At the end of this course, the students; 1) Will be able to prove the theoretical knowledge that he/she learns. 2) Will be able to develop an abstract thinking skills. 3) Will be able to use different techniques when solving problems. 4) Knows the proof methods.
MODE OF DELIVERY
Face to face
PRE-REQUISITES OF THE COURSE
No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT
no
COURSE DEFINITION
Explanation of axiom and theorem concepts, explanation of direct and indirect mathematical proof methods. Axioms and theorems about symbolic logic, applications about symbolic logic. Universal and existential quantifiers, explanation of the concept of set, operations related to the concept of set. Cartesian product set and graphic sketching, relation concept and properties, relation types, equivalence and order relations, properties of these relations. Constructing numbers with the help of equivalence classes. Function concept, encapsulating, one-to-one, constant, unit functions, composition of functions, inverse functions and applications related to functions.
COURSE CONTENTS
WEEK
TOPICS
1st Week
Propositions, Propositional connectives, Truth tables
2nd Week
Propositional Conjunctions, Truth tables
3rd Week
Methods of proof
4th Week
Sets, Quantifiers, Operations of sets
5th Week
Operations of sets
6th Week
Operations of sets, family of sets
7th Week
Relation and properties of relation
8th Week
MIDTERM EXAM
9th Week
Equivalence relation and equivalence classes
10th Week
Ordered relation and its properties
11th Week
Functions
12th Week
Operations on functions
13th Week
Operations and characteristics of the operations
14th Week
Algebraic structures and structure transformations
RECOMENDED 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 WORKLOAD
Activities
Number
Hours
Workload
Midterm exam
1
1,5
1,5
Preparation for Quiz
Individual or group work
12
3
36
Preparation for Final exam
1
30
30
Course hours
13
3
39
Preparation for Midterm exam
1
20
20
Laboratory (including preparation)
Final exam
1
1,5
1,5
Homework
3
4
12
Total Workload
140
Total Workload / 30
4,66
ECTS Credits of the Course
5
LANGUAGE OF INSTRUCTION
Turkish
WORK PLACEMENT(S)
No
KEY LEARNING OUTCOMES (KLO) / MATRIX OF LEARNING OUTCOMES (LO)
