Author Archives: Samuel Coskey

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

HW: Getting started with Sage

Here is an example of the kind of programming we might be doing in Sage. The problem: Create a visualization of integer divisibility. This is a widely open-ended problem and it has many interpretations and solutions. Here is how I will choose to interpret it today: Consider all pairs of integers $(n,m)$ as points on the $xy$-plane, and highlight all the points $(m,n)$ such that $n$ is divisible by $m$.

Let’s go through the steps for doing this one at a time. Continue reading


Math 287 is a relatively new course with two primary roles. First, it is a second course in proofs and problem solving. And second, it the first and last course in mathematical communication—reading, writing, listening, and speaking in the language of mathematics. In this class we will attack challenging, open-ended problems and practice discovering and proving theorems. We will do this work in groups, and explain our results both orally and on paper.

If you’re not excited already, take a look at the syllabus for more details about the course expectations and goals!