MT156 Abstract Mathematics II

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

Information

Code MT156
Name Abstract Mathematics II
Term 2024-2025 Academic Year
Semester 2. Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Dr. Öğr. Üyesi ELA AYDIN
Course Instructor
1 2
Dr. Öğr. Üyesi ELA AYDIN (A Group) (Ins. in Charge)


Course Goal / Objective

The aim of this course is construct number sets, introduce the basic concepts of algebra, understant the properties of finite and infinite sets, develop the ability to prove propositions.

Course Content

The content of this course is, construct number sets and introduce the basic concepts of algebra.

Course Precondition

None

Resources

S. Akkaş, H.H. Hacısalihoğlu, Soyut Matematik, Gazi Üniversitesi press No:43, Ankara, 1984. A. Dönmez., Kümeler Kuramı ve Soyut Matematik, Atatürk University press No. 638, Erzurum, 1987.

Notes

F. Çallıalp, Soyut Matematik, İstanbul Technical Üniv. İstanbul, 1995.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Builds the natural numbers set using the equivalent sets.
LO02 Make the principles of first and second inductionare equivalent and uses these principles to prove propositions.
LO03 Constructs integers using the natural numbers.
LO04 Expresses the fundamental theorem of arithmetic by the properties of integers .
LO05 Builds the set of rational numbers from integers .
LO06 Builds concept of the Cauchy sequence and the real numbers using Cauchy sequence of rational numbers.
LO07 Defines countable and uncountable sets.
LO08 Clasifies the sets about finite or infinite.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. 4
PLO02 Bilgi - Kuramsal, Olgusal Understands importance of basic consepts of Algebra, Analaysis and Topology. 4
PLO03 Yetkinlikler - Öğrenme Yetkinliği Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. 2
PLO04 Bilgi - Kuramsal, Olgusal Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. 2
PLO05 Bilgi - Kuramsal, Olgusal Understands the relationship between the different fields of mathematics and its relation to other disciplines.
PLO06 Bilgi - Kuramsal, Olgusal Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem.
PLO07 Bilgi - Kuramsal, Olgusal Comprehend and explain mathematical models such as formulas, graphs, tables and schema. 4
PLO08 Bilgi - Kuramsal, Olgusal Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter.
PLO09 Bilgi - Kuramsal, Olgusal Comprehends at least one of the computer programming languages.
PLO10 Bilgi - Kuramsal, Olgusal Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. 1
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities.
PLO13 Yetkinlikler - Öğrenme Yetkinliği Understands the programming techniques and shows the ability to do programming.
PLO14 Yetkinlikler - Öğrenme Yetkinliği Demonstrates the ability to study mathematics both independently and as a group.
PLO15 Bilgi - Kuramsal, Olgusal Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study.
PLO16 Bilgi - Kuramsal, Olgusal Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications.
PLO17 Bilgi - Kuramsal, Olgusal It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability.
PLO18 Bilgi - Kuramsal, Olgusal Gains the ability to use information technologies effectively for contemporary mathematical applications.
PLO19 Bilgi - Kuramsal, Olgusal Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields.
PLO20 Bilgi - Kuramsal, Olgusal Gains the consciousness of prefesional ethics and responsibility.


Week Plan

Week Topic Preparation Methods
1 Equivalent sets and construction of natural numbers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım
2 Mathematical induction and solving problems Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
3 Construction of integers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
4 Properties of integers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
5 Arithmetic in the set of integers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
6 Fundamental theorem of aritmetic and solving problems Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım
7 Euler s function Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
8 Mid-Term Exam Review of the topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav
9 Construction of rational numbers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
10 Field structures of rational numbers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım
11 Properties of rational numbers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
12 Cauchy sequence and construction of real numbers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım
13 Properties of the set of real numbers Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
14 Countability and cardinalities of sets Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım
15 Cardinalities of sets, final exam Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım
16 Term Exams Review of the topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Review of the topics discussed in the lecture notes and sources 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 5 70
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 15 15
Final Exam 1 30 30
Total Workload (Hour) 157
Total Workload / 25 (h) 6,28
ECTS 6 ECTS

Update Time: 12.06.2024 11:40