Syllabus Application
MATH 501
Analysis I
Faculty
Faculty of Engineering and Natural Sciences
Semester
Fall 2026-2027
Course
MATH 501 -
Analysis I
Time/Place
Time
Week Day
Place
Date
12:40-13:30
Mon
FENS-L058
Sep 28-Dec 31, 2026
09:40-11:30
Wed
FENS-L065
Sep 28-Dec 31, 2026
Level of course
Masters
Course Credits
SU Credit:3, ECTS:10
Prerequisites
-
Corequisites
-
Course Type
Lecture
Instructor(s) Information
Nihat Gökhan Göğüş
- Email: nggogus@sabanciuniv.edu
Course Information
Catalog Course Description
Lebesgue measure and integration on the line. Convergence theorems. General measure and integration. Lp spaces. Decomposition of measures. Radon Nikodym theorem. Product measures and Fubini's theorem.
Learning Outcomes:
| 1. | Use Caratheodery definition to construct Lebesgue-Stieltjes measure on the line and Lebesgue measure on any Euclidean space |
|---|---|
| 2. | Define and use convergence theorems |
| 3. | Define the Lebesgue Integral |
| 4. | Use Radon Nikodym theorem, product measures and Fubini's theorem to evaluate integrals. |
Course Objective
To teach the Measure Theory and Lebesgue Integration, together with some basic aplications to and connections with other parts of Analysis.
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Course Materials
Resources:
R. L. Wheeden, A. Zygmund, Measure and integral. An introduction to real analysis, 2nd ed. (2015) Taylor & Francis Group, LLC. We will cover Chapters 1-8 and Chapter 10.
W. Rudin, Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987. xiv+416 pp. ISBN: 0-07-054234-1
W. Rudin, Principles of mathematical analysis. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York-Auckland-Düsseldorf, 1976.
W. Rudin, Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987. xiv+416 pp. ISBN: 0-07-054234-1
W. Rudin, Principles of mathematical analysis. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York-Auckland-Düsseldorf, 1976.