Syllabus Application
Introduction to Mathematical Analysis
MATH 301
Faculty:
Faculty of Engineering and Natural Sciences
Semester:
Fall 2025-2026
Course:
Introduction to Mathematical Analysis - MATH 301
Classroom:
FENS-G032,FENS-L045
Level of course:
Undergraduate
Course Credits:
SU Credit:3.000, ECTS:6, Basic:6
Prerequisites:
-
Corequisites:
MATH 301R
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 and understand definitions, theorems, proofs. |
| 3. | Produce their "own" proofs in some cases. |
| 4. | Comprehend the structure of real numbers and the Euclidean space. Comprehend the basic theorems of Calculus. |
| 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.
Course Materials
Resources:
-
Technology Requirements:
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