MATZ116 Abstract Mathematics II

5 ECTS - 3-0 Duration (T+A)- 2. Semester- 3 National Credit

Information

Code MATZ116
Name Abstract Mathematics II
Term 2024-2025 Academic Year
Semester 2. Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 5 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Belirsiz
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. KAMURAN TARIM
Course Instructor
1


Course Goal / Objective

Introduce order preserving functions, lattices, well ordered sets, axiom of choice, Zorn?s lemma, Hausdorff maximal principal, well ordering principle, finite and infinite sets, countable and uncountable sets. Construction of IR real numbers set

Course Content

Order preserving functions; lattices; well-ordered sets; axiom of choice and its equivalences; countable and uncountable sets; number systems.

Course Precondition

none

Resources

Orhan Özer, Doğan Çoker, Kenan Taş, Soyut Matematik, İzgiYayınevi, Ankara, 1996

Notes

TİMUR KARAÇAY, SOYUT MATEMATİK - AKIL YÜRÜTMENİN BAŞLANGICI, SEÇKİN Yayınevi, 2016


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Defines order preserving function and order isomorphism
LO02 Proves basic propositions about maps which preserve ordering
LO03 Defines lattice, sublattice and complete lattice, gives some examples to the lattice
LO04 Defines well-ordered set, initial segment and solves some problems about well-ordered set and initial segment
LO05 Knows statements of axiom of choice, Hausdorff Maximal Principle, Zorn's Lemma and well ordering principle which are equivalent and proves some of the equivalences,
LO06 Defines finite, infinite, countable set and decides whether the given set countable or not,
LO07 Defines partially ordered sets and totally ordered sets, gives examples of these sets
LO08 Proves fundamental theorems about partially ordered sets and totally ordered sets.
LO09 Gives examples on notions used in the construction of real number system.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Has enough knowledge about mathematics. 5
PLO02 Bilgi - Kuramsal, Olgusal Has pedagogical knowledge about teaching profession and field.
PLO03 Bilgi - Kuramsal, Olgusal Implements classroom management approaches to be used in educational environments effectively.
PLO04 Bilgi - Kuramsal, Olgusal Prepares the learning environments in which appropriate teaching methods are used for effective mathematics education in accordance with development and age levels. 2
PLO05 Bilgi - Kuramsal, Olgusal Knows the relationship between Mathematics-Society-Environment-History and uses it in professional and daily life. 2
PLO06 Bilgi - Kuramsal, Olgusal Uses Turkish properly and effectively according to the rules. 1
PLO07 Bilgi - Kuramsal, Olgusal Selects and designs appropriate materials, in mathematics teaching. 1
PLO08 Bilgi - Kuramsal, Olgusal Monitors students' progress using different assessment and evaluation methods and techniques.
PLO09 Bilgi - Kuramsal, Olgusal Takes responsibility as an individual and as a team member to solve problems related to the field. 1
PLO10 Beceriler - Bilişsel, Uygulamalı Has life-long learning awareness.
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Shares his/her knowledge and skills, problems and solutions that he/she identified by means of oral and written communication with the expert and non-expert people. 3
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Uses information and communication technologies and other related materials for an effective mathematics teaching.
PLO13 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Has enough foreign language knowledge to follow foreign resources related to the field.
PLO14 Yetkinlikler - Öğrenme Yetkinliği Has the knowledge of the purpose, structure and functioning of the Turkish education system.
PLO15 Yetkinlikler - Öğrenme Yetkinliği Becomes a teacher who adheres to Atatürk's principles and revolutions. 1


Week Plan

Week Topic Preparation Methods
1 Increasing functions , order isomorphisms, lattices Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
2 Lattice and Borel algebras Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
3 Initial segments and well-ordered sets Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
4 Well-ordered sets and transfinite induction Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
5 Choice function ,axiom of choice and generalized Cartesian product Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
6 Zorn's lemma, Hausdorff maximal principle, well ordering principle and their equivalence Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
7 Finite and infinite sets Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
8 Mid-Term Exam Source 1,2 Ölçme Yöntemleri:
Yazılı Sınav
9 Countable and uncountable sets Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
10 Cantor theorem, Schröder-Benstein theorem. Countability of Q, uncountability of IR and similar applications Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
11 Number systems Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
12 Dedekind cuts 1 Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
13 Dedekind cuts 2 Source 1 Öğretim Yöntemleri:
Soru-Cevap, Anlatım
14 Construction of IR real number system 1 Source 1 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
15 Construction of IR real number system 2 Sorce 2 Öğretim Yöntemleri:
Anlatım, Soru-Cevap
16 Term Exams Prepare to exam Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Prepare to exam Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 3 42
Out of Class Study (Preliminary Work, Practice) 14 3 42
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 12 12
Final Exam 1 18 18
Total Workload (Hour) 114
Total Workload / 25 (h) 4,56
ECTS 5 ECTS

Update Time: 14.05.2024 02:28