Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Selected Topics in Algebra (17.0M535)

Type of studies	Title
Master Academic Studies	Mathematics in Engineering (Year: 1, Semester: Winter)

General information:

Category	Academic-general educative
Scientific or art field	Teorijska i primenjena matematika
ECTS	5

The main goal of the course is to train students for abstract thinking and acquire basic knowledge in the field of algebra with applications in computer and engineering. More specifically, the goals are for students to master lattices, closure operators, algebras of functions and relations over finite sets, and to be familiar with some modern applications, such as the constraint satisfaction problem problem, clone theory, coding or cryptology.

Students will be familiar with basic notions and results from the field of lattices, closure operators, algebras of functions and relations. In addition, they will have some basic knowledge of some of the modern applications, such as the constraint satisfaction problem, clone theory, coding theory, or cryptology.

Classical algebraic structures with applications. Lattices. Closure operators and Galois connections. Function and relation algebras on finite sets. Algebraic aspects of constraint satisfaction problems. Selected topics in some of the following fields: finite fields and polynomials, clone theory, constraint satisfaction problems, coding theory, cryptology.

The presentation of the theoretical part during the lectures is followed by the characteristic examples which contribute to better understanding of the subject matter. The students are expected to individually study the additional literature which they discuss with the course teacher during consultation hours.

Authors	Title	Year	Publisher	Language
Lidl, R., Pilz, G.	Applied abstract algebra	1998	Springer-Verlag, New York	English
Grätzer, G.	Universal algebra	1968	D. Van Nostrand Company, New Jersey	English

Course activity	Pre-examination	Obligations	Number of points
Practical part of the exam - tasks	No	Yes	40.00
Test	Yes	Yes	10.00
Oral part of the exam	No	Yes	30.00
Exercise attendance	Yes	Yes	5.00
Lecture attendance	Yes	Yes	5.00
Test	Yes	Yes	10.00