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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 co-requisites: 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 Up

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

  1. Apply the principles of inductive reasoning in different self-studies

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics

    Method of assessment

    1. Written exam
    2. Homework assignment
  2. Grasp and use main theorems and their proofs.

    Contribution to Program Outcomes

    1. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    2. Acquire scientific knowledge and work independently

    Method of assessment

    1. Written exam
  3. Develop different logical models and use them in applications.

    Contribution to Program Outcomes

    1. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    2. Design and conduct research projects independently
    3. Write progress reports clearly on the basis of published documents, thesis, etc

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
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: First-order 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 Up
Method of assessment Week number Weight (%)
Mid-terms: 8 20
Other in-term studies: 0
Project: 0
Homework: 3, 5, 7, 9, 11,13 30
Quiz: 4,12 20
Final exam: 16 30
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face 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 mid-term exam: 16 2
Mid-term: 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)
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