ECTS - Stochastic Processes
Stochastic Processes (MATH495) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Stochastic Processes | MATH495 | Elective Courses | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH392 |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | This course is intended primarily for the student of mathematics, physics or engineering who wishes to learn the notion of stochastic processes and get familiar with their common applications. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Basic notions of probability theory; reliability theory; notion of a stochastic process; Poisson processes, Markov chains; Markov decision processes. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Preliminaries: Probability, random events and random variables. Independence. | pp. 1 - 10 |
| 2 | Classical probability distributions, their properties. Random vectors. Coditional distribution and conditional expectation. | pp. 11 -14 |
| 3 | Reliability theory. Finding reliability function for different systems. Redundancy. | [1], pp. 29-33,pp 124-135. |
| 4 | Hazard rate function, the mean time to failure. | [1], pp. 228-236 |
| 5 | Definition and examples of stochastic processes, their types. | pp. 26-27, [1], pp. 294-300 |
| 6 | The Bernoulli and Poisson processes. Interarrival and waiting times. | pp. 31-36 |
| 7 | Non-homogeneous and compound Poisson processes. Midterm I | pp. 46 - 49 |
| 8 | Renewal processes. Erlang process. Renewal theorems. | pp. 55-60 |
| 9 | Markov chains: Markov property, transition probabilities, transition graph. The Chapman-Kolmogorov equations.Computation of n-th step transition probabilities. | pp. 100-103 |
| 10 | Classification of states and limiting probabilities. Equlibrium. | pp. 104-110 |
| 11 | Absorbing Markov chains. Fundamental matrix. | [1], pp. 392-402 |
| 12 | Midterm II. Continuous-time Markov chains. Kolmogorov’s equations. | pp.141-150 |
| 13 | Time reversibility. | pp. 156-158 |
| 14 | Applications of Markov chains. | pp. 118-122 |
| 15 | Review. | |
| 16 | Final exam. |
Sources
| Course Book | 1. Sheldon M. Ross, Stochastic processes, Wiley, 1983. |
|---|---|
| Other Sources | 2. K. S. Trivedi, Probability and Statistics with Reliability, Queueing, and Computer Science Applications, 2nd Edition, Wiley, 2002. |
| 3. J. G. Kemeny and J. L. Snell, Finite Markov chains, Springer, 1976. | |
| 4. S. Karlin, H. M. Taylor, A first course in stochastic processes, 2-nd Ed, Academic Press, 1975. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 4 | 20 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 40 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | |
|---|---|
| Percentage of Final Work | 100 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 3 | 48 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 4 | 10 | 40 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 12 | 24 |
| Prepration of Final Exams/Final Jury | 1 | 18 | 18 |
| Total Workload | 130 | ||