Information Package / Course Catalogue
| Course Code | : MAT214 |
| Course Type | : Area Elective |
| Couse Group | : First Cycle (Bachelor's Degree) |
| Education Language | : Turkish |
| Work Placement | : N/A |
| Theory | : 2 |
| Prt. | : 0 |
| Credit | : 2 |
| Lab | : 0 |
| ECTS | : 2 |
To introduce students to the formal notions of language, proof, semantics, and completeness with quantificational logic, in order to: • improve their understanding and appreciation of the foundations of mathematics and • provide the necessary background knowledge for later logic course units
Introduction. Review of propositional logic. Motivation for the study of predicate logic with examples of reasoning with quantifiers. Truth. Languages for predicate logic. Signatures and structures. Formulae, sentences and Tarski's definition of Truth. Logical consequence, logical equivalence and logical validity. Theories and models. Proof. An axiom system for predicate logic. The Soundness Thoerem. Consistency. Completeness. The completeness theorem for predicate logic. Simple applications.
| 1. | On successful completion of the course unit the students will appreciate how arguments involving predicates can be formalized semantically and syntactically and how these are connected (via the Completeness Theorem) |
| 2. | In simple cases be able to show that ‘A follows from B’ both by giving a semantic argument and by constructing a formal proof.In simple cases be able to show that ‘A does not follow from B’ by using semantics. |
| 3. | To be able to gain the skill of interpreting some interrelations among these concepts |
| 4. | To be able to use mathematical concepts in solving certain types of problems |
| 5. | To be able to develop analytical skills and apply to problems |
| 1. | H.B.Enderton, A Mathematical Introduction to Logic (second edition), Academic Press ISBN 0122384520, 2001. |
| 2. | D. van Dalen, Logic and Structure, Springer-Verlag, 3rd edition 1997. |
| 3. | A.G. Hamilton, Logic for Mathematicians, Cambridge University Press, revised edition 1988. |
| Type of Assessment | Count | Percent |
|---|---|---|
| Attending Lectures | 1 | %5 |
| Assignment | 1 | %5 |
| Midterm Examination | 1 | %30 |
| Final Examination | 1 | %60 |
| Activities | Count | Preparation | Time | Total Work Load (hours) |
|---|---|---|---|---|
| Lecture - Theory | 28 | 0 | 1 | 28 |
| Assignment | 2 | 0 | 2 | 4 |
| Quiz | 2 | 2 | 0 | 5 |
| Midterm Examination | 1 | 4 | 2 | 6 |
| Final Examination | 1 | 5 | 2 | 7 |
| TOTAL WORKLOAD (hours) | 50 | |||
PÇ-1 | PÇ-2 | PÇ-3 | PÇ-4 | PÇ-5 | PÇ-6 | PÇ-7 | PÇ-8 | PÇ-9 | PÇ-10 | PÇ-11 | PÇ-12 | PÇ-13 | PÇ-14 | PÇ-15 | PÇ-16 | PÇ-17 | PÇ-18 | |
OÇ-1 | 4 | 4 | 4 | 4 | 4 | 4 | 2 | |||||||||||
OÇ-2 | 4 | 4 | 4 | 4 | 4 | |||||||||||||
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OÇ-4 | ||||||||||||||||||
OÇ-5 | ||||||||||||||||||