Math471

Course Description form

Faculties and departments requiring this course (if any): Faculty of

       Science/Department of Mathematics.

Objectives:  Prefer In points

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,

          McGraw-Hill 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.