COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Abstract Mathematics II * MT   156 2 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 Type
Course Coordinator Dr. Lec. Uyesi Ela AYDIN
Instructors
Dr. Öğr. ÜyesiELA AYDIN1. Öğretim Grup:A
Dr. Öğr. ÜyesiELA AYDIN2. Öğretim Grup:A
 
Assistants
Goals
To construct number sets. To introduce the basic concepts of algebra, to understant the properties of finite and infinite sets. To develop the ability to prove propositions.
Content
To construct number sets. To introduce the basic concepts of algebra, to understant the properties of finite and infinite sets. To develop the ability to prove propo

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
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
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Equivalent sets and construction of natural numbers Review of the relevant pages from sources
2 Mathematical induction and solving problems Review of the relevant pages from sources
3 Construction of integers Review of the relevant pages from sources
4 Properties of integers Review of the relevant pages from sources
5 Arithmetic in the set of integers Review of the relevant pages from sources
6 Fundamental theorem of aritmetic and solving problems Review of the relevant pages from sources
7 Euler´s function Review of the relevant pages from sources
8 Mid-term exam Review of the topics discussed in the lecture notes and sources
9 Construction of rational numbers Review of the relevant pages from sources
10 Field structures of rational numbers Review of the relevant pages from sources
11 Properties of rational numbers Review of the relevant pages from sources
12 Cauchy sequence and construction of real numbers Review of the relevant pages from sources
13 Properties of the set of real numbers Review of the relevant pages from sources
14 Countability and cardinalities of sets Review of the relevant pages from sources
15 Cardinalities of sets, 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
TextbookF. Çallıalp, Soyut Matematik, İstanbul Technical Üniv. İstanbul, 1995.
Additional 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.