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Course Description Course Name : Combinatorics Course Code : MT 484 Course Type : Optional Level of Course : First Cycle Year of Study : 4 Course Semester : Spring (16 Weeks) ECTS : 5 Name of Lecturer(s) : Prof.Dr. HAYRULLAH AYIK Learning Outcomes of the Course : Understands counting principles. Understands Generalized Counting Principles. Recognizes nth order disarrangement Recognizes the Rook polinomial and solves problems using the Rook polinomial. Recognizes Generating Functions. Recognizes and uses First Order Generating Functions. Recognizes recurrence relations. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : Understanding counting principles and understanding Generalizations of Counting Principles, Recognizing nth order disarrangement, Recognizing Square polinom and solving problem using Square polinom, Recognizing Generating Functions, Recognizing and using First Order Generating Functions, Recognizing recurrence relations. Course Contents : Counting Principles, Generalized Counting Principles, Applications of Counting Principles, nth order disarrangement, Rook polinomal, Application of Rook polinomial, Generating Functions, First Order Generating Functions, Binomial Cofficient, Applications of Generating Functions, Recurrence relations, Second order linear homogeneous recurrence relations. Language of Instruction : Turkish Work Place : Faculty of Arts and Sciences Annex Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Counting Principles Review of the relevant pages from sources Lecture and discussion 2 Generalizations of Counting Principles Review of the relevant pages from sources Lecture and discussion 3 Applications of Counting Principles I Review of the relevant pages from sources Lecture and discussion 4 Applications of Counting Principles II Review of the relevant pages from sources Lecture and discussion 5 nth order disarrangement Review of the relevant pages from sources Lecture and discussion 6 Rook polinomial Review of the relevant pages from sources Lecture and discussion 7 Application of Rook polinomial I Review of the relevant pages from sources Lecture and discussion 8 Mid Term Exam Review Exam 9 Application of Rook polinomial II Review of the relevant pages from sources Lecture and discussion 10 Generating Functions Review of the relevant pages from sources Lecture and discussion 11 First Order Generating Functions Review of the relevant pages from sources Lecture and discussion 12 Binomial Cofficients Review of the relevant pages from sources Lecture and discussion 13 Applications of Generating Functions Review of the relevant pages from sources Lecture and discussion 14 Recurrence relations Review of the relevant pages from sources Lecture and discussion 15 Second order linear homogeneous recurrence relations Review of the relevant pages from sources Lecture and discussion 16/17 Final Exam Review of the relevant pages from sources Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Discrete and Combinatorial Mathematics an applied introduction, Ralph Grimaldi, Addison-Wesley Publishing Company,1994.  Discrete Mathematics and its Applications (Second Edition) , Kenneth H. Rosen Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 0 0 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Is able to prove Mathematical facts encountered in secondary school. 5 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 5 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 5 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 5 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 3 6 Expresses clearly the relationship between objects while constructing a model 5 7 Draws mathematical models such as formulas, graphs and tables and explains them 5 8 Is able to mathematically reorganize, analyze and model problems encountered. 5 9 Knows at least one computer programming language 5 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 0 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 3 42 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 119 Total Workload / 25 (h): 4.76 ECTS Credit: 5