Yazdır

Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
ADVANCED ANALYSIS I MAT 001 0 3 + 0 3 6
Ön Koşul Dersleri
Önerilen Seçmeli Dersler

1-Real Analysis

2-The Theory of Measure and Integral

Dersin Dili Türkçe
Dersin Seviyesi Yüksek Lisans
Dersin Türü ZORUNLU
Dersin Koordinatörü Prof.Dr. METİN BAŞARIR
Dersi Verenler Prof.Dr. METİN BAŞARIR
Dersin Yardımcıları
Dersin Kategorisi Alanına Uygun Temel Öğretim
Dersin Amacı

The aim of this course is to give some concepts which are related to graduate level in Mathematics.

 

Dersin İçeriği

Preliminaries (Sets, functions, the sequences of sets and numbers, countable sets), Measure concept (Some set classes, ring, sigma ring, algebra, sigma algebra, measurable sets, measure functions, outer measure, Lebesgue outer measure and Lebesgue measure), Measurable functions, Integral (Integral of basic functions, integral of positive functions, integrable functons, the relations between Lebesgue and Riemann integrals)

Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - Measurable sets and measurable functions introducing 1 - 2 - 3 - 4 - 14 - 15 - A - C -
2 - Lebesgue integral and Lebesgue measure knowing 1 - 2 - 3 - 4 - 14 - 15 - A - C -
3 - The relations between Lebesgue and Riemann integrals knowing 1 - 2 - 3 - 4 - 14 - 15 - A - C -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 14:Self Study 15:Problem Solving
Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
1 Preliminaries
2 Some Set Classes, Algebra, Sigma Algebra
3 Measure Concept
4 Outer Measure Concept
5 Lebesgue Outer Mesaure, Lebesgue Measure
6 Measurable Functions
7 Integral of Basic Functions
8 Integral of Positive Functions
9 Mid Exam
10 Integrable Functions
11 Fatou Lemma and Consequences
12 Bounded Convergence Theorem and Consequences
13 Lebesgue Convergence Theorem and Consequences
14 The Relations between Lebesgue and Riemann Integrals

Kaynaklar

Ders Notu
Ders Kaynakları

1- R.G.Bartle, The elements of real analysis, John Wiley and Sons, New York, 1964.

2- H.L.Royden, Real Analysis, MacMillan, New York, 1968.

3-P.R.Halmos, Measure Theory, Princeton, Springer, 1974.

4- S.K.Barberian, Measure and Integration, MacMillan, New York, 1965.

5- M.Balcı, Reel Analiz, Balcı Yayınları, , Ankara, 2000.


Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Student follows the current journals in his/her field and puts forward problems. X
2 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
7 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
8 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
9 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 50
KisaSinav 1 20
Odev 1 30
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Quiz 1 12 12
Assignment 1 4 4
Final examination 1 25 25
Toplam İş Yükü 157
Toplam İş Yükü /25(s) 6.28
Dersin AKTS Kredisi 6.28
; ;