GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
VECTOR MEASUREMENTS I/6321305
Course Title: VECTOR MEASUREMENTS I
Credits 3 ECTS 7.5
Course Semester 1 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
Gain a working knowledge of L^p-spaces
Decompose measures and appreciate the role this decomposition plays in the Radon-Nikodym & Riesz representation theorems
Understand the relationship between of functions of bounded variation and absolute continuity and the role they play in integral calculus
Understand the general concept of vector measure
Understand how vector measure on a Banach space is constructed
Work with real and vectorial measurable functions and understand their importance to the definition of the integral
Understand how vector measures may be used to construct integrals
Work with the properties of the Bochner integral
Use the relationship between the vectorial and Bochner integrals
Recognize the relationship between tensor products and vector measures
 -- MODE OF DELIVERY
  The mode of delivery of this course is face to face
 --WEEKLY SCHEDULE
1. Week  L^p-spaces
2. Week  The space of signed measures
3. Week  The Radon-Nikodym theorem
4. Week  Elementary properties of vector measures
5. Week  Countably additive vector measures
6. Week  Absolute continuity
7. Week  Real-valued v-measurable functions
8. Week  Vector-valued μ-measurable functions
9. Week  Bochner and Pettis integrals
10. Week  Compactness properties of integration operators
11. Week  Concavity of L^1(v) and the integration operator I_v for a vector measure v
12. Week  Tensor products of Banach spaces
13. Week  The least and greatest crossnorms
14. Week  Applications of tensor products and vector measures to Banach space theory
15. Week  
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
40
 Assignment
0
0
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Percent of In-term Studies  
40
 Percentage of Final Exam to Total Score  
60
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
3
42
 Weekly Tutorial Hours
14
0
0
 Reading Tasks
10
8
80
 Searching in Internet and Library
8
4
32
 Material Design and Implementation
4
2
8
 Report Preparing
0
0
0
 Preparing a Presentation
0
0
0
 Presentation
0
0
0
 Midterm Exam and Preperation for Midterm Exam
1
10
10
 Final Exam and Preperation for Final Exam
1
16
16
 Other (should be emphasized)
0
0
0
 TOTAL WORKLOAD: 
188
 TOTAL WORKLOAD / 25: 
7.52
 Course Credit (ECTS): 
7.5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To be able to develop their knowledge of theory and applications at master degree depending on the competencies acquired in undergraduate level.X
2To be able to recognize different problems encountered in mathematics and to be able to make studies for their solutions.X
3To be able to formulate new solutions with scientific methods mostly based on analysis and synthesis.X
4To be able to carry out his/her works either independently or in groups within a project considering his/her knowledge on the field he/she works in a critical approach.X
5To be able to continue his/her works considering social, scientific and ethical values.X
6To be able to follow scientific and social developments related to his/her field.X
7To be able to carry out his/her works within the framework of quality management, workplace safety and environmental awareness and to be able to present systematically his/her works using various methods like written, oral or visual.X
8To be able to use methods of accessing knowledge effectively in accordance with ethical values.X
9To be able to use knowledge in other disciplines by combining it with mathematical information.X
10To be able to make activities in the awareness of need for lifelong learning.X
11To be able to make connections between mathematical and social concepts and produce solutions with scientific methods.X
12To be able to use his/her mathematical knowledge in technology.X
 -- NAME OF LECTURER(S)
   (Assoc.Prof. Cüneyt ÇEVİK )
 -- WEB SITE(S) OF LECTURER(S)
   (websitem.gazi.edu.tr/site/ccevik)
 -- EMAIL(S) OF LECTURER(S)
   (ccevik@gazi.edu.tr)