Category Archives: Labs

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

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 1, iteration of linear functions

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