GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
LEBESQUE INTEGRAL/MAT516A
Course Title: LEBESQUE INTEGRAL
Credits 3 ECTS 5
Semester 10 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Türkçe
 -- NAME OF LECTURER(S)
  Prof.Dr. Ziya ARGÜN
 -- WEB SITE(S) OF LECTURER(S)
  www.gazi.edu.tr/~ziya
 -- EMAIL(S) OF LECTURER(S)
  ziya@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
They should be able to understand measure and integral concepts
They should be able to establish the properties of these concepts
They should be able to establish the relationship between these two concepts
They should be able to notice the the relationship between Riemann integral and Lebesque integral
They should be able to design effective lessons related with the integral concept at high school
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 -- PREREQUISITES AND CO-REQUISITES
  Before this course, the lectures should be taken like Calculus I (single variables), Analytic Geometry, Lnear Algebra, Multivariable Calculus and Topo
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  -
 --COURSE CONTENT
1. Week  the properties of sequences of sets: liminf, limsup and convergence of these
2. Week  Algebras and sigma Algebras of sets
3. Week  Definition of a measure and some well known measures: Counting, Lebesque,Borel...
4. Week  Definition of a outer measure and some well known measures: Counting, Lebesque,Borel...
5. Week  Definition of a measurable function and some examples
6. Week  Properties of measurable functions and their constructions
7. Week  Step functions and integral of pozitive functions
8. Week  integrable functions and their construcrions
9. Week  Fatou Lemma, convergence theorem and their applications
10. Week  The functions of Lebesque integrable and their properties
11. Week  Lebesque convergence theorem
12. Week  Typical applications of Lebesque convergence theorem
13. Week   Some famous inequalities in Functional Analysis: Hölder, Minkowsky..
14. Week  The comparison of the approaches of Lebesgue and Riemann to the integral concept
15. Week  
16. Week  
 -- RECOMMENDED OR REQUIRED READING
  H. L. Royden, “Real Analysis”, Macmillan Publishing Co. Inc., 1963. W. Rudin, “Real and Complex Analysis”, Mc Graw-Hill, 197
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Exploration, Discussion, Brain storm, Demonstration,Concept map, inquiry, problem solving, discovery, diagnostic, computer and internet based, explor
 -- WORK PLACEMENT(S)
  -
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
25
 Assignment
1
10
 Exercises
1
5
 Projects
1
10
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
50
 Contribution of Final Examination to Overall Grade  
50
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
14
2
28
 Practising Hours of Course Per Week
14
2
28
 Reading
0
 Searching in Internet and Library
0
 Designing and Applying Materials
14
2
28
 Preparing Reports
0
 Preparing Presentation
0
 Presentation
0
 Mid-Term and Studying for Mid-Term
0
 Final and Studying for Final
1
20
20
 Other
1
20
20
 TOTAL WORKLOAD: 
124
 TOTAL WORKLOAD / 25: 
4.96
 ECTS: 
5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1Acquisition of scientific thinking skillsX
2Making research and investigation independentlyX
3Acquisition of carefully observing and analytically thinking skillsX
4Acquisition of learning and teaching mathematics problemsX
5Comprehending, applying and explaining the importance of mathematical conceptsX
6Developing the thinking, producing, argumenting and probing abilitiesX
7Having the algorithm and sotftware writing abilities for solving computer supported problemsX
8Developing the ability of reaching information, evaluating and presenting informationX
9Improving yourself parallel to the developing technologyX
10Understands the disciplinary structure of mathematics, its historical development, related philosophical approaches and problems.X