Course Contents (as of July 1998):

MATH 5900. Discrete Mathematics & Graph Theory


5 credit hours.

Instructor : Dr. Peh Ng --

Time : As arranged in the (ME)^3 workshop schedule

Venue : TBA

OFFICE: Sci 241

PHONE: 589-6318

E-MAIL: pehng@cda.morris.umn.edu

Course Web Page: http://www.morris.umn.edu/~pehng/Quarters/Ma5900

COURSE MATERIALS:
Class notes and handouts (copyright Peh Ng).

PRE-REQUISITES FOR THIS COURSE: Willingness to work hard, to spend at least 2 hours daily on this course outside class, & to think analytically.

MATERIAL COVERED:

1. Language of Mathematics.
Sets; sequences and strings; relations; equivalence relations; matrices of relations.

2. Recurrence Relations.
(The discrete analog of differential equations). Definitions of different types of recurrence relations; solving recurrence relations; applications.

3. Basic graph theory & some applications.
Fundamentals of finite graphs and their representations such as vertex-arc incidence matrices or relational matrices. Selected applications from discrete and combinatorial optimization such as Minimum Cost Spanning Tree Problem, Euler Graphs, Shortest Paths, Maximum Flow, Critical Path Method - Project Evaluation Review Technique (CPM-PERT), etc... Algorithms such as Dijkstra's, Ford-Fulkerson, Floyd-Warshall, etc to solve these problems and the analysis will be presented. Representation of problems as Linear Programming models and solving them as $LP$'s.




GRADING:

1. One comprehensive exam - 100 points

2. In-class presentation - 100 points

3. Homework - (written and computer). 100 points

(Late assignments are NOT accepted; only legible and neatly written assignments will be graded. There will be NO make-up exams unless arrangements are made with the instructor PRIOR to the exams.)

Course Grades
GUARANTEED GRADE IF TOTAL PERCENTAGE x is
A 93 <= x <= 100
A- 90 <= x <= 92
B+ 87 <= x <= 89
B 83 <= x <= 86
B- 80 <= x <= 82
C+ 77 <= x <= 79
C 73 <= x <= 76
C- 70 <= x <= 72
D+ 67 <= x <= 69
D 60 <= x <= 66

PLEASE FEEL WELCOME TO SEE ME OUTSIDE OF THE CLASS, ANY TIME, IF YOU HAVE QUESTIONS, PROBLEMS, OR COMMENTS PERTAINING THE COURSE WORK.

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