Course Name Code Semester T+U Hours Credit ECTS
Advanced Analysis II MAT 006 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses <p>Advanced Analysis I</p>
Course Language Turkish
Course Level Doctorate Degree
Course Type Compulsory
Course Coordinator Prof.Dr. METİN BAŞARIR
Course Lecturers Prof.Dr. METİN BAŞARIR,
Course Assistants
Course Category Available Basic Education in the Field
Course Objective

The aim of this course is to give some concepts which are related to Phd level in Mathematics.

Course Content

Lp spaces, Convergence types, Convergence in Lp spaces, Convergence in Measure spaces, Derivative and Anti-derivative ( Integral of monotone functions, The functions of bounded vibrations, The derivative of anti-derivative, Absolute continuity)

# Course Learning Outcomes Teaching Methods Assessment Methods
1 Lp and L inifinite spaces knowing Lecture, Question-Answer, Drilland Practice, Testing, Homework,
2 Convergence types knowing Lecture, Question-Answer, Drilland Practice, Testing, Homework,
3 The relations of derivative and integral knowing Lecture, Question-Answer, Drilland Practice, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Preliminaries
2 Lp spaces
3 Some inequalities
4 Riesz-Fischer theorem
5 L infinite space
6 The concept of convergence
7 Convergence in Lp
8 The convergence in measure spaces
9 Mid Exam
10 Differential and integral
11 Integral of monotone functions
12 The functions of bounded vibrations
13 The derivations of anti-derivative
14 Absolute continuity
Course Notes
Course Resources

1- R.G.Bartle, The elements of real analysis, John Wiley and Sons, New York, 1964.

2- H.L.Royden, Real Analysis, MacMillan, New York, 1968.

3-P.R.Halmos, Measure Theory, Princeton, Springer, 1974.

4- S.K.Barberian, Measure and Integration, MacMillan, New York, 1965.

5- M.Balcı, Reel Analiz, Balcı Yayınları, , Ankara, 2000.

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 60
1. Ödev 20
1. Kısa Sınav 10
2. Ara Sınav 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Quiz 1 10 10
Assignment 1 4 4
Final examination 1 25 25
Total Workload 155
Total Workload / 25 (Hours) 6.2
dersAKTSKredisi 6