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 |
MAT6009 | Advanced Calculus I | Fall | 3 | 0 | 3 | 8 |
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 Riemann and Lebesgue integrals. He/She knows taking integrals by using definition of Lebesgue integral and its properties. |
Basic concepts, some important theorems and definitions on point sets, countability, measure theory, sets of measure zero, Lusin, Egoroff and Lebesgue theorems, unmeasurable sets, measurable functions, Riemann integral, applications of Lebesgue theory, general measure and integral theories. |
Week | Subject | Related Preparation | |
1) | Basic concepts, some important theorems on point sets. | ||
2) | Countability | ||
3) | Measure theory. | ||
4) | Measure theory (continue) | ||
5) | Sets of measure zero. | ||
6) | Lusin, Egoroff and Lebesgue theorems. | ||
7) | Unmeasurable sets. | ||
8) | Measurable functions, | ||
9) | Measurable functions(continue) | ||
10) | Riemann's integral, some applications of Lebesgue's theory. | ||
11) | Riemann's integral, some applications of Lebesgue's theory. | ||
12) | Theories of general measure and integral. | ||
13) | Theories of general measure and integral. | ||
14) | Theories of general measure and integral (continued) |
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 |