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Course Description form
CREDITS
COURSE
ENGLISH
ARABIC
TITLE
CODE /NO
CODE/NO.
Th.
Discrete
Math 471
471 ‫ر‬
3
Pr.
Tr.
TCH
3
Mathematics
Math 343
Pre-requisites
Brief contents, to be posted in university site and documents(4-5 lines):
Fundamentals of discrete mathematics - Countable and uncountable sets - pigeonhole
principle - Lattices and Boolean algebras - Graph theory: Graphs - digraphs, paths –
circuits – connectivity - Euler and Hamiltonian paths - shortest path problem - planar
graphs - Euler's formula for connected planar graphs, Kuratowski's Theorem. Trees spanning trees – trees - various algorithms - Computability theory: Finite state machines languages, grammars.
Faculties and departments requiring this course (if any)
Faculty of Science
Department of Mathematics
Objectives: Prefer In points
The objectives of this course are as follows:
1. To introduce to the students the basic concepts of Discrete Mathematics and its
applications.
2. To improve the students logical thinking and dexterity in solving problems.
3. For instance to understand how the cardinalities of natural and rational numbers
are equal while that of real numbers is different.
4. To introduce to the students various abstract mathematical structures including
Boolean algebra and lattices.
5. To introduce to the students graph theory with several applications and several
algorithms.
6. They must learn in this course the concept of abstract machines, the languages
and grammars.
7. They can use these concepts to under stand problems and theory in computer
science, abstract algebra, real and complex analysis, topology, manifolds, etc.
Contents: Prefer In points
1- Fundamental of Discrete Mathematic
2- Graph Theory
3- Trees
4- Boolean Algebras & Lattices
5- Modeling Computation
Course Outcomes:
A-
Knowledge:
(Specific facts and knowledge of concepts, theories, formula etc.)
From this course the students will get a general knowledge of discrete mathematics,
graph theory, Boolean algebras, abstract concepts of machines, grammars and languages.
A practical and simple example of an automaton is a vending machine. Several theorems
and their proofs in graph theory and Boolean algebras will mature them towards the
theoretical concepts of mathematics. They will study various algorithms in this course as
well.
B-Cognitive Skills
(Thinking, problem solving )
This is a very theoretical as well as practical course in nature and is closed to theoretical
computer science. The students will develop their thinking and their cognitive skills will
be improved by solving several applicable problems in counting, computability and graph
theory, and the theoretical problems in graph theory and Boolean algebras.
C- Interpersonal skills and responsibilities
(group participation, leadership, personal responsibility , ethic and moral
behavior, capacity for self directed learning)
In general, Mathematics teaches a very well skilled and disciplined life.
D- Analysis and communication:
(communication, mathematical and IT skills)
The students learn from this course how the practical ideas in nature can be given
a mathematical formulation and how to solve them by using tools in this subject.
Text book: Only one
Kenneth A Rosen; Discrete Mathematics and its Applications, Sixth Edition, McGrawHill International Edition, 2007.
Supplementary references
[1] E.G.Goodaiere and M.M.Parmenter; Discrete Mathematics with Graph Theory, Third
Edition, Pearson, Prentice Hall, 2006.
[2] B. Kolman, R.C.Busby and S.C.Ross; Discrete Mathematical Structures, Fifth
Edition, Pearson, Prentice Hall, 2004.
[3] L. Lesniak; Discrete Structures, Logic, and Computability, Jones
and Bartlett Publishers, 2002.
[4] R. Johnsonburg; Discrete Mathematics, Sixth Edition, Prentice Hall, 2004.
[5] P. Fletcher, H. Hoyle and C. Patty Foundations of Discrete Mathematics,
PWS-Cant Pub. Co., 1991.
[6] S. Epp. Discrete Mathematics with Applications, PWS-Cant Pub., Co., 1990.
Other Information Resources
Different web searches, like wikipedia, wolfram, kurriiki, ask, google, bing, etc.
Time table for distributing Theoretical course contents
Remarks
Experiment
Notation from Formal logic and set theory, countable and
uncountable sets.
Pigeonhole and generalized pigeonhole principles, binomial
coefficients.
Graphs, graph models, and terminologies, digraphs, multigraphs
Representing graphs and isomorphisms, duality, adjacency and
incidence matrices
Connectivity
Euler and Hamilton paths
Shortest path problems
Planar and non-planar graphs
Introduction to trees
Spanning & minimum spanning trees
Lattices, Boolean functions.
Boolean Algebras, Identities in Boolean algebras
Languages & Grammars
Finite-State machines with/without output, Examples from vending
machines, etc.
Homomorphisms, Language recognition.
Final exam.
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