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

  1. Counting: Recurrence relations, PIE
  2. Graphs and trees: basics, paths, planarity
  3. Graphs 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
Total Workload: 100
ECTS Credit (Total workload/25): 4