BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT3001 | Real Analysis I | Fall | 3 | 0 | 3 | 5 |
Basic information
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MOHAMED KHALIFA |
| Recommended Optional Program Components: | There is none. |
| 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. |
Learning Outcomes
|
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 |
Course Content
| The topology of IR, 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. |
Weekly Detailed Course Contents
| Week | Subject | Related Preparation |
| 1) | Topology of real numbers | |
| 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) | Banach spaces | |
| 11) | Banach spaces | |
| 12) | Fixed point theory and applications | |
| 13) | Orthonormal spaces and introduction to the Hilbert spaces | |
| 14) | Orthonormal spaces and introduction to the Hilbert spaces |
Sources
| Course Notes / Textbooks: | Royden, H. L. “Real Analysis”, 3rd ed. MacMillan Publishing Company (1988) |
| References: | . |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Quizzes | 5 | % 15 |
| Midterms | 2 | % 45 |
| Final | 1 | % 40 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 1 | 14 |
| Quizzes | 5 | 1 | 5 |
| Midterms | 2 | 10 | 20 |
| Final | 1 | 19 | 19 |
| Total Workload | 100 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |