# Discrete Mathematics and Combinatorics (MATH112) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Discrete Mathematics and Combinatorics MATH112 2. Semester 3 0 0 3 6
Pre-requisite Course(s)
None
Course Language English Compulsory Departmental Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Team/Group. Combinatorics and discrete mathematics are increasingly important fields of mathematics because of their extensive applications in computer science, statistics, operations research, and engineering. The purpose of this course is to teach students to model, analyze, and solve combinatorial and discrete mathematical problems. The students who succeeded in this course; understand and apply the basic combinatorial formulae and counting principles. solve linear recurrence relations. understand properties of binary relations. know basic notions of graph theory. Numbers and counting, countable and uncountable sets, continuum, the Pigeonhole Principle and its applications, permutations and combinations, combinatorial formulas, recurrence relations, principle of inclusion and exclusion, binary relations, elementary graph theory.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Numbers and Counting. Countable and Uncountable Sets. Cantor’s Theorem. Continuum. pp. 215-230
2 The Pigeonhole Principle, Its Generalizations and Applications. pp. 420-431
3 Permutations. pp. 313-329
4 The Fundamental Rule of Counting. pp. 349-355
5 Combinations. Combinatorial Formulas. pp. 356-361
6 Properties of Binomial Coefficients. Stirling’s Formula. pp. 362-370
7 The Principle of Inclusion and Exclusion. pp. 326-330
8 Recurrence Relations. Linear Recurrence Relations With Constant Coefficients pp. 457-475
9 Recurrence Relations. Linear Recurrence Relations With Constant Coefficients (Continued). pp. 476-490
10 Generating Functions. pp. 499-509
11 Relations on Sets pp. 571-578, pp. 584,585
12 Equivalence Relations pp. 597,599
13 Partial Ordering Relations and Lattices. pp. 632-648
14 Paths and Circuits. Euler and Hamiltonians Paths. pp. 649-700
15 Review
16 Final Exam

### Sources

Course Book 1. Susanna S. Epp, Discrete Mathematics with Applications, Brooks/Cole, 3rd Edition 2004. 2. Peter J. Cameron. Combinatorics: Topics, Techniques, Algorithms. Cambridge University Press, 2001 3. C. L. Liu. Elements of discrete mathematics. McGraw-Hill, 1985

### Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 8 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 4 20
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 20 20