Syllabus Spring 2007

Contemporary Mathematics 01 115-02
Monday and Wednesday 4:45-6:00
Robinson 310

Instructor: Professor Ira Fine
856-582-8032 iafine@comcast.net

Grading will be based on three tests (each 30%) and attendance (10%). Also a homework portfolio can be turned in at the end of the semester which can be used to raise your average a maximum of one grade. However to receive an “A” you must have an “A” test average. Tests and exams must be taken at the scheduled time except in the case of extreme emergency and I am notified beforehand.

I will be available for extra help as needed.

Text: Excursions in Modern Mathematics, Peter Tannenbaum, Prentice-Hall, 6th edition

Calculator: Any scientific or graphing calculator

Tentative test dates: February 14, March 21 and final test date to be announced

Topics to be covered: ( ) is the chapter number in the text

1. Fractal Geometry (12)
The Koch Snowflake
The Sierpinski Triangle
Self-Similarity
The Mandelbrot Set

2. Euler Circuits (5)
Routing Problems
Graphs
Euler’s Theorems

3. The Traveling-Salesman Problem (6)
Hamilton Circuits and Paths
Complete Graphs
Traveling-Salesman Strategies

4. Spiril Growth in Nature (9)
Fibonacci Numbers
The Golden Ratio

5. The Mathematics of Population Growth (10)
Linear Growth
Exponential Growth
Gnomons

6. Symmetry (11)
Rigid Motions
Reflections
Rotations
Translations

7. Fair Division (3)
Fair Division Games
Two Players: The Divider-Chooser Method
The Lone-Divider Method
The Lone-Chooser Method

8. Chances, Probabilities and Odds (15)
Sample Spaces
The Multiplication Rule
Permutations and Combinations

9. Descriptive Statistics (14)
Graphical Descriptions
Variables
Numerical Summaries of Data

10. The Mathematics of Networks (7)
Trees
Minimum Spanning Trees
Kruskal’s Algorithm

11. The Mathematics of Voting (1)
Preference Ballots
The Plurality Method
The Borda Count Method
Pairwise Comparisons

Grading scale including plus and minus: A 90-100
B 80-89
C 70-79
D 60-69
F 0-59