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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5059 REAL ANALYSIS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics (English) Mathematics (English)

Course Objective

The aim of the course is to introduce the basic concepts of Maesure Theory, Lebesgue integral and differentiation.

Learning Outcomes of the Course Unit

1   willbe able to understan Lebesgue Measure. 2   will be able to understand measurable functions. 3   will be able to understand Lebesgue integral. 4   will be able to relate Differentiation and integration. 5   will be able to understand L_p spaces.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Review for Riemann integrability 2 General measure theory. 3 Lebesgue measure. 4 Examples of measurable sets. 5 Approximation of measurable sets. 6 Measurable functions. 7 Modes of convergence. Egorov s Theorem. 8 Midterm 9 Lebesgue integral 10 Differentiation of Monotone functions. 11 Differentiation of an integral. 12 Lebesgue Decomposition Theorem. 13 Classical Banach spaces, L_p. 14 Riesz Represantation Theorem.

Recomended or Required Reading

Textbook(s): Real Analysis, 3rd Edition; H.L. Royden, Macmillan Publishing Company, 1988. Supplementary Book(s): The Elements of Integration and Lebesgue Measure, Robert G. Bartle, John Wiley & Sons, 1995. References: Introductory Real Analysis, A. N. Kolmogorov, S.V. Fomin, Dover Publications, 1970.

Planned Learning Activities and Teaching Methods

Lecture Notes Text Book(s) Solving Problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

To be announced.

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 6 78 Preparation for midterm exam 1 15 15 Preparation for final exam 1 24 24 Final 1 3 3 Midterm 1 3 3 Project Assignment 4 3 12 TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 5 5 5 5 5 5 5 5 LO.2 5 5 5 5 5 5 5 5 LO.3 5 5 5 5 5 5 5 5 LO.4 5 5 5 5 5 5 5 5 LO.5 5 5 5 5 5 5 5 5