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Information
| Unit | INSTITUTE OF SOCIAL SCIENCES |
| ECONOMETRICS (MASTER) (WITH THESIS) | |
| Code | IEM715 |
| Name | Introduction to Analysis |
| Term | 2022-2023 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ERSİN KIRAL |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
To provide the students with the necessary information in linear models and multivariate analysis
Course Content
Basic terms and concepts in the matrix theory, column space, null space, subspace, and Echelon form, type of mxn matrices g-inverse, solution of systems of equations, matrix derivative and properties of positive definit and nnd matrices.
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | understands the measure theory |
| LO02 | knows lebesgue integration of real and complex functions |
| LO03 | knows Riezs representation theorem which is one of the important theory of functional analysis and some results of it |
| LO04 | learns Lebesgue measure in Euclidean spaces |
| LO05 | knows Hahn-Banach theorem which is one of the important theory of Real analysis |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | definition of measures and elementary properties of measures | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 2 | Step and simple functions | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 3 | Integration of positive functions and integration and complex functions | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 4 | Topological preliminaries (Urysohn lemma and partition of unity) | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 5 | Riezs representation theorem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 6 | Regularity properties of Borel measures | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 7 | Lebesgue measures in Euclidean spaces | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Study the relevant sections in the textbook and solve problems | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Continuity properties of measurable functions | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 10 | convex functions and some inequalities | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 11 | Lp spaces | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 12 | Banach spaces | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 13 | Baires theorem and consequences of Baires theorem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 14 | Hahn-Banach theorem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 15 | Radon-Nikodym theorem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Study the relevant sections in the textbook and solve problems | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Study the relevant sections in the textbook and solve problems | Ölçme Yöntemleri: Yazılı Sınav |