Syllabus ( MATH 303 )
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Basic information
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Course title: |
Real Analysis I |
Course code: |
MATH 303 |
Lecturer: |
Prof. Dr. Emil NOVRUZ
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ECTS credits: |
7 |
GTU credits: |
3 (3+0+0) |
Year, Semester: |
3, Fall |
Level of course: |
First Cycle (Undergraduate) |
Type of course: |
Compulsory
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Language of instruction: |
English
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Mode of delivery: |
Face to face
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Pre- and co-requisites: |
Math 111 or Math 101 |
Professional practice: |
No |
Purpose of the course: |
To introduce the concepts of Lebesgue and Measure Integral. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Explain measurable sets and Lebesgue measure.
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
Method of assessment
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Written exam
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Explain the Lebesque integration.
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
Method of assessment
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Written exam
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Distinguish the relationship between Lebesgue and Riemann integral .
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
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Exhibiting professional and ethical responsibility.
Method of assessment
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Written exam
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Contents
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Week 1: |
Real number sets |
Week 2: |
Outer measure and its properties,algebra of measurable sets |
Week 3: |
Lebesque Measure, Borel sets |
Week 4: |
Measurable functions and its properties |
Week 5: |
Egoroff and Lusin theorems |
Week 6: |
Convergence in terms of measure. |
Week 7: |
The Lebesque integral and properties. |
Week 8: |
Passage to the limit in the integral |
Week 9: |
Lebesque’s, Fatou’s and Levi’s theorems. Midterm Exam. |
Week 10: |
Comparison of the Lebesque and Riemann integrals |
Week 11: |
Product measures, Fubini’s theorem |
Week 12: |
Monotone functions, bounded variation and absolutely continuous functions |
Week 13: |
Absolutely continuity of Lebesque integral |
Week 14: |
Construction of a function depending on its derivative |
Week 15*: |
- |
Week 16*: |
Final exam |
Textbooks and materials: |
H.L. Royden, “Real analysis”; “ Introductory real analysis” A. N. Kolmogorov, S. V. Fomin translated and edited by Richard A. Silverman. |
Recommended readings: |
“Elements of real analysis” David A. Sprecher.; “Introduction to real analysis” , Robert G. Bartle, Donald R. Sherbert. |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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Method of assessment |
Week number |
Weight (%) |
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Mid-terms: |
9 |
40 |
Other in-term studies: |
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0 |
Project: |
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0 |
Homework: |
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0 |
Quiz: |
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0 |
Final exam: |
16 |
60 |
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Total weight: |
(%) |
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Workload
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Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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Courses (Face-to-face teaching): |
3 |
14 |
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Own studies outside class: |
5 |
14 |
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Practice, Recitation: |
0 |
0 |
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Homework: |
0 |
0 |
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Term project: |
0 |
0 |
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Term project presentation: |
0 |
0 |
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Quiz: |
0 |
0 |
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Own study for mid-term exam: |
12 |
3 |
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Mid-term: |
2 |
1 |
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Personal studies for final exam: |
12 |
2 |
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Final exam: |
2 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
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