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Course Description Course Name : Combinatorics Course Code : İSB491 Course Type : Optional Level of Course : First Cycle Year of Study : 4 Course Semester : Fall (16 Weeks) ECTS : 5 Name of Lecturer(s) : Prof.Dr. SELAHATTİN KAÇIRANLAR Learning Outcomes of the Course : solve counting rules problems solve permutations, combinations, and the problems of fragmentation ordered and unordered solve the Principle of Inclusion and Exclusion problems find the number of solutions of the equation n unknowns in a set of positive integers, write and solve recurrence relations understand producer functions solve recurrence equations using generating functions solve random walk and the problems of ingrown Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To teach basic ideas of combinatorics Course Contents : Odd rules, permutation, combination, repeated permutation and combination, partitions, the minimax principle, the integer solutions of the equation x1+x2+.....+xn=k, recurrence relations, recurrence relations with constant coefficients, Fibonacci sequence, generating functions, the solutions of recurrence relations using generating functions. 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 rules, permutations Source reading Lecture, discussion and problem-solving 2 Combination Source reading Lecture, discussion and problem-solving 3 Ordered and Unordered Partitions Source reading Lecture, discussion and problem-solving 4 The Principle of Inclusion and Exclusion Source reading Lecture, discussion and problem-solving 5 solutions of the equation n unknowns on set of positive integers Source reading Lecture, discussion and problem-solving 6 Recurrence relations Source reading Lecture, discussion and problem-solving 7 Solutions of equations of the reduction Source reading Lecture, discussion and problem-solving 8 Mid-term Exam Rewview the topics discussed in the lecture notes and sources Written exam 9 generating functions Source reading Lecture, discussion and problem-solving 10 to solve reduction equations with the help of generating functions Source reading Lecture, discussion and problem-solving 11 to solve reduction equations with the help of generating functions Source reading Lecture, discussion and problem-solving 12 Random walk and the player goes down Source reading Lecture, discussion and problem-solving 13 Some counting problems Source reading Lecture, discussion and problem-solving 14 Some probability problems Source reading Lecture, discussion and problem-solving 15 Some probability problems Source reading Lecture, discussion and problem-solving 16/17 Final exam Rewview the topics discussed in the lecture notes and sources Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Öztürk, F. (1995). Kombinatorik. A.Ü.F.F. Döner sermaye işletmesi yayınları, no:30 Required Course Material(s)  Balakrishnan, V. K. (1995). Schaum´s outline of theory and problems of combinatiorics. McGraw-Hill New York.  Russell, M. (2003). Combinatorics . Wiley-Interscience. Hoboken, NJ   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 80     Homeworks/Projects/Others 5 20 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 Utilize computer systems and softwares 0 2 Apply the statistical analyze methods 0 3 Make statistical inference(estimation, hypothesis tests etc.) 0 4 Generate solutions for the problems in other disciplines by using statistical techniques 0 5 Discover the visual, database and web programming techniques and posses the ability of writing programme 0 6 Construct a model and analyze it by using statistical packages 0 7 Distinguish the difference between the statistical methods 0 8 Be aware of the interaction between the disciplines related to statistics 0 9 Make oral and visual presentation for the results of statistical methods 0 10 Have capability on effective and productive work in a group and individually 1 11 Develop scientific and ethical values in the fields of statistics-and scientific data collection 1 12 Explain the essence fundamentals and concepts in the field of Probability, Statistics and Mathematics 5 13 Emphasize the importance of Statistics in life 1 14 Define basic principles and concepts in the field of Law and Economics 0 15 Produce numeric and statistical solutions in order to overcome the problems 4 16 Construct the model, solve and interpret the results by using mathematical and statistical tehniques for the problems that include random events 3 17 Use proper methods and techniques to gather and/or to arrange the data 0 18 Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs 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 5 1 5     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 15 15 Total Workload: 114 Total Workload / 25 (h): 4.56 ECTS Credit: 5