EP30.FSF1107 — Real Analysis

This course provides a rigorous and comprehensive foundation in Real Analysis, emphasizing both theoretical depth and analytical rigor. The content is organized into four major components. The course begins with classical analysis on the real line, covering limits, continuity, differentiability, Riemann integration, and the fundamental concepts of compactness and completeness. It then introduces measure theory, including sigma-algebras, outer measures, the construction of the Lebesgue measure, measurable functions, the Lebesgue integral, and key convergence theorems.

The course further explores metric and normed spaces, focusing on metric topology, completeness, compactness, normed spaces, and Banach spaces. Building on this framework, students study spaces, including their definitions, fundamental inequalities such as Hölder’s and Minkowski’s inequalities, completeness, duality, and selected applications in probability theory and economics.

Real Analysis serves as a core course for advanced undergraduate and graduate-level study in mathematics and provides essential theoretical foundations for optimization, econometrics, probability theory, and related quantitative disciplines.

Requirements for taking final /terminal exams

Students are allowed to take the final exam if their attendance score reaches 5 points or more (on the scale of 10).

Requirements for attending classes

Students are responsible for attending all classes. In case of absence from school due to force majeure reasons, sufficient and reasonable proofs must be provided. For each absence, 1 point will be deducted 1 point. Students who miss any classes more than 3 times, with or without reason, will be considered as failing to complete the course and have to re-register.

Students will be awarded points for constructive comments, these points are added to attendance points and group assignments.

Groups who do not submit the group work will receive a score of 0 (zero). Late submissions will be deducted for each day of late submission.

Requirements for in-class behaviour

The course is conducted on the principle of respecting learners and lecturers. Any behaviour that affects the teaching and learning process is strictly prohibited.

Students must come to class on time. Students who are late more than 10 minutes after class starts will not be allowed to attend the class. Do not make noise and affect others during the learning process.

Laptops and tablets are only used for the purpose of taking notes for and calculating for lectures and exercises, absolutely forbidden to use for other purposes.