INTERNATIONAL BURCH UNIVERSITY
Faculty of Engineering and Natural Sciences
Department of Information Technologies
2013-2014

SYLLABUS
Code Name Level Year Semester
MTH 203 Discrete Mathematics Undergraduate 2 Fall
Status Number of ECTS Credits Class Hours Per Week Total Hours Per Semester Language
Compulsory 4 2 + 2 100 ENGLISH

 Instructor Assistant Coordinator Harun Šiljak, Assist. Prof. Dr. Harun Šiljak, Assist. Prof. Dr. [email protected] no email

COURSE OBJECTIVE
• Introduce the fundamental topics and techniques in discrete and combinatorial reasoning
• Introduce wide variety application of Discrete mathematics in Computer Science

COURSE CONTENT
Week
Topic
1. Propositional logic: application, equivalences
2. Propositional logic: quantifiers, rules of inference.
3. Set theory: set operations, functions, sequences.
4. Set theory: cardinality of sets, matrices.
5. Relations: properties, representations
6. Boolean algebra: functions, gates, minimization
7. Functions, algorithms and computational complexity
8. Induction and recursion: mathematical induction and recursive algorithms
9. Number theory: modular arithmetic, integer representations
10. Number theory: congruences and cryptography
11. Counting: Permutations, combinations and identities
12. Counting: Recurrence relations, PIE
13. Graphs and trees: basics, paths, planarity
14. Graphs and trees: Applications of trees, spanning trees.

LABORATORY/PRACTICE PLAN
Week
Topic
1. Propositional logic: application, equivalences
2. Propositional logic: quantifiers, rules of inference.
3. Set theory: set operations, functions, sequences.
4. Set theory: cardinality of sets, matrices.
5. Relations: properties, representations
6. Boolean algebra: functions, gates, minimization
7. Functions, algorithms and computational complexity
8. Induction and recursion: mathematical induction and recursive algorithms
9. Number theory: modular arithmetic, integer representations
10. Number theory: congruences and cryptography
11. Counting: Permutations, combinations and identities

 Counting: Recurrence relations, PIEGraphs and trees: basics, paths, planarityGraphs and trees: Applications of trees, spanning trees.

TEACHING/ASSESSMENT
Description
• Lectures
• Excersises
• Assignments
Description (%)
Method Quantity Percentage (%)
Homework30
Midterm Exam(s)30
Final Exam140
Total: 100
Learning outcomes
• • Apply theory and techniques from discrete methods, combinatorial and graph theory in the applications of computer science.
• • Establish knowledge and understanding of data structures ,theory of computer languages and the analysis of algorithms using the theory and technique from discrete mathematics.
TEXTBOOK(S)
• 1. K. Rosen, Discrete mathematics and its applications, McGraw-Hill, 7th edition, 2012
• 2. R. Grimaldi, Discrete and Combinatorial Mathematics: an applied introduction, Addison Wesley, 5th ed., 2004
• 3. Ž. Jurić, Diskretna matematika za studente tehničkih nauka, Elektrotehnički fakultet Sarajevo, 2011.

ECTS (Allocated based on student) WORKLOAD
Activities Quantity Duration (Hour) Total Work Load
Lecture (14 weeks x Lecture hours per week)12525
Laboratory / Practice (14 weeks x Laboratory/Practice hours per week)12525
Midterm Examination (1 week)12525
Final Examination(1 week)12525
Preparation for Midterm Examination 0
Preparation for Final Examination40