Math 3322:  Discrete Modeling I

Spring 2005


Instructor:                  Dr. Mary Garner   

Office:                         Science 522

Phone:             770-423-6664

Fax:                             770-423-6629


Web Page:       


Office Hours:            2 PM – 3 PM Tues and Thurs

                                   10 AM – Noon Wed

                                   Other times by appointment.

            The student is required to use WEBCT in this course, and through          WEBCT, the student can ask questions of the instructor or the class as a whole.

Text:                           DeMaio & Watson, Introductory Combinatorics and Graph Theory

Time:                          3:30 PM – 4:45 PM Tuesdays and Thursdays

Location:                    CL1003         


Technology requirements: 

You must access WEBCT to obtain the syllabus, assignments, announcements, important dates, other supplemental materials, and solutions to assigned problems. A calculator is not required but would be very useful.


Catalog Description:

Prerequisite:  MATH 1113 or MATH 2590.

An elementary introduction to topics and methods in discrete mathematics motivated by a series of real-world problems. Topics include matrices, graphs, counting and recursion.


Learning Outcomes:

At the end of the course, the student will be able to:

  1. Understand and apply techniques of enumeration including the multiplication rule and sum rule, and differentiate between combinations and permutations.
  2. Understand and successfully apply the binomial theorem.
  3. Understand and manipulate the binomial and multinomial coefficients.
  4. Identify and represent discrete functions in both recursive and closed forms.
  5. Complete a proof by mathematical induction.
  6. Complete a combinatorial proof.
  7. Calculate discrete probabilities and explain and justify procedures for calculating those probabilities.
  8. Understand and use the basic terminology of graph theory, and use graph theory to create mathematical models.
  9. Identify Eulerian and Hamiltonian graphs and use the properties of these graphs to solve problems.
  10. Identify the independence number and clique number of a graph.
  11. Identify matchings and covers of graphs and use their properties to solve problems.
  12. Identify properties of subgraphs and graphical degree sequences.



In this course there will be an emphasis on written communication of concepts. Any work to be handed in and any answers on tests must be written in complete, grammatically correct English sentences. Your work should be clear, coherent, complete and correct. As a guide for write-ups, you need to explain the method used to determine the answer including why this method was selected.


Grading Policy:

There will be 3 in class tests worth 100 points each and a comprehensive, cumulative final worth 100 points. There will be no make-up tests. The final exam grade will replace the lowest test grade if the exam grade is higher. There will be approximately 110 points of homework, quizzes, and WEBCT and in-class assignments. This will be counted as 100 points toward a total of 500 points. (So a person could get 110 out of 100 points on quizzes and assignments and thus accumulate a bonus of 10 points.) No late assignments will be accepted or graded. The grading scale is:


                        450 – 500      A

                        400 – 449      B

350 – 399             C

300 – 349            D

0 – 299            F


Important Dates:

Feb 3 (Thursday)            Test 1

Mar 3 (Thursday)            Test 2

March 5 – 11               Spring break

April 5 (Tuesday)             Test 3

May 1                          Last day of classes

May 3 (Tuesday)             Final examination 3:30 – 5:30.



Regular attendance is assumed and will be monitored. Note that students cannot make-up tests or assignments. Students are responsible for all material covered and any announcements made in class or posted on WEBCT. The instructor strongly urges each student to form a study team with one or two other students. Please notify the instructor in advance if you know you will be absent for certain class periods due to religious holidays or personal obligations. We can work together to ensure that such absences do not cause hardships in the course.



Students choosing to withdraw from this course without academic penalty must do so by March 4, 2005.  Withdrawal forms can be obtained from the Office of the Registrar.  The completed form must be approved by the Registrar.  A student who stops attending class or fails to complete course requirements will be assigned a failing grade if official withdrawal has not been completed.  There is a new University policy on the total number of withdrawals a student may have (see 2004-2005 Undergraduate Catalogue

p. 42).


Academic Integrity:

Every KSU student is responsible for upholding the provisions of the Student Code of Conduct, as published in the Undergraduate and Graduate Catalogs. Section II of the Student Code of Conduct addresses the University ’s policy on academic honesty, including provisions regarding plagiarism and cheating, unauthorized access to University materials, misrepresentation/falsification of University records or academic work, malicious removal, retention, or destruction of library materials, malicious/intentional misuse of computer facilities and/or services, and misuse of student identification cards. Incidents of alleged academic misconduct will be handled through the established procedures of the University Judiciary Program, which includes either an “informal ”resolution by a faculty member, resulting in a grade adjustment, or a formal hearing procedure, which may subject a student to the Code of Conduct ’s minimum one semester suspension requirement.


Students are expected to comply with the above standards.  It must be emphasized that failure to comply with Academic Integrity standards will be taken seriously.



Note:  The information contained in this syllabus is subject to change at any time with proper notification.


Grading Rubrics


You will be encountering two types of problems in this course:  one requiring a specific numerical answer or a range of numerical answers, and the other requiring that you write out a proof of a mathematical statement.


Type I:  Problems asking for a numerical answer or range of numerical answers.


These problems will generally be worth 10 points, assigned according to the following guidelines. Remember, you need to explain the method used to determine the answer and why this method was selected.





The answer is incorrect, and the work shown or plan described, if any, is irrelevant.


The answer is incorrect, but the explanation or work shown indicates some correct and relevant reasoning.


One of the following characteristics applies.

·        The answer is incorrect, but a correct approach is described and a correct plan is partially implemented.

·        The answer is correct. The explanation lacks clarity and/or is incomplete but does indicate some correct and relevant reasoning.



One of the following characteristics applies.

·        The answer is incorrect due to a minor flaw in plan or an algebraic error, but the explanation is clear and complete.

·        The answer is correct, but the explanation lacks clarity and/or is incomplete, but does indicate mostly correct and relevant reasoning.



All of the following characteristics must be present.

·        The answer is correct.

·        The explanation is clear.

·        The explanation includes complete implementation of a mathematically correct plan.


Note:  An explanation consists of sentences and words not a sequence of equations or computations.


Type II:  Proofs.


These problems will also generally be worth 10 points, assigned according to the following guidelines.





No proof is provided and/or a disorganized, random sequence of statements is provided.


The proof is begun correctly, perhaps one step is completed, but the proof is not completed.


The proof is begun correctly, several steps are completed, but the conclusion is not clearly proved.


The proof is largely correct, but organization is lacking and/or some explanation/justification is missing or inaccurately stated.


The proof is correct, well-stated, clear and organized. No important elements are missing.