Advanced Topics In Discrete Mathematics

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Not Required

Course Contents

Set theory, Logical propositions, Mathematical proof methods, Relations and functions, Boolean algebra and logical functions, Number and coding theory, Logarithms, probability, Asymptotic notations, Sums, Combinatorial theory, basic counting rules, permutations, combinations, Generating functions, simple and exponential productive functions, Reccurence relations and solutions, homogeneous and non-homogeneous iteration relations, Graph Theory, simple and directional graphs, commitment in graphs, Euler and Hamilton graphs, Graph coloring and planar graphs, Tree structures and applications, binary trees, coverage trees, Coverage Tree problems, Kruskal’s and greedy algorithm, Shortest path problems, Finite state machines and automata, Finite state machines, acceptors and string recognition, cnverters, turing machines

Weekly Schedule

1) Set theory, Logical propositions, Mathematical proof methods
2) Relations and functions, Boolean algebra and logical functions
3) Number and coding theory, Logarithms, probability
4) Asymptotic notations, Sums
5) Combinatorial theory, basic counting rules, permutations, combinations
6) Generating functions, simple and exponential productive functions
7) Reccurence relations and solutions, homogeneous and non-homogeneous iteration relations
8) Graph Theory, simple and directional graphs, commitment in graphs, Euler and Hamilton graphs
9) Midterm exam
10) Graph coloring and planar graphs
11) Tree structures and applications, binary trees, coverage trees
12) Coverage Tree problems, Kruskal’s and greedy algorithm
13) Shortest path problems
14) Finite state machines and automata
15) Finite state machines, acceptors and string recognition, cnverters, turing machines
16) Final exam

Recommended or Required Reading

1- Introductory Discrete Mathematics, V.K. Balakrishnan Dover Publ.
2- Discrete Mathematics and its Applications K.H.Rosen Mc.Graw Hill.

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Discussion
4) Group Study
5) Problem Solving
6) Project Based Learning

Assessment Methods and Criteria

Contribution of Semester Studies to Course Grade	50%
Number Percentage Semester Studies Midterm Examination 1 40% Project 1 60%
Contribution of Final Examination to Course Grade	50%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Required