TÜRKÇE
ENGLISH
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 |
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 | ||