Syllabus

Ternopil Ivan Puluj National Technical University

Каф. математичних методів в інженерії

Discrete mathematics

syllabus

1. Educational programs for which discipline is mandatory:

# Educational stage Broad field Major Educational program Course(s) Semester(s)
1 bachelor's 12. Інформаційні технології 122. Комп’ютерні науки та інформаційні технології (бакалавр) 1 2
2 bachelor's 12. Інформаційні технології 123. Комп’ютерна інженерія (бакалавр) 1 2

2. The course is offered as elective for all levels of higher education and all educational programs.

3. Information about the author of the course

Full name Oleh Yasniy
Academic degree Sc.D.
Academic title Prof.
Link to the teacher`s page on the official website of the University http://library.tntu.edu.ua/personaliji/a/ja/jasnij-oleh-petrovych/
Е-mail (in the domain tntu.edu.ua)

4. Information about the course

Study hours structure Lectures: 18
Practical classes: 36
Laboratory classes: 0

Amount of hours for individual work: 0
ECTS credits: 4.5
Teaching language english
Form of final examination credit
Link to an electronic course on the e-learning platform of the university https://dl.tntu.edu.ua/bounce.php?course=1394

5. Program of discipline

The place of academic discipline in the structural and logical scheme of study according to the educational program

List of disciplines based on learning results from this discipline

Комп’ютерні системи обробки текстової, графічної та мультимедійної інформації
Probability Theory and Mathematical Statistics
Комп'ютерні мережі (Computer Networks)
Теорія ймовірностей, імовірнісні процеси та математична статистика

Contents of the academic discipline

Lectures (titles/topics)

Lecture 1. Logic And Sets. Sentences. Tautologies and Logical Equivalence. Sentential Functions and Sets. Set Functions. Quantifier Logic. Negation.
Lecture 2. Relations and Functions. Relations. Equivalence Relations. Equivalence Classes. Functions.
Lecture 3. The natural numbers. Introduction. Induction.
Lecture 4. Division And Factorization. Division. Factorization. Greatest Common Divisor. An Elementary Property of Primes.
Lecture 5. Languages. Introduction. Regular Languages.
Lecture 6. Finite State Machines. Introduction. Pattern Recognition Machines. An Optimistic Approach. Delay Machines. Equivalence of States. The Minimization Process. Unreachable States.
Lecture 7. Finite State Automata. Deterministic Finite State Automata. Equivalence of States and Minimization. Non-Deterministic Finite State Automata. Regular Languages. Conversion to Deterministic Finite State Automata. A Complete Example.
Lecture 8. Turing Machines. Introduction. Design of Turing Machines. Combining Turing Machines. The Busy Beaver Problem. The Halting Problem.
Lecture 9. Groups And Modulo Arithmetic. Addition Groups of Integers. Multiplication Groups of Integers. Group Homomorphism.
Approved by the department
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