ABSTRACT MATHEMATICS

EMT105

Course Code: EMT105
Semester: First Term (Fall)
Theory+Practice: 3 + 0
ECTS: 5

Course Type

Compulsory Course

Course Level

Bachelor's Degree

Year of Study

Semester

First Term (Fall)

ECTS

Name of Lecturer(s)

Professor Miraç Çetin Keskin

Learning Outcomes

At the end of this course, the students;

Will be able to prove the theoretical knowledge that he/she learns.
Will be able to develop an abstract thinking skills.
Will be able to use different techniques when solving problems.
Know the proof methods.

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

None

Course Description

Explanation of axiom and theorem concepts, explanation of direct and indirect mathematical proof methods. Axioms and theorems related to symbolic logic, applications related to symbolic logic. Universal and existential quantifiers, explanation of set concept, operations related to set concept. Cartesian product set and graph drawing, relation concept and properties, relation types, equivalence and order relations, properties of these relations. Constructing numbers with the help of equivalence classes, the concept of function, into, overlapping, one-to-one, constant, unit functions, composition of functions, inverse functions and applications related to functions.

Course Contents

WEEK	TOPICS
1^st Week	Propositions, propositional connectives, truth tables
2^nd Week	Propositional conjunctions, truth tables
3^rd Week	Methods of proof
4^th Week	Sets, quantifiers, operations of sets
5^th Week	Operations of sets
6^th Week	Operations of sets, family of sets
7^th Week	Relation and properties of relation
8^th Week	Midterm
9^th Week	Equivalence relation and equivalence classes
10^th Week	Ordered relation and its properties
11^th Week	Functions
12^th Week	Operations on functions
13^th Week	Operations and characteristics of the operations
14^th Week	Algebraic structures and structure transformations
15^th Week	General review

Recommended or Required Reading

H.Hilmi Hacısalihoğlu, S.A., Z.Ö., A.S.,Soyut Matematik G.Ü. Yayınları,1984.
Soyut Matematik, Çallıalp F., Birsen Yayınevi, 2009
Soyut Matematik, Prof.Dr. Orhan Özer, Prof. Dr. Doğan Çoker,Prof.Dr. Kenan Taş
Soyut Matematiğe Giriş, Timur Karaçay

Planned Learning Activities and Teaching Methods

Lecture
Questions/Answers
Problem Solving

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	40
Total(%)		40
Contribution of In-term Studies to Overall Grade(%)		40
Contribution of Final Examination to Overall Grade(%)		60
Total(%)		100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Midterm exam	1	2	2
Preparation for Quiz
Individual or group work	13	4	52
Preparation for Final exam	1	30	30
Course hours	13	3	39
Preparation for Midterm exam	1	24	24
Laboratory (including preparation)
Final exam	1	2	2
Homework
Total Work Load			149
Total Work Load / 30 (h)			4.96
ECTS Credit of the Course			5

Language of Instruction

Turkish

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4
K1
K2
K3
K4
K5
K6
K7
K8
K9	X	X	X	X
K10	X	X	X	X