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 |
MAT6010 | Advanced Calculus II | Fall | 3 | 0 | 3 | 12 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
Course Objectives: | To teach fundamental concepts of real analysis, teaching fundamental proof methods, to gain ability of solving theoretical questions. |
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. |
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. |
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 |
Course Notes: | 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. |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | % 0 | |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | % 0 | |
Homework Assignments | % 0 | |
Presentation | % 0 | |
Project | 1 | % 20 |
Seminar | % 0 | |
Midterms | 1 | % 30 |
Preliminary Jury | % 0 | |
Final | 1 | % 50 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 30 | |
PERCENTAGE OF FINAL WORK | % 70 | |
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 | 3 | 42 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 1 | 60 | 60 |
Homework Assignments | 0 | 0 | 0 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 1 | 26 | 26 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 30 | 30 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |