PBIS 187: Problem based Inquiry Seminar
PBIS 187 – Problem-Based Inquiry Seminar ( 4 sections) Spring 2012
Sections 001 & 003
Can we count infinity? Are some infinite sets larger than others? Do you use ATM’s? Credit cards? Are coincidences as truly amazing as they first appear? These are just some of the questions we will tackle in PBIS 187. We will discuss topics from Number Theory, Geometry, and Probability. You will fine tune your critical thinking skills and discover that math is all around you. We will be solving some interesting problems and discover that problems that seem relatively easy are not yet proven. Get ready to apply problem solving techniques and learn that mathematics doesn’t need to be scary.
Sections 002 & 004
The main two topics are the basic principles of counting and elementary graph theory. Both topics belong to the mathematical field called combinatorics.
In the counting section we look at permutations, combinations, induction, and some probability. The emphasis is on concrete problems.
In the graph theory section we look at directed graphs and undirected ones, networks, graph colorings, planar graphs, trees, etc. The emphasis here is on concrete examples.
We also revisit the counting section after the graphs. We tackle some more complex counting problems armed with a new bag of tricks ( i.e., graph theory). The goal here is to develop a mathematical aesthetic sense. But these are still concrete and easily-stated problems.