MATH 030: Exploring Contemporary Mathematics

Introduction:

This course surveys a number of mathematical topics all of recent interest, including financial, population and ecological systems models, critical path problems, mathematical symmetry groups, and weighted voting systems.
Instructor:
Michael Henle
Office Hours: Tuesday and Thursday 2:30-4:30 in King 202, Friday 5:00-6:00
Phone: X8383 or 775-7676
Course Objectives:
  • To experience mathematics as an abstract deductive theory
  • To experience mathematica as applied to social problems.
  • To practice problem solving in an abstract context.
  • To practice communication in a technical language.
    • Evaluations:
    Homework
    Carefully written problem solutions (due Tuesdays)
    Weekly Quizzes (on Fridays)
    Exams
    Two Hour Exams (October 12 and December 7)
    Final Exam (Friday, December 21 at 9 AM)
    Plus
    Two Extended Problem Solutions (due October 19 and December 14)
    Outline of the Semester: 
    Week of                Topics
    September 4          Financial models
    September 10        Graphs and Euler circuits
    September 17        Hamiltonian circuits, the TSP, greedy algorithms
    September 24        Ecological spreadsheet models
    October 1              Critical paths and scheduling
    October 8              Propositional calculus and syllogisms
    October 15            Boolean algebra and deduction systems
    Fall Break
    October 29            Exploratory data analysis
    November 5           Sampling and confidence statements
    November 12         Voting systems
    November 19         Weighted voting systems and dimension
    November 26         Measuring voter power
    December 3           Symmetry transformations, rosettes and friezes
    December 10         Network symmetry groups