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Information
| Code | MT155 |
| Name | Abstract Mathematics I |
| Term | 2023-2024 Academic Year |
| Semester | 1. 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 |
Dr. Öğr. Üyesi ELA AYDIN
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
This course aims to give student the ability to think abstractly, to prove mathematical facts and introduce the basic concepts of analysis and algebra.
Course Content
The content of this course is, think abstractly, prove mathematical facts and introduce the basic concepts of analysis and 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 | Express the concept of proposition. |
| LO02 | Proves theorems the concept of sets about the set. |
| LO03 | Knows the concept of relation and the properties of equivalence equation. |
| LO04 | Defines the order relation, explains the concepts of exact order and well ordering. |
| LO05 | Identifies that a function is a specific relation and the specific type functions. |
| LO06 | Defines the concept of operation and binary and unary operations. |
| LO07 | Defines the concept of groups,rings,fields, vector spaces and modules. |
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. | 5 |
| 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. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to express the basic theories of mathematics both correctly. | 2 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 1 |
| 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. | 2 |
| 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. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | 1 |
| 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 | 1 |
| 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. | 1 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | 1 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 1 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 1 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 1 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 1 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 1 |
| 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. | 1 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Propositions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 2 | Basic proof techniques | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 3 | Set theory | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 4 | Operations on sets | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 5 | Relations and their properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 6 | Equivalance relation and partitions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 7 | Order relations and its properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 10 | operations, unary, binary and n-ary operations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 11 | External and internal operations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 12 | Algebraic structures, Groups and its basic properties. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 13 | Rings and fields | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 14 | The structure of module | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 15 | The structure of vector space, final exam | Review of the relevant pages from sources | Öğretim Yöntemleri: Problem Çözme |
| 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 | ||