GRADUATE SCHOOL
PH.D. In Applied Mathematics and Statistics
IE 502 | Course Introduction and Application Information
Course Name |
Probabilistic Systems Analysis
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Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
IE 502
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
Prerequisites |
None
|
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Course Language |
English
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Course Type |
Elective
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Course Level |
Second Cycle
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Mode of Delivery | - | |||||
Teaching Methods and Techniques of the Course | Problem SolvingLecture / 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;
|
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. |
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Core Courses | |
Major Area Courses | ||
Supportive Courses | ||
Media and Management Skills Courses | ||
Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
Week | Subjects | Related Preparation |
1 | Probability concept, Conditional Probability, and Bayes Theorem | |
2 | Random variable, Expectation, and Variance | |
3 | Basic univariate discrete probability distributions | |
4 | Basic univariate continous probability distributions | |
5 | Two-dimensional joint discrete and continuous distributions, Covariance, Correlation and Introduction to Random processes | |
6 | Two-dimensional joint discrete and continuous distributions, Covariance, Correlation and Introduction to Random processes (Cont’d) | |
7 | Midterm Exam | |
8 | Discrete-time Markov chains: Definitions, Modeling and the Chapman-Kolmogorov equation | |
9 | Discrete-time Markov chains: State classification and First step analysis | |
10 | Discrete-time Markov chains: Absorbing chains and Long-run analysis | |
11 | Poisson Processes: Definition and Properties | |
12 | Poisson Processes: Non-homogeneous and Compound Poisson processes | |
13 | Continuous time Markov chains: Concepts and Birth-death processes | |
14 | Continuous time Markov chains: Transition probability function and calculation of transition probabilities | |
15 | Review of the Semester | |
16 | Final Exam |
Course Notes/Textbooks | [1] Ross, Sheldon. Introduction to Probability Models, 11th edition, Academic Press, 2014. ISBN: 978-0124079489 [2] Taylor, Howard M. and Karlin, Samuel. An Introduction to Stochastic Modeling, 3rd Edition, Academic Press, 1998, ISBN: 978-0-12-684887-8. [3] Frederick S. Hillier, Gerald J. Lieberman, Introduction to Operations Research, 10th Edition, 2010 Mc GrawHill, ISBN: 9780071267670 |
Suggested Readings/Materials | [4] Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena, Scientific, 2008. ISBN: 9781886529236. [5] Sheldon Ross, Stochastic Processes, 2nd edition, Wiley, 1995. ISBN: 978-0471120629 |
EVALUATION SYSTEM
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 Exams | ||
Midterm |
1
|
35
|
Final Exam |
1
|
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 |
ECTS / WORKLOAD TABLE
Semester Activities | Number | Duration (Hours) | Workload |
---|---|---|---|
Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
Study Hours Out of Class |
16
|
5
|
80
|
Field Work |
0
|
||
Quizzes / Studio Critiques |
0
|
||
Portfolio |
0
|
||
Homework / Assignments |
3
|
15
|
45
|
Presentation / Jury |
0
|
||
Project |
0
|
||
Seminar / Workshop |
0
|
||
Oral Exam |
0
|
||
Midterms |
1
|
24
|
24
|
Final Exam |
1
|
28
|
28
|
Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
#
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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, |
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2 | To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts, |
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3 | To have the ability of defining and verifying problems in Mathematics and Statistics, |
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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, |
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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, |
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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, |
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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, |
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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. |
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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, |
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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, |
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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, |
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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, |
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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, |
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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, |
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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
NEWS |ALL NEWS
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Lecturers of Izmir University of Economics (IUE) Department of Mathematics will be studying the features of a new module in invariant theory