ECTS - Introduction to Real Analysis
Introduction to Real Analysis (MATH351) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Introduction to Real Analysis | MATH351 | 5. Semester | 4 | 0 | 0 | 4 | 7 |
| Pre-requisite Course(s) |
|---|
| MATH136 |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | The aim of the course is providing a familiarity to concepts of the real analysis, such as, limit, continuity, differentiation, connectedness, compactness, convergence etc. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | A review of sets and functions, real numbers (or system), countable and uncountable sets, sequences of real Numbers (Cauchy sequences), Uniform Convergence of Sequences of functions, Metric Spaces, Compactness and Connectedness, Contraction Mapping Theorem, Arzela-Ascoli Theorem, Extension Theorem fo Tietze, Baire?s Theorem. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Real Number System: Axioms, Some Consequences of the Least Upper Bound Property | Read the related pages in the text book |
| 2 | Absolute value and intervals, Sequences of Real Numbers | Read the related pages in the text book |
| 3 | Accumulation Points: Theorems of Bolzano and Weierstras | Read the related pages in the text book |
| 4 | Limit Superior and Inferior | Read the related pages in the text book |
| 5 | Metric Spaces: Examples, Open and Closed Subsets | Read the related pages in the text book |
| 6 | Sequences in a Metric Space | Read the related pages in the text book |
| 7 | Midterm Exam | |
| 8 | Contiunity of Functions, Cartesian Product of Metric Spaces | Read the related pages in the text book |
| 9 | Completion of a Metric Space | Read the related pages in the text book |
| 10 | Compactness and Connectedness: Compact Sets, Compactness and Convergence of Sequences | Read the related pages in the text book |
| 11 | Continuity and Compactness, Connectedness | Read the related pages in the text book |
| 12 | Connected Components | Read the related pages in the text book |
| 13 | Applications: Contraction Mapping Theorem | Read the related pages in the text book |
| 14 | The Arzela-Ascoli Theorem, Extension Theorem of Tietze | Read the related pages in the text book |
| 15 | Baire’s Theorem | Read the related pages in the text book |
| 16 | Final |
Sources
| Other Sources | 1. An introduction to Real Analysis, T. Terzioğlu, Matematik Vakfı. |
|---|---|
| 2. Real Analysis, H. L. Royden, Prentice-Hall | |
| Course Book | 3. Principles of Mathematical Analysis, W. Rudin, 3rd Edition 1976, McGraw-Hill Inter. Edit. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | - | - |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 60 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 3 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | |||
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | |||
| Prepration of Final Exams/Final Jury | |||
| Total Workload | 0 | ||