Description:

This course is designed to present the beauty, scope, practical applications and relevance of mathematics. It will focus on applications of general interest drawn primarily from the social and biological sciences and business. Topics will be placed in a historical context, and mathematical reasoning will be stressed. Many of the applications will be computer-oriented. 3 hrs./wk.

Associated Costs: These are additional (out-of-pocket) expense considerations that students should expect in addition to the course tuition, fees, and textbooks. $0 to $100.

Supplies: Refer to the instructor's course syllabus for details about any supplies that may be required.

Textbook(s): For information see - http://bookstore.jccc.net

Course Fees: NONE

Course Objectives:

Upon successful completion of this course the student should be able to:

1. Construct mathematical models using graphs, trees, difference equations, and matrices.
2. Determine Eulerian and Hamiltonian paths and circuits.
3. Utilize graph theory to find efficient solutions to routing, scheduling, and networking problems.
4. Analyze selection methods in light of fairness criteria.
5. Find terms of sequences and sums of sequences.
6. Utilize recursive techniques in applications.
7. Perform matrix operations.
8. Develop and solve linear programming problems.
9. Utilize sequences and/or matrices to analyze the behavior of processes.
10. Place discrete mathematical topics in their historical context.
11. Utilize technology to solve discrete problems.

Content Outline & Competencies:

I. Graphs and Trees
   A. Define Euler paths and circuits.
   B. Identify Euler paths and circuits
   C. Define Hamilton paths and circuits.
   D. Identify Hamilton paths and circuits.
   E. Determine optimal solutions to routing problems.
   F. Define network.
   G. Define spanning tree.
   H. Determine optimal solutions to network problems.
   I. Discuss Euler’s and Hamilton’s contributions to graph theory

II.  Social Choice
   A. Introduce mathematically-oriented voting methods
   B. Define ballot counting.
   C. Define voting methods.
   D. Determine election winners and rankings.
   E..Define voting power.
   F.  Calculate power distributions.
   G. Define fair-division problems.
   H. Calculate a solution to fair-division problems.
   I. Define apportionment.
   J. Calculate a solution to apportionment problems.
   K. Discuss the effect of apportionment methods in the U.S. Congress

III. Recursion and Difference Equations
   A. Introduce sequences and functions in the context of recursion.
   B. Define recursive growth problems.
   C. Calculate recursive growth sequences.
   D. Introduce Fractals

IV. Matrices
   A. Define matrix operations.
   B. Utilize matrices to solve systems of equations.
   C. Define a linear programming problem.
   D. Calculate solutions to linear programming problems using augmented
matrices and an appropriate calculator.
   E. Calculate solutions to linear programming problems using the simplex
method and an appropriate calculator.

Methods of Evaluation of Competencies:

Evaluation of student mastery of course competencies will be accomplished using the following methods:

Unit Exams, Unit Papers and/or Unit Projects  40% - 80%
Homework, Quizzes and/or Small Projects        0% - 50%
Final Exam**                                  10% - 40%

**The final exam must count at least as much as any unit exam, unit paper
or unit project. In any course where unit exams are not proctored, the
instructor may require that the student score at least a 70% on the final
exam to earn a ‘C’ for the course. At the instructor's discretion, the
grade on all or any part of the final exam may replace any lower test
score.

Caveats:

1. The majority of mathematics courses are sequential. Students must earn a grade of C or higher in a prerequisite mathematics course to progress to its subsequent mathematics course.
2. In accordance with the assertion made on your billing statement, during the first two weeks of the semester, if a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course. He/she will be allowed to enroll in the appropriate lower level math course on a space available basis with an even exchange of tuition. After the first two weeks, students who have not met the prerequisite(s) will be dropped from the course with no refund of tuition.

Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.