Graduate
Institute of Graduate Studies
Mathematics And Computer Science
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Riesz Spaces

Course CodeSemester Course Name LE/RC/LA Course Type Language of Instruction ECTS
YMB0025 Riesz Spaces 3/0/0 DE Turkish 7
Course Goals
Understanding the general theory of Riesz spaces. 
Prerequisite(s) -
Corequisite(s) -
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.)
Instructor(s) Assist. Prof. Dr. Uğur Gönüllü
Course Assistant(s)
Schedule Day, hours, XXX Campus, classroom number.
Office Hour(s) Instructor name, day, hours, XXX Campus, office number.
Teaching Methods and Techniques Lecture and Homework
Principle Sources de Jonge E., Van Rooij A.C.M. Introduction to Riesz spaces, Mathematisch Centrum, 1977.
Other Sources

1-       Luxemburg W.A.J., Zaanen A.C.  Riesz Spaces, Volume 1, 1971.

2-       Fremlin D.H.- Topological Riesz Spaces and Measure Theory, 1974.

3-       Luxemburg W. A. J. Some aspects of the theory of Riesz spaces, University of Arkansas, 1979.

4-       Aliprantis C.D., Burkinshaw O., Positive Operators, Springer, 2006.

Course Schedules
Week Contents Learning Methods
1. Week Preliminaries Lecture and Homework
2. Week Riesz Subsapces and Riesz Homomorphisms Lecture and Homework
3. Week Disjointness Lecture and Homework
4. Week Archimedean and Dedekind Complete Riesz Spaces Lecture and Homework
5. Week Order Bounded Linear Functionals Lecture and Homework
6. Week Extension Theorems Lecture and Homework
7. Week Integral and Singular Functionals Lecture and Homework
8. Week Normed Riesz Spaces Lecture and Homework
9. Week Dual Spaces Lecture and Homework
10. Week Bounded Integral and Bounded Singular Functionals Lecture and Homework
11. Week Representation Theorems Lecture and Homework
12. Week The Yosida Representation Theorem Lecture and Homework
13. Week L-spaces and M-spaces Lecture and Homework
14. Week Hermitian Operators Lecture and Homework
15. Week
16. Week
17. Week
Assessments
Evaluation tools Quantity Weight(%)
Midterm(s) 1 20
Homework / Term Projects / Presentations 5 60
Final Exam 1 20


Program Outcomes
PO-1Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6Use information and communication technologies with computer software in advanced level.
PO-7Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1I. Understanding the basic properties of Riesz spaces.
LO-2II. Understanding the basic properties of order bounded operators.
LO-3III. Understanding extension theorems and representation theorems.
LO-4IV. Understanding the concepts of L-spaces and M-spaces.
LO-5V. Understanding the normed Riesz space.
Course Assessment Matrix:
Program Outcomes - Learning Outcomes Matrix
 PO 1PO 2PO 3PO 4PO 5PO 6PO 7PO 8PO 9PO 10