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Information
| Code | MT302 |
| Name | Measure Theory |
| Term | 2024-2025 Academic Year |
| Semester | 6. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ŞEHMUS FINDIK |
| Course Instructor |
1 2 |
Course Goal / Objective
The aim of this course is to introduce the Lebesgue integral within the Riemann integral which the students are already familiar with.
Course Content
In this course, measurable sets, measurable functions, measurement, integrable functions, Lebesgue integral are covered.
Course Precondition
None.
Resources
Lebesgue Measure and Integration (Lebesgue Ölçüsü ve İntegrali), P. K.; Gupta, V. P. and Jain, Pankaj (Translator: Tuncay Tunç)
Notes
Lebesgue Measure and Integration (Lebesgue Ölçüsü ve İntegrali), P. K.; Gupta, V. P. and Jain, Pankaj (In English)
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Identifies measurable sets. |
| LO02 | Defines measurable functions. |
| LO03 | Defines the concept of measurements. |
| LO04 | Defines the Lebesgue integral. |
| LO05 | Compares Lebesgue and Riemann integrals. |
| LO06 | Defines the Lebesgue spaces. |
| LO07 | Improves the ability of abstract thinking. |
| LO08 | Generalizes the Riemann integral. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 3 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 4 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 3 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 3 |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Measurable sets and measurable functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Properties of measurable functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap, Alıştırma ve Uygulama |
| 3 | Measurable sets and functions, problem solving | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Examples of measurements and measurement. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap, Alıştırma ve Uygulama |
| 5 | Solving problems on measurement. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap, Alıştırma ve Uygulama |
| 6 | Definition and properties of integrals. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Solving integral problems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Integrable functions and Lebesgue integral. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Comparison of the Lebesgue and Riemann integral. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Integrable functions, problem solving | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap, Alıştırma ve Uygulama |
| 12 | Lebesgue spaces. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Properties of Lebesgue spaces | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Lp spaces | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Problem solving. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||