• Turkish
  • English
Course Code: 
MATH 351
Semester: 
Fall
Course Type: 
Core
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
8
Course Language: 
English
Course Objectives: 
Introduction to measure theory. Learning integration with respect to any measure and Lebesgue Integration and related results.
Course Content: 

Measure in plane. Lebesgue measure of sets. Measure as a function of sets. Measurable functions. Egorov and Luzin's theorems. Lebesgue integral. Fatou's theorem. Comparison of Lebesgue and Riemann integrals. Differentiation of indefinite Lebesgue integral. Functions of bounded variations. Radon-Nikodym theorem. Product measures. Fubini's theorem. Lebesgue-Stieltjes and Riemann-Stieltjes integrals Riesz representation theorem.

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Teaching Methods

Assessment Methods

1) Knows the fundamental theorems in measure theory.

1-2

A-B

Course Flow

Week

Topics

Study Materials

1

Introduction, Extended Real Number System, Measurable Functions and their combinations

 

2

Measures, Measure Spaces, Charges

 

3

Simple Functions and Their Integral, Integral of Non-negative Extended Real Valued Measurable Functions

 

4

Monotone Convergence Theorem, Fatou’s Lemma, Properties of The Integral

 

5

Integrable Real Valued Functions, Lebesgue Dominated Convergence Theorem

 

6

Normed Linear Spaces, Lp Spaces, Hölder’s Inequality

 

7

Minkowski’s Inequality, the Copleteness Theorem

 

8

Decomposition of Measure

 

9

Decompositon  of  Measure  Continued

 

10

Generation of Measures

 

11

Generation of Measured  Continued

 

12

Product Measures

 

13

Product Measures Continued

 

14

Reviev of the Course

 

Recommended Sources

Textbook

The Elements of Integration, Robert G. BARTLE

Additional Resources

 

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

80

Quizzes

5

10

Assignments

7

10

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

50

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

50

Total

 

100

 

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

No

Program Learning Outcomes

Contribution

1

2

3

4

5

1

The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)

x

 

 

 

 

2

Acquiring fundamental knowledge on fundamental research fields in mathematics

 

 

x

 

 

3

Ability form and interpret the relations between research topics in mathematics

 

 

x

 

 

4

Ability to define, formulate and solve mathematical problems

 

x

 

 

 

5

Consciousness of professional ethics and responsibilty

 

 

 

x

 

6

Ability to communicate actively

x

 

 

 

 

7

Ability of self-development in fields of interest

 

 

x

 

 

8

Ability to learn, choose and use necessary information technologies

 

 

x

 

 

9

Lifelong education

 

 

x

 

 

ECTS

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

3

42

Hours for off-the-classroom study (Pre-study, practice)

14

5

70

Mid-terms (Including self study)

2

15

30

Quizzes

5

1

5

Assignments

7

3

21

Final examination (Including self study)

1

20

20

Total Work Load

 

 

188

Total Work Load / 25 (h)

 

 

7.52

ECTS Credit of the Course

 

 

8