MAT5007 Real AnalysisBahçeşehir UniversityDegree Programs APPLIED MATHEMATICS (TURKISH, NON-THESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
APPLIED MATHEMATICS (TURKISH, NON-THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5007 Real Analysis Fall 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Assoc. Prof. ERSİN ÖZUĞURLU
Recommended Optional Program Components: 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 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.

Weekly Detailed Course Contents

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

Sources

Course Notes / Textbooks: Real Analysis: Modern Techniques and Their Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts), Gerald B. Folland.
References: .

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 7 % 30
Presentation 1 % 30
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 16 3 48
Presentations / Seminar 1 40 40
Homework Assignments 7 14 98
Final 1 14 14
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To apply mathematical principles to real world problems.
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.