MATH 55 SYLLABUS

Spring 1996

Text: Mathematical Modeling ln the Secondary School Curriculum,

Edited by Frank Swetz and J.S. Hartzler, National Council for Teachers of Mathematics, 1991. (Referred to as [MM] below).
See brief outline.

Note: Due to technical difficulties, some links may be broken

Topics covered

I. Combinatorics Topics Sets Operations with Sets Venn diagrams the Inclusion-Exclusion Principle Tree diagrams Sequential Counting Principle Permutations Combinations The Travelling Salesman Problem The Ticket Problem The Shapley-Shubik Power Index Group Projects Modeling 3 sets using a Venn Diagram, and deriving the Inclusion-Exclusion Principle for 3 Sets Using the Model Calculating the Shapley-Shubik Power Index involving 5 or more people The handshake problem Calculator Project Travelling Salesman Problem [MM] Exercise 14 (When Four Equals Three Equals Two)
II. Probability Topics Probability as Proportion Classical Probability Conditional Probability Independent Events Properties of Probability and Conditional Probability Bayes' Theorem Medical Screening Random Numbers Binomial Trials Multiple Choice Exams Sampling to Estimate Probability Wildlife Population Survey Sensitive Question Survey Group Projects Random Sampling Estimation of Population Size "Capture-Recapture" Sensitive question Survey The Grocery Problem Determining False Positive and False Negative Calculator Project Generation of Random Numbers [MM] Exercise 1 (Wildlife Population Survey) Exercise 4 (The Grocery Store Problem)
III. Equations and Inequalities Topics Delivering the Mail Managing a Deer Population Paper Rolls Simple Interest Banker's Discount Time Payments Group Projects Mail and Deer Problems Under Additional Assumptions Extensions of the Paper Rolls problem Calculator Project Programming the Deer and Finance Problems [MM] Exercise 7 (Delivering the Mail) Exercise 10 (Managing a Deer Population) Exercise 13 (Paper Rolls)
IV. The Cartesian Coordinate System Topics Distance Formula Cost of a Long-Distance Telephone Call Graphing Linear Equations and Inequalities Supply and Demand Equations Getting the Word Out Group (and Calculator) Project Programming Cost of Long Distance Call [MM] Exercise 3 (Cost of a Long-Distance Telephone Call) Exercise 11 (Getting the Word Out)
V. Statistics Topics Portraying Data Measures of Central Tendency Measures of Dispersion Grading on a Curve Cryptology Group Project Analysis of Test Scores Cryptology Deciding Authorship Median and Optimization [MM] Exercise 5 (Facility Location)
VI. Exponential Functions Topics Growth Decay Difference Equations Compound Interest Effective Annual Yield Amortization interpolation/extrapolation Group Project Checking the Accuracy of EAY listed Calculator Project Programming Compound Interest and Population Problems [MM] Exercise 18 (Making Money: Investing in a CD) Exercise 19 (Population Growth in the United States)

See full outline.

This page is maintained by John Noonan, Department of Mathematics. Comments, suggestions and questions should be directed to John at

noonan@math.temple.edu

Last modified April 25, 1996.