Discrete Math - Following Counting with Graph Theory

As in past years, I started my discrete math class with the unit on counting. This unit tends to be cerebral as their is a lot of looking at and understanding patterns coupled with complex reasoning. I was then following the counting unit with a unit on number theory and cryptography, which tends to be more of the same in terms of a lot of intense reasoning and pattern recognition.

This year I decided to follow the counting unit with a unit on graph theory. I wanted to switch the order partly because I wanted to cover a bit more in graph theory than I had time for in the past. The other reason was seeing more connections between counting and graph theory.

The unexpected benefit of this change is that the graph theory unit is much more of a hands-on unit, where students draw graphs and have physical models with which to work. This is a break from the more abstract activities in counting or number theory. The class energy has risen considerably along with better engagement.

I am still fleshing out how the entire graph theory unit will play out but the major points to cover are:

• Euler paths and circuits
• Hamiltonian paths and circuits (covering existence theorems without delving into TSP)
• Planar graphs including 
• Complete and complimentary graphs
• Proofs with graphs

I still need to gauge how much time to use and still leave enough time to adequately cover number theory and cryptography.

As I finalize the extended graph theory unit I will post an unit outline.