Syllabus Application
MATH 571
Introduction to Mathematical Analysis
Faculty
Faculty of Engineering and Natural Sciences
Semester
Fall 2026-2027
Course
MATH 571 -
Introduction to Mathematical Analysis
Time/Place
Time
Week Day
Place
Date
10:40-12:30
Thu
FENS-L045
Sep 28-Dec 31, 2026
10:40-11:30
Fri
FASS-G062
Sep 28-Dec 31, 2026
Level of course
Masters
Course Credits
SU Credit:3, ECTS:10
Prerequisites
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Corequisites
MATH 571R
Course Type
Lecture
Instructor(s) Information
Dimitrios Papathanasıou
Course Information
Catalog Course Description
The least upper bound property in R, equivalents and consequences. Metric spaces. Completeness, compactness, connectedness. Functions,continuity. Sequences and series of functions. Contraction mapping theorem and applications to calculus: Inverse and implicit function theorems.
Learning Outcomes:
| 1. | Comprehend the language of analysis |
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| 2. | Read definitions, theorems, proofs. |
| 3. | Produce "own" proofs in simpler cases. |
| 4. | Comprehend the structure of real numbers and the Euclidean space. |
| 5. | Comprehend the topology of the Euclidean space. |
| 6. | Comprehend the notion and use the facts of continuity. |
| 7. | Comprehend the notion and use the facts of differentiability. |
| 8. | Comprehend the notion and use the inverse and implicit function theorems. |
| 9. | Comprehend the notion and use the facts of Riemann integrals. |
Course Objective
Learning the basics of mathematical analysis; i.e. basic theorems and basic techniques in analysis.
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