Departments Supervised by the Rectorate · İZÜ Seçmeli Dersler · Undergraduate
ECTS: 3 T+P+L: 2+0+0 IZU Common Elective
Coordinator: Prof. Dr. İbrahim GÜNEY
Instructors: Prof. Dr. İbrahim GÜNEY
Course Objective
To introduce the approaches to philosophy of mathematics and learn the axiomatic approach to philosophy in mathematics.
Course Content
Ontology and epistemology of mathematics.Proposition and meanings of some mathematical expressions. Foundations of mathematics, methods and philosophical problems on mathematics. Objectivity in Mathematics and applying to real life. Studies of Frege, Russel, Hilbert, Brouwer, and Gödel. Basic theories in mathematics philosophy: Logisicm, Formalism, Structuralism and Intuitionism.
Course Learning Outcomes
- Student explain philosophic importance of mathematical logic.
- Student express the meanings of mathematical expressions.
- Student explain the relation between philosophy of mathematics and philosophy of education.
- Student explain basic theories of philosophy of mathematics.
- Student explain researchers who are the leaders on development of philosophy of mathematics and their studies.
- Student can express the modern inclinations, problems and researces in mathematics education
Core Area Distribution
(14) Teacher Training and Education Science%30 (22) Humanities%40 (44) Physical Sciences%10 (46) Mathematics and Statistics%20
Teaching Methods
ExpressionQuestion-AnswerDiscussionBrain StormingProblem Solving
Assessment & Evaluation
Testing (Essay / Tests: True-Falls, multiple-choice, short answer, matching)
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 14 | 2 | 28 |
| Out of Class Study Period | 19 | 2 | 38 |
| Midterm | 1 | 4 | 4 |
| Quiz | 0 | 0 | 0 |
| Assignment | 0 | 0 | 0 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 5 | 5 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Course Introduction and Introduction to the Philosophy of Mathematics | Introduction of the course |
| 2 | Crises in Mathematics; The first crisis is irrational numbers, The second crisis is infinitesimal calculus. | Resource Book |
| 3 | Third crisis: Non-Euclidean geometries Fourth crisis: Paradoxes | Resource Book |
| 4 | Philosophical views on the foundations of mathematics | Resource Book |
| 5 | The purpose of using variables in mathematics. | Resource Book |
| 6 | The purpose of using quantifiers in mathematics. | Resource Book |
| 7 | Types of questions used by mathematics | Resource Book |
| 8 | Midterm | Midterm |
| 9 | Propositional logic and truth tables | Resource Book |
| 10 | The Concept of Proof | Resource Book |
| 11 | Methods of Proof | Resource Book |
| 12 | The concept of axioms | Resource Book |
| 13 | Properties sought in axioms | Resource Book |
| 14 | The axiomatic structure of mathematics | Resource Book |
| 15 | Course Evaluation | Course Evaluation |
| 16 | Final | Final |