FACULTY OF ARTS AND SCIENCES
Department of Mathematics
SOCIAL MEDIA
MATH 314 | Course Introduction and Application Information
| Course Name |
Measure Theory
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 314
|
Fall/Spring
|
3
|
0
|
3
|
6
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
First Cycle
|
|||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | ||||||
| Course Objectives | This course aims to provide learning of measure theory which is one of the most essential tool for mathematics and statistics. The main concepts in this course are Lebesque measure and the Lebesque integral. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | The Riemann integral; Measure, null sets, outer measure; Lebesque measurable sets and Lebesque measure; Monotone convergence theorems; Integrable functions, The Dominated Convergence Theorem. |
|
|
Core Courses | |
| Major Area Courses |
X
|
|
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Notation and basic set theory, Sets and functions | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 1-30 |
| 2 | Countable and uncountable sets: examples. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 33 |
| 3 | The Riemann integral. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 88 |
| 4 | σ-algebra. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part II 216 |
| 5 | Measure, Null sets. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 61 |
| 6 | Outer measure. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 69 |
| 7 | Lebesque measurable sets. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 71 |
| 8 | Lebesque measure. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 71 |
| 9 | Borel sets, Measurable functions. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 65 |
| 10 | Lebesque Integral, Monotone Convergence Theorems. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 102-108 |
| 11 | Integrable functions, The Dominated Convergence Theorem. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part III 281 |
| 12 | Relation to the Riemann integral. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part I 88 |
| 13 | Banach spaces. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part II 235 |
| 14 | Duality, Distribution. | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 Part II |
| 15 | Semester Review | |
| 16 | Final Exam |
| Course Notes/Textbooks | "Real Analysis" by H.L. Royden, Prentice Hall, 3rd Edition, 1988. ISBN: 8120309731 |
| Suggested Readings/Materials |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
2
|
60
|
| Final Exam |
1
|
40
|
| Total |
| Weighting of Semester Activities on the Final Grade |
2
|
60
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
14
|
3
|
42
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
0
|
||
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
30
|
60
|
| Final Exam |
1
|
30
|
30
|
| Total |
180
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. |
X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. |
X | ||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. |
|||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. |
X | ||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
|||||
| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. |
|||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
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| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. |
|||||
| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. |
|||||
| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. |
X | ||||
| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. |
|||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
|||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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