Syllabus ( MATH 561 )

Basic information


Course title: 
Mathematical Logics 
Course code: 
MATH 561 
Lecturer: 
Assoc. Prof. Dr. Selçuk TOPAL

ECTS credits: 
7.5 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
2/1, Fall and Spring 
Level of course: 
Second Cycle (Master's) 
Type of course: 
Area Elective

Language of instruction: 
English

Mode of delivery: 
Face to face

Pre and corequisites: 
None 
Professional practice: 
No 
Purpose of the course: 
To give introduction to the mathematical backgrounds for formal reasoning and practical knowledge in the different formal theories development. 



Learning outcomes


Upon successful completion of this course, students will be able to:

Apply the principles of inductive reasoning in different selfstudies
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics
Method of assessment

Written exam

Homework assignment

Grasp and use main theorems and their proofs.
Contribution to Program Outcomes

Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results

Acquire scientific knowledge and work independently
Method of assessment

Written exam

Develop different logical models and use them in applications.
Contribution to Program Outcomes

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Design and conduct research projects independently

Write progress reports clearly on the basis of published documents, thesis, etc
Method of assessment

Written exam

Homework assignment


Contents


Week 1: 
Introduction: Mathematical logic as a language of mathematics. Its syntax and semantics. 
Week 2: 
Induction and recursion on the set of natural numbers. Illustrative examples. Polish notation. 
Week 3: 
Propositional logic. The syntax of propositional logic: standard and Polish notation, recursive definitions. 
Week 4: 
Truth assignment and semantic implication. Boolean functions and connectives. 
Week 5: 
Syntactic implication. Examples of deduction. The notion of a model. 
Week 6: 
Theorems on soundness and completeness. Compactness theorem. 
Week 7: 
Firstorder logics. Their syntax and semantics. Structures and relationships between structures. Substitutions. 
Week 8: 
Midterm exam 
Week 9: 
Predicates. Quantifiers. Prenex normal forms. 
Week 10: 
Quantifier elimination: motivation and definition 
Week 11: 
Examples of Formal Theories. I. Introduction to axiomatic set theory. 
Week 12: 
2. Formal arithmetic. Its system of axioms. 
Week 13: 
Arithmetic functions and relations 
Week 14: 
Developing basic set theory. Cartesian products. Relations and functions. Orderings. 
Week 15*: 
Natural numbers and induction. Sets (finite and infinite) and classes. 
Week 16*: 
Final exam 
Textbooks and materials: 
1. Joseph N.Mileti, “Mathematical logic for mathematicians”, 2. E.Mendelson, “Introduction to Mathematical logic” 
Recommended readings: 
Makaleler, Internet kaynakları 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
8 
20 
Other interm studies: 

0 
Project: 

0 
Homework: 
3, 5, 7, 9, 11,13 
30 
Quiz: 
4,12 
20 
Final exam: 
16 
30 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
3 
14 

Practice, Recitation: 
0 
0 

Homework: 
5 
6 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
2 
2 

Own study for midterm exam: 
16 
2 

Midterm: 
2 
1 

Personal studies for final exam: 
16 
2 

Final exam: 
2 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



>