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Information
| Code | IEM715 |
| Name | Introduction to Analysis |
| Term | 2022-2023 Academic Year |
| Semester | . Semester |
| 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 | Doç. Dr. ERSİN KIRAL |
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 |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explains contemporary concepts about Econometrics, Statistics, and Operation Research | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Explains relationships between acquired knowledge about Econometrics, Statistics, and Operation Research | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explains how to apply acquired knowledge in the field to Economics, Business, and other social sciences | |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Performs conceptual analysis to develop solutions to problems | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Models problems with Mathematics, Statistics, and Econometrics | |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Interprets the results obtained from the most appropriate method to predict the model | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Synthesizes the information obtained by using different sources within the framework of academic rules in a field that does not research | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Searches for new approaches and methods to solve problems being faced | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Presents analysis results conveniently | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Collects/analyzes data in a purposeful way | |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Converts its findings into a master's thesis or a professional report in Turkish or a foreign language | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Develops solutions for organizations using Econometrics, Statistics, and Operation Research | |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs an individual work to solve a problem with Econometrics, Statistics, and Operation Research | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads by taking responsibility individually and/or within the team | |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it constantly renews itself by following the current developments in the field of study | |
| PLO17 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code | |
| PLO18 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Interprets the feelings, thoughts and behaviors of the related persons correctly/expresses himself/herself correctly in written and verbal form | |
| PLO19 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues | |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values |
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 |