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IMO 106 - Abstract Mathematics

Faculty of Education · Secondary School Mathematics Education · Undergraduate

ECTS: 5 T+P+L: 2+0+0 Compulsory
Coordinator: Dr. Öğr. Üyesi Hatice İNANKIL

Course Objective

This course aims to gain mathematical and abstract thinking skills; to teach the difference between axiom and theorem and mathematical proof techniques.

Course Content

Explanation of axiom and theorem. Explanation of direct and indirect mathematical proof methods. Axioms and theorems related to symbolic logic, symbolic logic related applications. Universal and existential quantifiers, explanation of the concept of set, operations related to the set concept. Cartesian product set and graphic drawing, relation concept and properties, relation types, equivalence and order relations, properties of these relations. Construction of numbers with the help of equivalence classes. Concept of function, including, covering, one-to-one, fixed, unit functions, the combination of functions, functions related to inverse functions and functions. The concept of force in sets, finite and infinite sets.

Course Learning Outcomes

  1. Ability to use abstract thinking skills.
  2. To be able to use mathematics knowledge in other disciplines.
  3. Comprehend the properties of propositions and sets
  4. To be able to explain the basic concepts of functions and relations.
  5. To be able to follow current and contemporary developments in the profession.

Core Area Distribution

(14) Teacher Training and Education Science%20 (46) Mathematics and Statistics%80

Teaching Methods

ExpressionQuestion-AnswerDiscussionExercise and PracticeBrain StormingSelf studyProblem Solving

Assessment & Evaluation

Testing (Essay / Tests: True-Falls, multiple-choice, short answer, matching)

ECTS / Workload

ActivityQuantityDuration (h)Total Workload
Course Duration (Including Exam Week)16232
Out of Class Study Period14684
Midterm155
Quiz000
Assignment000
Practice000
Final177

Course Schedule

WeekSubjectPreparation
1Propositions and algebra of propositionsSolve the questions given in the course.
2Proof techniquesAlgebra of propositions -Problem SolvingReview of previous subjects
3Sets and algebra of setssolve the questions given in the course
4Cluster sets, partition of cluster sets, product setsreview of the former lesson
5Relations, inverse of the relationship, combination of relations, equivalence relations and equivalence classes, ordered relationsTo do research on the related subject
6Partial ordered relation and ordered relationTo do research on the related subject
7Functions, bijective functions, combination of functionssolve the questions given in the course
8MidtermMidterm
9Ramadan MubarakRamadan Mubarak
10OperationsTo do research on the subject
11solve the questions given in the course
12Operationsreview related research
13Cardinality of the sets, Postulats for integersTo do research on the related subject
14Cardinality of the sets, Postulats for integersTo do research for the subject
15Divisibilitywork on related topic
16finalfinal