COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Introduction to Stochastic Processes I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 307
Fall
3
0
3
7
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives This course aims to provide basic theory and applications of the theory of stochastic processes.
Learning Outcomes The students who succeeded in this course;
  • will be able to define appropriate stochastic process models.
  • will be able to classify finite and countable Markov chains.
  • will be able to find equilibriums of finite Markov chains.
  • will be able to analyze Poisson process.
  • will be able to analyze birth and death processes.
Course Description This course studies basic properties of finite and countable Markov chains. The accent is made on their asymptotic properties. The course also discusses branching process and Poisson process and their various applications. The last mention of this course is birth and death processes and their applications in queueing theory.

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Definition of stochastic process
2 Poisson process Chapter 2
3 Poisson process (continuation) Chapter 2
4 Interarrival and waiting time distributions Chapter 2
5 Birth-and-death process Chapter 5
6 Birth-and-death process (continuation) Chapter 5
7 Queuing models Chapter 5
8 Midterm exam
9 Canonical Representation of Poisson Processes
10 Finite Markov chains Chapter 4
11 Finite Markov chains (continuation) Chapter 4
12 Countable Markov chains Chapter 5
13 Continuous-time Markov chains Chapter 5
14 Continuous-time Markov chains (continuation) Chapter 5
15 Review for Final exam -
16 Review of the semester
Course Notes/Textbooks “Stochastic Processes“ by Sheldon Ross.
Suggested Readings/Materials “Probability Theory“ by A.Borovkov and “Introduction to Stochastic Processes“ by G.F.Lawler.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
2
20
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
50
Total

Weighting of Semester Activities on the Final Grade
4
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
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
15
4
Field Work
Quizzes / Studio Critiques
2
5
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
32
Final Exams
1
40
    Total
190

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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