MAZ501: Discrete Math (2011-2012)
CURRICULUM PROGRAM: Mathematics
COURSE TITLE: Discrete Math
CALENDAR YEAR: 2011-2012
GRADE LEVEL: 10-12
COURSE LENGTH: 36 weeks
Major Concepts/Content: This discrete mathematics course by design shows a different view of mathematics than as seen in traditional mathematics courses. It is an applications driven course that is based upon the study of events that occur in small, or discrete, chunks. Discrete concepts are used extensively in business, industry, government, and the digital world. The major areas of study are counting and probability, graph theory, the mathematics of social choice (voting and fair division), and coding and encryption. Some of the questions investigated in discrete math are: What does a bar code mean? What is the most efficient way a delivery truck can visit ten destinations? Should you buy a lottery ticket?
Major Instructional Activities: Probability applications include predicting outcomes using combinations, permutations, and counting principles. Mathematics of social choice investigates election theory and fair division. The graph theory component is comprised of the following: (1) graphs and directed graphs- shortest paths and graph coloring; (2) various trees; and (3) circuits and networks. The role of coding and encryption in the digital world will be investigated. The concept of recursion is a strategy embedded throughout discrete studies. Concepts will be explored and simulated using a variety of technology tools.
Major Evaluative Techniques: The assessments, formal and informal, will be used to describe and identify student progression toward the discrete mathematics expectations. Students will be asked to demonstrate the depth of their knowledge through tasks which mirror realistic situations. Students will be required to develop verbal, written and technological skills in the process of solving the problem as well as use critical thinking in working towards a solution.
Course Objectives: Upon completion of the course, students will be able to use:
- graphs of vertices and edges to model a problem situation.
- critical path analysis to solve scheduling problems.
- graph coloring techniques.
- minimal spanning trees to solve problems.
- codes, including error-correcting codes, and decoding techniques.
- bin-packing techniques to solve problems.
- tree diagrams, Venn diagrams and other pictorial representations to find the number of outcomes in a problem situation.
- the fundamental counting principle to find the number of outcomes.
- combinatorial reasoning to solve problems.
- counting techniques to solve problems.
- simulations to solve counting and probability problems.
- election theory techniques to analyze election data.
- weighted voting techniques to decide voting power within a group.
- fair division techniques to divide continuous objects.
- fair division techniques to solve apportionment problems.
- recursive thinking to solve problems.
- matrices to organize data and solve problems.