euclid’s algorithm for finding the greatest common divisor of two numbers. You will investigate questions such as how efficient is this algorithm? How many steps does it take to complete? How often does the gcd of two numbers turn out to be exactly 7? or 8? How often are two numbers relatively prime?
In this lab, you will explore what happens when you apply a linear function $ax+b$ again and again to a given initial value $x_0$. Using Sage to help you automate your investigations, you will observe the iteration process for many values of $a$, $b$, and $x_0$. If all goes well, patterns will start to emerge…. I will give you gidance on how to write your findings, and after a couple weeks, you will hand in a fancy article. Continue reading