COURSE INTRODUCTION AND APPLICATION INFORMATION


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 Solving
Lecturing / 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;
  • Discuss a scientific paper that involves stochastic models
  • Model any process that evolves over time.
  • Make scientific predictions about the future of a process using the models and techniques of stochastic processes.
  • Compare and contrast the models and techniques used in stochastic processes with those of other industrial engineering/operations research tools.
  • Classify the stochastic processes models.
  • Derive the equations of stochastic models, follow the proofs of theorems, and prove the validity of a solution.
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

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

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

 

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 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

ECTS / WORKLOAD TABLE

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

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
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