| 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 |
| MAT5007 | Real Analysis | 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: | 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 |
| The topology of R, Cauchy sequences, The concepts of lower and upper limit, General topics on functions, Concepts of equivalent metrics, Complete metric spaces, Contractions, Normed vector spaces, Banach spaces, Fixed point theorem and its applications, Orthonormal spaces and introduction to Hilbert spaces. |
| Week | Subject | Related Preparation | |
| 1) | Topoloy of R | ||
| 2) | Cauchy sequences | ||
| 3) | Concepts of upper and lower limits | ||
| 4) | General topics on functions | ||
| 5) | Equivalent metrics | ||
| 6) | Complete metric spaces | ||
| 7) | Contraction mappings | ||
| 8) | Normed vector spaces | ||
| 9) | Normed vector spaces | ||
| 10) | Normed vector spaces | ||
| 11) | Banach spaces | ||
| 12) | Banach spaces | ||
| 13) | Fixed point theory and applications | ||
| 14) | Orthonormal spaces and introduction to the Hilbert spaces | ||
| Course Notes: | Real Analysis: Modern Techniques and Their Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts), Gerald B. Folland. |
| References: | . |
| 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 | 7 | % 30 |
| Presentation | 1 | % 30 |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | % 0 | |
| 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 | 16 | 3 | 48 |
| 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 | 0 | 0 | 0 |
| Presentations / Seminar | 1 | 40 | 40 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 7 | 14 | 98 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 0 | 0 | 0 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 14 | 14 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |