Graduate Education Institute · Mathematics Education · Master
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.
Required Resources
Klasik mantığa giriş, İbrahim Emiroğlu
Klasik Mantık, Necati Öner
An Introduction to Mathematical Reasoning, Matthew M. Conroy and Jennifer L. Taggart, University of Washington
Recommended Resources
Research articles,
Core Area Distribution
Teaching Methods
Assessment & Evaluation
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 16 | 3 | 48 |
| Out of Class Study Period | 31 | 4 | 124 |
| Midterm | 1 | 8 | 8 |
| Quiz | 0 | 0 | 0 |
| Assignment | 0 | 0 | 0 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 8 | 8 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | طبيعة الرياضيات و التفكير الرياضي | Introduction of the course |
| 2 | What is reasoning? Types of reasoning. | Resource Book |
| 3 | Levels of Thinking and the Teaching of Reasoning | Resource Book |
| 4 | Propositional Logic and Argument Validity | Resource Book |
| 5 | Variables and Quantifiers: The Formal Language of Mathematics | Resource Book |
| 6 | The Concept of Proof; Direct and Contrapositive Proof | Resource Book |
| 7 | Proof by Contradiction and Proofs Involving Quantifiers | Resource Book |
| 8 | Midterm exam | Midterm |
| 9 | Sets and Reasoning on Sets | Resource Book |
| 10 | Proof by Induction | Resource Book |
| 11 | Relations and Equivalence | Resource Book |
| 12 | Congruences and Modular Arithmetic | Resource Book |
| 13 | Functions | Resource Book |
| 14 | Cardinality and Infinity | Resource Book |
| 15 | ||
| 16 | Final | Final |