|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Abstract Mathematics I *||MT 155||1||3||3||6|
|Prerequisites and co-requisites|
|Recommended Optional Programme Components||None|
|Language of Instruction||Turkish|
|Course Level||First Cycle Programmes (Bachelor's Degree)|
|Course Coordinator||Dr. Lec. Uyesi Ela AYDIN|
This course aims to give student the ability to think abstractly, to prove mathematical facts and introduce the basic concepts of analysis and algebra.
to give student the ability to think abstractly, to prove mathematical facts and introduce the basic concepts of analysis and algebra.
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|1||Propositions||Review of the relevant pages from sources|
|2||Basic proof techniques||Review of the relevant pages from sources|
|3||Set theory||Review of the relevant pages from sources|
|4||Operations on sets||Review of the relevant pages from sources|
|5||Relations and their properties||Review of the relevant pages from sources|
|6||Equivalance relation and partitions||Review of the relevant pages from sources|
|7||Order relations and its properties||Review of the relevant pages from sources|
|8||Mid-term exam||Review of the topics discussed in the lecture notes and sources|
|9||Functions||Review of the relevant pages from sources|
|10||operations, unary, binary and n-ary operations||Review of the relevant pages from sources|
|11||External and internal operations||Review of the relevant pages from sources|
|12||Algebraic structures, Groups and its basic properties.||Review of the relevant pages from sources|
|13||Rings and fields||Review of the relevant pages from sources|
|14||The structure of module||Review of the relevant pages from sources|
|15||The structure of vector space, final exam||Review of the relevant pages from sources|
|16-17||Final exam||Review of the topics discussed in the lecture notes and sources|
|Recommended or Required Reading|
|Textbook||F. Çallıalp, Soyut Matematik, İstanbul Technical Üniv. İstanbul, 1995.|
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.