MAT5017 ProbabilityBahçeşehir UniversityDegree Programs APPLIED MATHEMATICS (TURKISH, NON-THESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
APPLIED MATHEMATICS (TURKISH, NON-THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5017 Probability Fall 3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Dr. GENCO FAS
Recommended Optional Program Components: None
Course Objectives: The course will provide an introduction to stochastic processes for whose applications in engineering, managerial sciences and service sector are described. M

Learning Outcomes

The students who have succeeded in this course;
Students will be learned stochastic modelling and processes

Course Content

Markov chains and Poisson Processes follow a brief review of fundamentals of probability. Besides; renewal, regenerative and queueing processes are mentioned. Inventory control and finance are two additonal topics to the course.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Introduction: Fundamental concepts of probability
2) Some Basic Discrete and Continuous Distributions
3) Introduction to Stochastic Processes, Definitions, Conditional Expectation and Variance.
4) Branching Processes
5) Two-dimensional Random Walk and Bernoulli Processes
6) Discrete-time Markov Chains (Definitions, Classifications, Transition Matrix)
7) Limiting and Stationary Distributions
8) Exponential Distribution
9) Poisson Processes
10) Continuous-time Markov Chains
11) Limiting Probabilities, Hitting Probabilities and Times
12) Queueing Theory
13) Little's Law and Applications
14) Introduction to Brownian Motion

Sources

Course Notes / Textbooks: Introduction to Probability Models, Sheldon Ross, Academic Press, 9th Edition
References: Probability and Statistics for Engineers and Scientists, Walpole, Myers, Myers, Ye, Prentice Hall, 8th edition.

Introduction to Probability, Bertsekas, Tsitliklis

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 14 % 10
Quizzes 2 % 10
Homework Assignments 2 % 10
Midterms 1 % 30
Final 1 % 40
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 9 126
Presentations / Seminar 2 2 4
Homework Assignments 3 8 24
Midterms 1 2 2
Final 1 2 2
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To apply mathematical principles to real world problems.
11) 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.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.