Department of Mathematics

Syllabus
1701.115 – Contemporary Mathematics (Fall, 2007)
MW 4:45-6:00 Robinson 305

Instructor: B. Drury

Text: Excursions in Modern Mathematics, Tannenbaum, Prentice-Hall, 6th edition, 2007.

Content:

I. Statistics (approx. 4 weeks)
A. Elementary Sampling Theory and Experimental Design
1) Random sampling and bias
2) Experimental design

B. Descriptive Statistics
1) Graphical descriptions and exploratory data analysis
2) Measures of location and variability
3) Regression line and correlation
C. Probability
1) The frequency concept of probability
2) Mathematical description of probability and expectation –
How these are used in gambling, lotteries, and insurance
3) Sampling distributions with an emphasis on the difference
Between discrete and continuous distribution
4) Central Limit Theorem and Law of Large Numbers
D. Inferential Statistics
1) Confidence intervals
2) Lurking variables
3) Chi-square statistic

II. Discrete Mathematical Models (approx. 3 weeks)
A. Euler Circuits
1) Graphs as mathematical models
2) Graphs, edges, and vertices and their assumptions
3) Valence and the existence of Euler circuits

B. Hamiltonian Circuits
1) Algorithms for finding a minimum-cost Hamiltonian circuit
2) Trees, sets, and counting techniques
3) Traveling Salesman Problem (TSP)

C. Directed Graphs and Scheduling
1) Directed Graphs
2) Critical Paths
3) Priority list scheduling

III. Topics in the Mathematics of Social Choice (approx. 3 weeks)
A. The Mathematics of Voting
1) Plurality Method and Condorcet Criterion
2) Borda Count Method
3) Sequential Pairwise Voting and the Pareto Condition
4) Arrow’s Impossibility Theorem
5) Weighted Voting and the Banzaf Power Index
B. Discrete Models of Continuous Data
1) Relationship between Integers and Rational Numbers
2) Examples of apportionment problems:
a. Electoral College
b. House of Representatives
c. College class scheduling
3) Balinsky-Young Theorem

IV. Geometry (approx. 3 weeks)
A. Symmetry, Patterns, Tilings
1) Symmetry
a. As an aesthetic or non-mathematical idea
b. Isometry of the plane
c. Using the classification of all isometries of the plane
d. Concept of a Group
2) Tilings
a. Regular, periodic, and nonperiodic tilings of the plane
b. Plane geometry, algebra, and deduction
B. Mensuration, Growth, and Form
1) Mensuration formulae for areas and volumes of common shapes
2) Geometric similarity and the scaling of real objects
3) Surface area and volume
C. Fractal Geometry

Grading Policy:

Mid-Term Exam #1 (20%) - Wednesday, September 26th
Mid-Term Exam #2 (20%) - Wednesday, October 17th
Mid-Term Exam #3 (20%) - Wednesday, November 7th
Project (5%) - due Monday, December 3rd
Homework (10%)
Final Exam (25%) - Week of December 17th

Attendance Policy:

Attendance is mandatory. If a student is absent or tardy (A/T) from class and the A/T is excused then the student must provide the instructor a written note explaining the A/T when the student returns to class. Otherwise, the A/T will be considered unexcused. For example, absences due to a personal/family/medical emergency are excused but those due to a transportation/scheduling problem are not. Each student is allowed a total of three unexcused A/T’s; thereafter the instructor reserves the right to drop a student’s course grade by one letter. Students will only be allowed to make up work for excused absences. Please refer to Rowan’s policy on class attendance (see the Rowan undergraduate catalog.)

Classroom Rules:

Students will abide by Rowan’s student code of conduct and policy on academic honesty (please refer to the Rowan undergraduate catalog). Improper behavior will not be tolerated. As a courtesy to other classmates, students are asked not to leave their seats during class except for emergencies or unless prior arrangements have been made with the instructor. Please use the restrooms before class begins.

Accommodation Policy:

Your academic success is important. If you have any documented disability that may have an impact upon your work in this class, please contact me. Students must provide documentation of their disability to the Academic Success Center in order to receive official University services and accommodations. The Academic Success Center can be reached at 856-256-4234. The Center is located on the 3rd floor of Savitz Hall. The staff is available to answer questions regarding accommodations or to assist you in your pursuit of accommodations. We look forward to working with you to meet your goals.