MATHEMATICS (TURKISH, PHD)
PhD	TR-NQF-HE: Level 8	QF-EHEA: Third Cycle	EQF-LLL: Level 8

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT6010	Advanced Calculus II	Fall Spring	3	0	3	8

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 :	Assoc. Prof. ERSİN ÖZUĞURLU
Recommended Optional Program Components:	None
Course Objectives:	To teach fundamental concepts of real analysis, teaching fundamental proof methods, to gain ability of solving theoretical questions.

Learning Outcomes

The students who have succeeded in this course;
He/She knows measure spaces and measurable functions.
He/She knows convergence theorems.
He/She knows Bounded variation space.
He /She knows Lp spaces.
He/She knows outer measures.
He/She knows Lebesgue-Stieltjes integral.
He/She recodnise integral operators.
He/She knows Caratheodory outer measure.

Course Content

Measure Spaces, measurable sets, integration, general convergence theorems, bounded variation space, Lp spaces, outer measure and measurability, extension theorem, Lebesgue_Stieltjes integral, product measures, integral operators, extension with null sets, Caratheodory outer measure, Haussdorff measures.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Measure spaces.
2)	Measurable functions, integration.
3)	General convergence theorems.
4)	Space of bounded variation.
5)	Radon-Nikodym Theorem, Lp Spaces.
6)	Radon-Nikodym Theorem, Lp Spaces (continued)
7)	Outer measure and measurability.
8)	Extension theorem.
9)	Lebesgue-Stieltjes integral.
10)	Product measures.
11)	Integral operators
12)	Integral operators (continued)
13)	extension with null sets.
14)	Caratheodory outer measure

Sources

Course Notes / Textbooks:	Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 1999, Wiley Publications.
References:	H. L. Royden, Real Analysis, 1988, Prentice-Hall, Inc. So Bon Chae, Lebesgue integration, 1998, Springer Verlag. A. N. Kolmogorov, S. V. Fomin, Introductory Real Analysis 2000, Dover Publications. Paul R. Halmos, Measure Theory, 1978, Springer Verlag.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Project	1	% 20
Midterms	1	% 30
Final	1	% 50
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 30
PERCENTAGE OF FINAL WORK		% 70
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	3	42
Project	1	60	60
Midterms	1	26	26
Final	1	30	30
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.	5
2)	Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.	5
3)	Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.	5
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.	4
6)	Ability to use mathematical knowledge in technology.
7)	To apply mathematical principles to real world problems.	4
8)	Ability to use the approaches and knowledge of other disciplines in Mathematics.	4
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.	5
10)	To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data.	4
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.	5
12)	To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.	5