Mathematics (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH122

Course Name:

Combinatorics and Probability

Semester:

Spring

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Araş. Gör. GAMZE AKAR UYSAL

Course Lecturer(s):

Asst. Prof. Dr. Doğa Can Sertbaş

Course Assistants:

Course Objective and Content

Course Objectives:	The course aims to teach fundamental concepts related to counting techniques and probability theory, and to gain the ability to use these concepts in solving problems in advanced areas of mathematics.
Course Content:	The content of the course consists of the basic principle of counting, permutations, combinations, the binomial theorem, inclusion-exclusion and pigeonhole principles, recurrence relations, generating functions, basic probability theory, conditional probabilities, Bayes’ formula and independent events.

Learning Outcomes

The students who have succeeded in this course;
1) Use the concepts of permutation and combination to solve counting problems
2) Understand methods for the calculation of the coefficients using the binomial theorem.
3) Applies the fundamental principles of combinatorics to counting problems.
4) Calculates the general formula of recurrence relations, such as Fibonacci numbers.
5) Comprehends the fundamental topics in probability theory, such as conditional probability and independent events.

Course Flow Plan

Week	Subject	Related Preparation
1)	The basic principle of counting, sets and the number of subsets
2)	Permutations and the number of ordered subsets
3)	Combinations and the number of subsets of a given size
4)	Binomial coefficients and the Pascal’s triangle
5)	Inclusion-exclusion and the pigeonhole principles
6)	Recurrence relations
7)	Generating functions
8)	Midterm Exam
9)	Sample space and events
10)	Axioms of probability
11)	Sample spaces having equally likely outcomes
12)	Conditional probabilities
13)	Bayes’ Formula
14)	Independent events

Sources

Course Notes / Textbooks:	Grimaldi, R. P., Discrete and Combinatorial Mathematics: An Applied Introduction, 5th ed., 1999, Pearson Addison-Wesley. Ross, S. M., A First Course in Probability, 8th ed., ISBN-13: 978-0-13-603313-4, 2010, Pearson Prentice Hall.
References:	L. Lovász, J. Pelikán and K. Vesztergombi, “Discrete Mathematics, Elementary and Beyond,” Springer-Verlag, New York, 2003; R. L. Graham, D. E. Knuth and O. Patashnik, “Concrete Mathematics: A Foundation for Computer Science,” Addison-Wesley Publishing Company, Boston, 1989.

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	2
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.	3
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.	3
4)	Have the ability to think analytically and use the time effectively in the process of deduction.	3
5)	Have the ability to search the literature, understand and interpret scientific articles.
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Application	13	0	1		13
Study Hours Out of Class	13	0	4		52
Midterms	1	0	15		15
Final	1	0	25		25
Total Workload					144