Examines mathematical theories and concepts within their historical and cultural contexts. Topics vary with instructor and may include mathematical symmetries, the organization and modeling of space, cryptology, mathematical models of social decision making, and/or theories of change and strategy.
Spring 2012. In this course, we will learn how to translate real life problems into graph theoretical problems. Graph theory does not require much mathematical knowledge besides high school algebra. On the other hand, it does require some mathematical maturity, and this is why calculus I (BCUSP 124) is required. One of the mathematical skills that we will be working on throughout the course is proof writing. We will be looking at four main types of proofs: direct proof, contradiction, contraposition, and induction. Besides writing proofs, we will concentrate on applications which graph theory is full of!
Student learning goals
• Learn the precise mathematical vocabulary related to graph theory.
• Fully understand at least five real-world applications such as balanced graphs in social science, bracing framework, phasing traffic lights, job scheduling, job matching, the sportswriter paradox, genetics, and decision making.
• Develop skills to clearly communicate mathematical ideas. This will be achieved by working collaboratively, by verbally describing mathematical information to your peers, and by doing a facilitation at the end of the quarter.
• Become familiar and comfortable with different notions related to graph theory such as digraphs, Eulerian and Hamiltonian graphs, spanning trees, and bipartite graphs.
General method of instruction
Some lectures. Group work. Oral presentations.
BCUSP124 (calc 1).
Class assignments and grading
Written Homework: 30% Oral Homework: 15% Final project (facilitation): 55%