Math 366
Discrete Methods
Professor: Dr. Curtis Bennett
Office: UH 2775
Email: cbennett@lmu.edu
Webpage: http://myweb.lmu.edu/cbennett
Office Hours: MW: 10:00-11:00, M: 1:00-2:00, T: 900-10:00
Textbook: Applied Combinatorics by Alan Tucker
Prerequisites: MATH 132, MATH 248
Course Meeting Times: MWF: 9:00 am, Uhall 2727
Phone: 338-5112
Catalogue Description: An introduction to graph theory; trees; coloring; Eulerian circuits.
Combinatorics; permutations, and combinations; recurrence relations.
General Description: This class will present topics from discrete mathematics with a slight
emphasis on those topics most important to computer programming. Discrete mathematics is the
study of structures that are fundamentally discrete in nature in that they do not require continuity.
In this introductory class, we will study graph theory and counting theory.
Course Objectives:
1) For students to be able to solve problems involving the basic counting principles and
theorems.
2) For students to be able to define generating functions, calculate the coefficients of generating
functions, and to use generating functions to solve counting problems.
3) For students to be able to solve recurrence relations using a variety of methods.
4) For students to improve their ability to write, read, and create proofs.
5) For students to be able to solve problems from graph theory involving edge- and vertexcounting, involving circuits, and on the coloring of graphs.
6) For students to be able to prove elementary properties of graphs and trees.
7) For students to be able to define graph, edge, vertex, Eulerian circuit, Hamiltonian circuit,
vertex and edge coloring, and an isomorphism of graphs.
Course Policies:
Attendance: Attendance will be expected in this mathematics class. Failure to attend class on a
regular basis will lead to a lowering of the student’s grade.
Missed Work: If a student should miss an assignment due to a documented University sponsored
event or religious holiday, arrangements should be made with the instructor prior to the absence.
You are expected to complete missed assignments and make arrangements to turn them in. I
reserve the right to deduct points from assignments that are turned in late (half the points for each
day late).
Academic Honesty: The standards of academic honesty at Loyola Marymount University (pages
57-59 of the 2006-07 LMU Bulletin) will be enforced. The minimum penalty for a violation for
submitting work other than your own will be failure on the examination or assignment.
Grading:
Tests: Three tests, (two midterms and a final) will be given during the semester.
Dates of midterms:
Final Exam Period:
MATH 366: Discrete Mathematics
This syllabus is subject to change throughout the semester.
Homework: For each section covered in lecture there will be a homework assignment. The
homework problems are designed to promote deeper understandings of important mathematical
concepts (that you should learn). As a result, conferencing with other students in the class is
permissible; however, copying of work from any source is not. Individuals may work as a group,
but the responses to homework problems must be written up individually. In addition, many
studies have shown that an important part of solving complex problems is for the problem-solver
to encounter a difficulty in the problem, take a break and return to the problem fresh. Since you
will encounter complex problems in this course, I highly recommend that when you are given a
problem set that you should look at every problem the day the set is assigned for at least a couple
of minutes, and that you should then be sure to have worked on every problem for at least 5
minutes in the first two days. I am extremely concerned that you recognize when your work is
correct (and hence incorrect). Thus I give substantially more partial credit for an incomplete yet
correct answer than I will for incorrect work. In addition, I expect all homework to be written up
neatly. Most mathematicians will have one or two “drafts” of their solutions to problems, the first
draft consisting of the basic outline of the solution (with no or few mathematical gaps) and the
final draft being well written. I highly suggest that you approach the problems sets with this
notion in mind. There is a high probability that at some point in the semester I will have students
evaluate and/or present each other’s work. The point of this will be to help you learn to write
clearly and concisely, to help you learn to write for someone that understands the material at a
level similar to yourself, and to help you learn to evaluate and read mathematics.
Grades will be computed in the following manner:
Midterms
Homework/Writing Assignments
Final (May 6, 8-10 )
Total
20% each
20%
40%
100%
The exact scale for grading will be decided at the end of the term. However, students receiving
90% of all points will get an A, students receiving 80% of all points will get at least a B, students
receiving 70% of all possible points will get at least a C, and students receiving 60% of possible
points will get at least a D.
Import Dates:
Jan. 17:
Jan. 19:
Feb. 13:
March 7-15:
March 20:
March 27:
April 10:
May 6:
Last day to drop class for 100% tuition
University Holiday - MLK day.
Tentative date for Exam 1
Spring Break
Last day to withdraw from a class.
Tentative Date for Exam 2.
University Holiday – Good Friday
Final Exam: 8-10, Uhall 2727
MATH 366: Discrete Mathematics
This syllabus is subject to change throughout the semester.