Syllabus Application
MATH 501
Analysis I
Faculty
Faculty of Engineering and Natural Sciences
Semester
Fall 2025-2026
Course
MATH 501 -
Analysis I
Time/Place
Time
Week Day
Place
Date
12:40-13:30
Wed
FENS-L029
Sep 29, 2025-Jan 3, 2026
13:40-15:30
Thu
FENS-L065
Sep 29, 2025-Jan 3, 2026
Level of course
Masters
Course Credits
SU Credit:3, ECTS:10
Prerequisites
-
Corequisites
-
Course Type
Lecture
Instructor(s) Information
Gökalp Alpan
- Email: gokalp.alpan@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.
Course Learning Outcomes:
| 1. | Use Caratheodery definition to construct Lebesgue-Stieltjes measure on the line and Lebesgue measure on any Euclidean space |
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| 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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