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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS IMÖ 1004 ABSTRACT MATHEMATıCS ıı COMPULSORY 3 0 0 5

Offered By

ELEMENTARY MATHEMATICS TEACHER EDUCATION

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR SERKAN NARLI

Offered to

ELEMENTARY MATHEMATICS TEACHER EDUCATION

Course Objective

To internalize the concept of function, which is the basis for many areas of mathematics, to learn the concept of isoquantity (countable-uncountable sets) and to use the language of mathematics.

Learning Outcomes of the Course Unit

1   1. To comprehend the basic concepts and features of functions. 2   2. Understanding the operation and its features 3   3. Perceiving the concept of finitude-infinity in the context of equivalence and applying it to sets and other mathematical issues. 4   4.Prove the important theorems in the literature about cardinality. 5   5. To understand mathematical expressions, to produce comments and solutions. 6

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Domain set, image set, target set, inverse image sets in functions 2 Injective, surjective and bijective function, identity map 3 Order Preserving Transformations 4 The General Definition of the Concept of Operation 5 Basic Philosophy of Equivalence in Sets 6 Discussion of Infinite Sets in Terms of Equivalence 7 Determining Infinite Sets That Can Be Equivalent to Natural Numbers 8 Midterm 9 Determining Infinite Sets That Can Be Equivalent to Natural Numbers 10 Discussing the Existence of Infinite Sets That Cannot Be Equivalent to Natural Numbers, Proof that the Set of IR Real Numbers Is Not Equivalent to the Set of Natural Numbers 11 Discussion of the Equivalence of Open Intervals to the Set of IR Real Numbers 12 The cardinality of function set 13 The cardinality of power set 14 Countable and uncountable sets, cardinal numbers 15 Final Exam

Recomended or Required Reading

Zekeriya Güney, Murat Özkoç (2015). Soyut Matematik, Dinazor Kitabevi Fethi Çallıalp, (1995) Örneklerle Soyut Matematik, Istanbul Teknik Üniversitesi Yayınları

Planned Learning Activities and Teaching Methods

Lecture, discussion, question-answer, problem solving, active learning techniques, group work.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Midterm 2 FN Semester final exam 3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60 4 BUT Make-up note 5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

Assessment of students is measured by midterm exams, assignments and final exams in line with the learning outcomes.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

serkan.narli@deu.edu.tr

Office Hours

Will be announced at the beginning of the semester.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 20 20 Preparation for final exam 1 20 20 Midterm 1 1 1 Final 1 1 1 TOTAL WORKLOAD (hours) 120

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 PO.14 PO.15 LO.1 5 3 5 4 4 5 4 4 LO.2 3 1 4 5 5 4 5 4 5 LO.3 3 4 5 4 4 5 5 4 LO.4 3 5 5 5 4 4 5 5 4 LO.5 4 4 5 4 4 5 4 4 LO.6