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| MAT7340 | Mathematical Modelling Under Uncertanity | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | Prof. Dr. İhsan Ünver | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is to teach the kind of uncertainities and model these uncertainities. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn system and concept of mathematical modelling. | 1,2,3,4 | 1 | | PO - 2 : | learn methods of uncertainities and to apply these to problems. | 1,2,3,4 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| System, concept of mathematical modelling , concept of uncertainity and its numerical evulating: Entropy and its properties, , entropy of stochastic experiment, using fuzzy theory in mathematical analysis of uncertaintity , uncertainity in finance market and the methods of decreasing risk. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Mathematical model
| | | Week 2 | Uncertainty and its types: randomness, chaos and fuzziness | | | Week 3 | Numerical estimation of uncertainty | | | Week 4 | Conditional entropy. Entropy of the complex systems | | | Week 5 | Entropy of the discrete probability distributions
| | | Week 6 | Entropy of the discrete probability distributions
Entropy of the absolute continuous probability distributions
| | | Week 7 | The basic concepts of the chaos theory. Modeling of the chaotic systems.
| | | Week 8 | Mathematical analysis of the uncertainty by using fuzzy sets theory: fuzzy logic, fuzzy set,
membership function
| | | Week 9 | Mid-term exam | | | Week 10 | Types of the membership function, alfa-section set | | | Week 11 | Operations on fuzzy relations | | | Week 12 | Fuzzy cartesian product | | | Week 13 | Fuzzy approach to probability | | | Week 14 | Probability of the fuzzy event and fuzzy probability. | | | Week 15 | Measurement of the fuzziness: measurement by using entropy and metrical distance | | | Week 16 | End-of-term exam | | | |
| 1 | Akdeniz F. , , 1998; Olasılık ve İstatistik. Baki Kitabevi, Adana. | | | 2 | Aliev R.A., Aliev R.R., 2001; Soft Computing and its Applications. Word Scientific.
| | | 3 | Baykal N., Beyan T., 2004;Uzman sıstemler ve denetleyiciler. Bıcaklar kitabevi, Ankara. | | | 4 | Şiryayev V.İ., 2007; Finans pazarı modelleri. Moskova. | | | |
| 1 | Lee K. , 2005;First course on fuzzy theory and applications. Springer. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 08/04/2016 | 2 | 50 | | End-of-term exam | 16 | 26/05/2016 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Ödev | 3 | 14 | 42 | | Total work load | | | 42 |
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