GRADUATE SCHOOL
M.SC. in Computer Engineering (Without Thesis)
STAT 562 | Course Introduction and Application Information
| Course Name |
Combinatorial Analysis and Discrete Distributions
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
STAT 562
|
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 | - | |||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | - | |||||
| Course Objectives | The course aims to provide basic combinatorical methods used in probability theory and illustrates many definitions of combinatorial analysis for students who would like to focus on discrete random events and their distributions. The course aims to discuss many univariate and multivariate discrete distributions. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | Pigeonhole Principle, Permutations, Combinations, The Binomial Coefficients, Discrete random variables with their probability distributions, The inclusionExclusion Principle and Applications, Recurrence Relations and Generating Functions. |
|
|
Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | What is Combinatorics? | Introductory Combinatorics Prentice Hall: Chapter 1, (4:26) |
| 2 | Permutations, combinations and finite probability | Introductory Combinatorics Prentice Hall:, (44:71) |
| 3 | The Pigeonhole Prinicple | Introductory Combinatorics Prentice Hall: (26:39) |
| 4 | Generating Permutations and Combinations | Introductory Combinatorics Prentice Hall: (83:94) |
| 5 | Applications of permutations and combinations in probability | |
| 6 | Partial orders and equivalence relations | Introductory Combinatorics Prentice Hall: (106:117) |
| 7 | The Binomial Theorem, The multinomial theorem, partially ordered sets | Introductory Combinatorics Prentice Hall:, (124:147) |
| 8 | Midterm Exam | |
| 9 | The Inclusion Exclusion Principle | Introductory Combinatorics Prentice Hall: (160:185) |
| 10 | The Inclusion Exclusion Principle | Introductory Combinatorics Prentice Hall: (160:185) |
| 11 | Recurrence relations and generating functions | |
| 12 | Axioms of probability | A first course in Probability by S.Rosse, Prentice Hall: (24:64) |
| 13 | Discrete random variables | A first course in Probability by S.Rosse, Prentice Hall: (122:166) |
| 14 | Runs and tests of randomness | Nonparametric Statistical Inference by J.D. Gibbons, S. Chakraborti, CRC Press: (75:96) |
| 15 | Review | |
| 16 | Review |
| Course Notes/Textbooks | Introductory Combinatorics by Richard A.Brualdi, Prentice Hall |
| Suggested Readings/Materials | A first course in Probability, S. Ross, Prentice Hall. Nonparametric Statistical Inference, J.D. Gibbons, S. Chakraborti, CRC Press |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments |
2
|
10
|
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
2
|
50
|
| Final Exam |
1
|
40
|
| Total |
| Weighting of Semester Activities on the Final Grade |
60
|
|
| Weighting of End-of-Semester Activities on the Final Grade |
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 |
15
|
6
|
90
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
2
|
6
|
12
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
20
|
40
|
| Final Exam |
1
|
35
|
35
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information. | X | ||||
| 2 | Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations. | X | ||||
| 3 | Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines. | X | ||||
| 4 | Is informed about new and upcoming applications in the field and learns them whenever necessary. | X | ||||
| 5 | Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions. | X | ||||
| 6 | Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs. | X | ||||
| 7 | Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process. | X | ||||
| 8 | Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility. | X | ||||
| 9 | Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale. | X | ||||
| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. | X | ||||
| 11 | Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications. | X | ||||
| 12 | Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest