| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Combinatoric | MAT630 | Elective | Doctorate degree | 1 | Fall | 8 |
Name of Lecturer(s)
Prof. Dr. Neşe ÖMÜR
Associate Prof. Dr. Yücel TÜRKER ULUTAŞ
Learning Outcomes of the Course Unit
1) Explain the concepts of combinatoric, permutation and combination.
2) Use integer functions, recurrence relations and special numbers in studies.
3) Use generating functions for problem solving.
4) Obtain new sums involving binomial coefficients.
5) Develop effective study skills.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Algebra
Course Contents
Combinatorics, Pigeonhole principle, permutations and combinations, sums, integer functions, number theory, Binomial coefficients, some number sequences, recurrence relations, special numbers(Stirling, Catalan, Eulerian Harmonic and Bernoulli numbers), generating functions, discrete probability, asymptotics
Weekly Schedule
1) What is combinatorics?2) Pigeonhole Principle
3) Permutations and combinations
4) Sums
5) Integer functions
6) Number theory
7) Binomial coefficients
8) Midterm examination/Assessment
9) Some number sequences
10) Recurrence relations
11) Special numbers(Stirling, Catalan, Euler numbers)
12) Special numbers (Harmonic, Bernoulli numbers)
13) Generating functions
14) Discrete probability
15) Asymptotics
16) Asymptotics
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Demonstration
6) Group Study
7) Case Study
8) Self Study
9) Problem Solving
10) Project Based Learning
Assessment Methods and Criteria
Contribution of Semester Studies to Course Grade |
20% |
|||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
||||||||||||
Contribution of Final Examination to Course Grade |
80% |
|||||||||||
Total | 100% | |||||||||||
Language of Instruction
Turkish
Work Placement(s)
Not Required