Mathematical Models and Problem-Solving
This course will meet for an hour of each session in a standard classroom where students will investigate problems, discuss strategies for solving mathematical challenges, and formulate models from the natural sciences; most of the investigations will be undertaken in small groups. Another hour of each meeting will take place in a computer laboratory where the students will evaluate problems, activities, and models using Excel and Geometers' Sketchpad. Students will be assessed on the basis of their performance during class meetings, the quality of their homework assignments, and their exposition on a final group project.
Examples of the problems and activities in the course include the following:
+Which numbers can be represented as the sum of two or more consecutive integers?
+ Model the evolution of an infection given a law for the spread of the infection.
+ Describe the polyhedra that can be constructed from faces that are pentagons and hexagons.
+ Describe the evolution of an advantageous gene among communities that lie along a river.
+ Determine the maximum area of a quadrilateral that has given side lengths.
+ Use Geometers' Sketchpad to generate a fractal.
+ Given the birthrates, survival rates, and initial populations for each 10-year age group, determine the age distribution of the population in subsequent decades.
+ A power plant is to be located near three cities. Where should the plant be located such that the sum of the distances to the three cities is as small as possible?