TR
11111

COURSE INTRODUCTION AND APPLICATION INFORMATION

dm.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Fall/Spring
Prerequisites
None
Course Language
Course Type
Elective
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • will be able to use families of sets, σ-algebras, Borel sets.
  • will be able to apply theory of integral and understand the definition and basic properties of integral with respect to a measure.
  • will be able to use Caratheodory construction, product measures, Fubini’s theorem.
  • will be able to use monotone convergence theorem, dominated convergence theorem.
  • will be able to calculate Lebesgue integral.
Course Description

 



Course Category

 Core Courses
Major Area Courses
X
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Notation and basic set theory, Sets and functions Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
2 Countable and uncountable sets: examples. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
3 The Riemann integral. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
4 σ-algebra. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
5 Measure, Null sets. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
6 Outer measure. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
7 Lebesque measurable sets. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
8 Lebesque measure. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
9 Borel sets, Measurable functions. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
10 Lebesque Integral, Monotone Convergence Theorems. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
11 Integrable functions, The Dominated Convergence Theorem. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
12 Relation to the Riemann integral. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
13 Banach spaces. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
14 Duality, Distribution. Real Analysis Third Edition H.L. Royden Prentice Hall, New Jersey.
15 Review of semester.
16 Review of semester.
Course Notes/Textbooks The extracts above and exercises will be given.
Suggested Readings/Materials None.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
10
15
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
2
50
Final Exam
1
35
Total

Weighting of Semester Activities on the Final Grade
12
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
1
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
10
1
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
25
Final Exams
1
20
    Total
143

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

 X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

 X
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

 X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

 X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

 X
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

 X
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

 X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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