To improve the problem solving skills in the field of basic analysis of the students.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
S. Axler, Measure, Integration & Real Analysis, Springer, 2020.
Other Sources
G. Folland, Real Analysis: Modern Techniques and Their Applications.
K. Rana, An Introduction to Measure and Integration, Second Edition, Narosa, 2005.
H. L. Royden, Real Analysis, Third edition, Prentice-Hall of India, 1995.
W. Rudin, Real and Complex Analysis, Third edition, McGraw-Hill, International Editions, 1987.
T. Tao, An Introduction to Measure Theory, Graduate Studies in Mathematics, AMS, 2011.
Course Schedules
Week
Contents
Learning Methods
1. Week
Review: Riemann Integral
Oral presentation and applications
2. Week
Measures: Outer Measure on R
Oral presentation and applications
3. Week
Measurable Spaces and Functions
Oral presentation and applications
4. Week
Measures and Their Properties
Oral presentation and applications
5. Week
Lebesgue Measure
Oral presentation and applications
6. Week
Convergence of Measurable Functions
Oral presentation and applications
7. Week
Convergence of Measurable Functions
Oral presentation and applications
8. Week
Integration with Respect to a Measure
Oral presentation and applications
9. Week
Limits of Integrals & Integrals of Limits
Oral presentation and applications
10. Week
Hardy–Littlewood Maximal Function
Oral presentation and applications
11. Week
Derivatives of Integrals
Oral presentation and applications
12. Week
Products of Measure Spaces
Oral presentation and applications
13. Week
Iterated Integrals
Oral presentation and applications
14. Week
Lebesgue Integration on Rn
Oral presentation and applications
15. Week
Final Exam
Exam
16. Week
Final Exam
Exam
17. Week
Final Exam
Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Homework / Term Projects / Presentations
1
50
Final Exam
1
50
Program Outcomes
PO-1
Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2
Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3
Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4
Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5
Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6
Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7
Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9
Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Understand sequences and series, and discuss their properties.
LO-2
Understand limits and continuity of functions.
LO-3
Understand the differentiability and prove the fundamental theorems about it.
LO-4
Recognize convex functions.
LO-5
Learn elementary inequalities and optimization problems.
LO-6
Recognize the anti-derivative and Riemann integrals and apply them.
