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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT432 |
| Name | Measure Theory |
| Term | 2018-2019 Academic Year |
| Semester | 8. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Üniversite Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ŞEHMUS FINDIK |
| Course Instructor |
Prof. Dr. ŞEHMUS FINDIK
(Bahar)
(A Group)
(Ins. in Charge)
|
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
Measurable sets, measurable functions, measurement, integrable functions, Lebesgue integral
Course Precondition
Resources
Lebesgue İntegral Kuramına Giriş, R.G. Bartle, Translate: Alev Topuzoğlu - Şafak Alpay
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Identifies measurable sets. |
| LO02 | Understands measurable functions. |
| LO03 | Defines measurements. |
| LO04 | Understands the Lebesgue integral. |
| LO05 | Understands the difference between Lebesgue and Riemann integrals. |
| LO06 | Defines the Lebesgue spaces. |
| LO07 | Improves the ability of abstract thinking. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | |
| PLO09 | - | Comprehends at least one of the computer programming languages. | |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | - | 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. | |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Measurable sets and measurable functions. | Review of the relevant pages from sources | |
| 2 | Properties of measurable functions. | Review of the relevant pages from sources | |
| 3 | Measurable sets and functions, problem solving | Review of the relevant pages from sources | |
| 4 | Examples of measurements and measurement. | Review of the relevant pages from sources | |
| 5 | Solving problems on measurement. | Review of the relevant pages from sources | |
| 6 | Definition and properties of integrals. | Review of the relevant pages from sources | |
| 7 | Solving integral problems | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | |
| 9 | Integrable functions and Lebesgue integral. | Review of the relevant pages from sources | |
| 10 | Comparison of the Lebesgue and Riemann integral | Review of the relevant pages from sources | |
| 11 | Integrable functions, problem solving | Review of the relevant pages from sources | |
| 12 | Lebesgue spaces. | Review of the relevant pages from sources | |
| 13 | Properties of Lebesgue spaces | Review of the relevant pages from sources | |
| 14 | Lp spaces | Review of the relevant pages from sources | |
| 15 | Problem solving. | Review of the relevant pages from sources | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |