Course Name | Probabilistic Systems Analysis |
Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
---|---|---|---|---|---|
IE 502 | Fall/Spring | 3 | 0 | 3 | 7.5 |
Prerequisites | None | |||||
Course Language | English | |||||
Course Type | Elective | |||||
Course Level | Second Cycle | |||||
Mode of Delivery | - | |||||
Teaching Methods and Techniques of the Course | Problem SolvingLecturing / Presentation | |||||
Course Coordinator | ||||||
Course Lecturer(s) | ||||||
Assistant(s) | - |
Course Objectives | Most problems encountered in scientific research requires acquaintance with stochastic models and the solution techniques used for these models. The stochastic versions of deterministic problems may also be defined and modelled. Using the models and techniques taught in this course, solution approaches will be sought to problems that are stochastic in nature or to the stochastic versions of deterministic problems. The student will gain the ability to build and analyze models. |
Learning Outcomes | The students who succeeded in this course;
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Course Description | The course involves defining and modelling a stochastic process and solving the problems related to the stochastic process being investigated. The underlying theory will be taught, followed by applications that illustrate the use of a stochastic process. |
Related Sustainable Development Goals | |
| Core Courses | |
Major Area Courses | ||
Supportive Courses | ||
Media and Managment Skills Courses | ||
Transferable Skill Courses |
Week | Subjects | Required Materials |
1 | Probability Models and Axioms; Conditioning and Bayes' Rule; Independence | Related chapter of course book |
2 | Counting; Discrete Random Variables; Probability Mass Functions; Expectations | Related chapter of course book |
3 | Joint PMFs; Multiple Discrete Random Variables | Related chapter of course book |
4 | Continuous Random Variables; Multiple Continuous Random Variables; Continuous Bayes' Rule | Related chapter of course book |
5 | Derived Distributions, Convolution; Covariance and Correlation | Related chapter of course book |
6 | MIDTERM | |
7 | Stochastic Processes: Bernoulli Process; Poisson Process - I | Related chapter of course book |
8 | Stochastic Processes: Poisson Process - II | Related chapter of course book |
9 | Stochastic Processes: Poisson Process – III | Related chapter of course book |
10 | Markov Chains – I & II | Related chapter of course book |
11 | Markov Chains – I & II | |
12 | Markov Chains – III | Related chapter of course book |
13 | Markov Chains – IV | Related chapter of course book |
14 | Project Presentations | Related chapter of course book |
15 | Review of the semester | Related chapter of course book |
16 | Final Exam |
Course Notes/Textbooks | Ross, Sheldon. Introduction to Probability Models, 11th edition, Academic Press, 2014. ISBN: 978-0124079489 Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena, Scientific, 2008. ISBN: 9781886529236. Taylor, Howard M. and Karlin, Samuel. An Introduction to Stochastic Modeling, 3rd Edition, Academic Press, 1998, ISBN: 978-0-12-684887-8. |
Suggested Readings/Materials | Sheldon Ross, Stochastic Processes, 2nd edition, Wiley, 1995. ISBN: 978-0471120629 |
Semester Activities | Number | Weigthing |
Participation | 1 | 10 |
Laboratory / Application | ||
Field Work | ||
Quizzes / Studio Critiques | ||
Portfolio | ||
Homework / Assignments | 1 | 20 |
Presentation / Jury | ||
Project | ||
Seminar / Workshop | ||
Oral Exam | ||
Midterm | 1 | 35 |
Final Exam | 35 | |
Total |
Weighting of Semester Activities on the Final Grade | 3 | 65 |
Weighting of End-of-Semester Activities on the Final Grade | 1 | 35 |
Total |
Semester Activities | Number | Duration (Hours) | Workload |
---|---|---|---|
Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
Study Hours Out of Class | 16 | 5 | 80 |
Field Work | |||
Quizzes / Studio Critiques | |||
Portfolio | |||
Homework / Assignments | 3 | 15 | |
Presentation / Jury | |||
Project | |||
Seminar / Workshop | |||
Oral Exam | |||
Midterms | 1 | 25 | |
Final Exams | 28 | ||
Total | 198 |
# | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
1 | To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies, | |||||
2 | To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts, | |||||
3 | To have the ability of defining and verifying problems in Mathematics and Statistics, | |||||
4 | With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application, | |||||
5 | In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently, | |||||
6 | To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way, | |||||
7 | To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way, | |||||
8 | To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual. | |||||
9 | To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently, | |||||
10 | To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics, | |||||
11 | As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values, | |||||
12 | As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them, | |||||
13 | To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results, | |||||
14 | To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science, | |||||
15 | In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule. |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest