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	-
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Prof. Dr. İsmihan BAYRAMOĞLU
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

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	will be able to solve counting problems using permutations and combinations
2	will be able to solve problems using the Pigeonhole Principle
3	will be able to use the Binomial and Multinomial Theorems
4	will be able to use the inclusion and excluison principle to solve problems
5	will be able to construct recurrence relations
6	will be able to solve recurrence relations
7	will be able to use moment generating functions to solve problems
8	will be able to use discrete random variables and their distributions

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.

Course Category	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	Learning Outcome
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	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6	LO 7	LO 8
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

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	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	-	-	-