Syllabus Application
Introduction to Mathematical Analysis
MATH 571
Faculty:
Faculty of Engineering and Natural Sciences
Semester:
Fall 2025-2026
Course:
Introduction to Mathematical Analysis - MATH 571
Classroom:
FENS-G032,FENS-L045
Level of course:
Masters
Course Credits:
SU Credit:3.000, ECTS:10
Prerequisites:
-
Corequisites:
MATH 571R
Course Type:
Lecture
Instructor(s) Information
Nihat Gökhan Göğüş
- Email: nggogus@sabanciuniv.edu
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.
Course Learning Outcomes:
| 1. | Comprehend the language of analysis |
|---|---|
| 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.
We learn already in high school that integration plays a central role in mathematics and physics. One encounters usual Riemann integrals in the notions of area or volume, when solving a differential equation, in the fundamental theorem of calculus, in Stokes' theorem, or in classical and quantum mechanics. One purpose of this course is to introduce more advanced tools and notions of Mathematics such as metric spaces, uniform convergence of sequence of functions and their relation with differentiation and integration.
Course Materials
Resources:
Michael C. Reed, Fundamental Ideas of Analysis, John Wiley & Sons, Inc., 1998. We will cover the first 6 chapters, we will skip some sections. Detailed weekly schedule is at the end of the syllabus.
Technology Requirements:
None.