| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT3002 | Real Analysis II | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MAHMOUD JAFARI SHAH BELAGHI |
| Course Objectives: | The aim of the course is to give to the student to learn enough examples, theorems and techniques in analysis to be well prepared for the standart graduate courses in topology, measure theory and functional analysis. |
|
The students who have succeeded in this course; Able to use the basic examples, theorems and techniques for the standart graduate courses in topology, measure theory and functional analysis |
| Abstract measure space, Sigma-additivity;measurable functions and its properties; integral in an abstract measure space and its properties; general convergence theorems; signed measure, Hahn decomposition theorem; absolutely continuous measure, singular measure; The Radon-Nikodym theorem; Lebesque decomposition theorem; Lp- spaces; outer measure, The extension of measure; inner measure, various convergence types; Fourier series and Fourier integral |
| Week | Subject | Related Preparation | |
| 1) | Abstract measure space, Sigma-additivity | ||
| 2) | measurable functions and its properties | ||
| 3) | integral in an abstract measure space and its properties | ||
| 4) | integral in an abstract measure space and its properties | ||
| 5) | general convergence theorems | ||
| 6) | signed measure, Hahn decomposition theorem | ||
| 7) | Hahn decomposition theorem | ||
| 8) | absolutely continuous measure, singular measure | ||
| 9) | The Radon-Nikodym theorem | ||
| 10) | Lebesque decomposition theorem | ||
| 11) | Lp spaces | ||
| 12) | outer measure, The extension of measure | ||
| 13) | inner measure, various convergence types | ||
| 14) | Fourier series and Fourier integral | ||
| 15) | Final exam | ||
| 16) | Final exam | ||
| Course Notes: | “ Introductory real analysis” A. N. Kolmogorov, S. V. Fomin, translated and edited by Richard A. Silverman, Dover Publishing (1975) |
| References: | "Real & Complex Analysis", Rudin, W., McGraw-Hill (1986); “Real analysis”, H.L. Royden, MacMillan Publishing Company (1988); "Real Analysis: Modern Techniques and Their Applications " Gerald B. Folland, Wiley Publishing Company (1999) |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 16 | % 0 |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 5 | % 10 |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 50 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 5 | 2 | 10 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 15 | 30 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 15 | 15 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |