FACULTY OF ARTS AND SCIENCES
Department of Mathematics
SOCIAL MEDIA
MATH 307 | 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
|
6
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Required
|
|||||
| Course Level |
First Cycle
|
|||||
| Mode of Delivery | face to face | |||||
| Teaching Methods and Techniques of the Course | Lecture / Presentation | |||||
| 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;
|
| 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. |
|
|
Core Courses |
X
|
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Definition of stochastic process | Sheldon Ross, “Preliminaries” chap. 1 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 41. |
| 2 | Poisson process | Sheldon Ross, “The Poisson Process” chap. 2 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 59. |
| 3 | Poisson process (continuation) | Sheldon Ross, “The Poisson Process” chap. 2 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 61. |
| 4 | Interarrival and waiting time distributions | Sheldon Ross, “The Poisson Process” chap. 2 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 64. |
| 5 | Nonhomogenous Poisson Process | Sheldon Ross, “The Poisson Process” chap. 2 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 79. |
| 6 | Compound Poisson Process | Sheldon Ross, “The Poisson Process” chap. 2 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 82. |
| 7 | Midterm exam | |
| 8 | Renewal Theory | Sheldon Ross, “Renewal Theory” chap. 3 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 98. |
| 9 | Renewal Theory | Sheldon Ross, “Renewal Theory” chap. 3 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 106. |
| 10 | Finite Markov chains | Sheldon Ross, “Finite Markov chains” chap. 4 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 163. |
| 11 | Finite Markov chains (continuation) | Sheldon Ross, “Finite Markov chains” chap. 4 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 170. |
| 12 | Continuous-time Markov chains | Sheldon Ross, “Continuous-time Markov chains” chap. 5 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 231. |
| 13 | Continuous-time Markov chains (continuation) | Sheldon Ross, “Continuous-time Markov chains” chap. 5 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 240. |
| 14 | Martingale | Sheldon Ross, “The Poisson Process” chap. 6 Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995), 295. |
| 15 | Semester review | - |
| 16 | Final exam |
| Course Notes/Textbooks | Sheldon Ross, Stochastic Processes, 2nd Edition (United States of America: John Wiley, 1995) ISBN-13: 978-0471120629 |
| Suggested Readings/Materials | Lawler G.F., Introduction to Stochastic Processes, 2. Baskı ( Chapman and Hall/CRC; 2006), ISBN-13:978-1584886518 |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments |
1
|
30
|
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
1
|
30
|
| Final Exam |
1
|
40
|
| Total |
| Weighting of Semester Activities on the Final Grade |
2
|
60
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
| 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 |
14
|
3
|
42
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
3
|
10
|
30
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
24
|
24
|
| Final Exam |
1
|
36
|
36
|
| Total |
180
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. |
X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. |
X | ||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. |
|||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. |
|||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
X | ||||
| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. |
|||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
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| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. |
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| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. |
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| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. |
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| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. |
|||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
|||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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