William Paterson University of New Jersey
College of Science and Health
Department of Mathematics
Course Outline
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Title of Course, Course Number and Credits:
Advanced Discrete Mathematics – Math 4110
3 credits
Description of Course:
This is an advanced course in discrete mathematics primarily dealing with discrete
dynamical systems, algorithms, combinatorics and Graph Theory. Emphasis is placed on
complexity of algorithms, on existence and optimization problems in Graph Theory and on
associated algorithms.
Course Prerequisites:
Math 2020 or CS 2600
Course Objectives:
1. Discrete methods: The finite nature of certain problems in terms of discrete states
and/or discrete time.
2. Graph theory: A graph as a discrete model for problems in computer science and
mathematics.
3. Combinatorics: The mathematics of enumeration.
Student Learning Outcomes. Students will be able to :
a. Demonstrate ability to think critically and analytically by modeling problems from social and
natural sciences with graphs to provide answers in clear, coherent, and convincing manner.
b. Formulate and solve problems from social and natural sciences in terms of discrete states and/or
discrete time by inspection of graphs, application specific analysis, and general mathematical
theory.
c. Enumerate combinatorial objects using an array of powerful tools introduced in the course.
d. Work effectively in groups on projects that require an understanding of graph theory and
combinatorics.
e. Locate and use information on discrete mathematics and its applications.
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Topical Outline of the Course Content:
1. Discrete Structures
Elements of Graph Theory
Covering circuits and Graph Coloring
Trees and Searching
2. Enumeration
Arrangements and selections- a review of basic counting principles.
Generating functions.
Recurrence relations.
Inclusion-exclusion
Guidelines/Suggestions for Teaching Methods and Student Learning Activities:
This course is taught as a combination of lectures, computer demonstrations and student
Advanced Discrete Mathematics – Math 4110
presentations on selected topics. Strong emphasis will be given to applications, developing
mathematical models and interpretation of results. The computer algebra system
Mathematica has a package of 230 combinatorial commands that are bundled together and
called Combinatorica. The student is expected to use this package as an aid to understanding
the material introduced and as a research tool to solve complex problems modeled by a
discrete structure
8. Guidelines/Suggestions for Methods of Student Assessment (Student Learning Outcomes)
Through quizzes, tests, and final examination (cumulative with emphasis on the second part
of the course). Project: Project in which each student is to prepare a topic for presentation to
the class or for Mathematics Awareness Month as a short seminar. Topics on application
problems will be provided.
Homework: Homework will be assigned regularly and students should submit their work
along with computer printouts. Problems which are not routine and of considerable length
will be examined by the instructor.
Classroom Participation :
This is a senior course that requires active participation of all the students taking the course.
Classroom participation is counted towards the final grade.
9. Suggested Reading, Texts and Objects of Study:
Tucker, Alan; Applied Combinatorics, John Wiley & sons, New York
10. Bibliography of Supportive Texts and Other Materials:
1. Roberts, Fred S.; Applied Combinatorics, Prentice Hall, New Jersey.
2. Behzad, M., Chartrand, G., et al, Graphs and Digraphs,
3. Aho, Hopcroft and Ullman, Data Structures & Algorithms, Addison-Wesley, New York.
4. Ford and Fulkerson, Flows in Networks, Princeton University Press, Princeton.
5. Harary and Palmer, Graphical Enumeration.
6. Wilf, Herbert S.; Generating functionology, Academic Press.
11. Preparer’s Name and Date:
Prof. S. Maheshwari, Spring 1991
12. Original Department Approval Date:
Spring 1991
13. Reviser’s Name and Date:
Prof. R. Rieper, Spring 1998 and
Prof. M. Zeleke, Spring 1999.
14. Departmental Revision Approval Date:
Spring 2000
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