Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Applied Abstract Algebra (17.D0M08L)

Native organizations units: No data

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Godina: 1, Summer)
Doctoral Academic Studies	Mathematics in Engineering (Godina: 1, Summer)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	10

Educational goal:

The objective of the course is that a young researcher understands the basic algebraic concepts and methods, and at the same time master the basic knowledge of algebraic structures, lattices, Boolean algebras, finite fields, and applications in coding theory and cryptology. Through reading and analysis of open research problems, the goal is for PhDs to be slowly involved into research groups.

Educational outcome:

Young reserchers will be able to demonstrate knowledge in abstract algebra with focus on applied theories, to demonstrate knowlegde and understanding of fundamental algebraic concepts, to demonstrate knowlegde and understanding of lattices, Boolean algebras, finite fields, algebraic structures, and applications in coding theory and cryptology. Students will understand and be able to prove fundamental results and solve algebraic problems using appropriate techniques.

Course content:

Lattices. Boolean Algebras. Finite Fields. Algebraic Structures. Coding Theory. Cryptology. Study by doing research includes active following of primary scientific sources, organisation and presentation of seminal papers from the field of Abstract Algebra, i.e. algorithm construction and programming practical problems that require knowledge in abstract algebra.

Teaching methods:

The teaching process consists of theoretical part, lectures and practical classes where various practical problems are solved using the knowledge acquired during lectures. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Literature:

Authors	Title	Year	Publisher	Language
Burris S., Sankappanavar H. P.	A Course in Universal Algebra	1981	Springer-Verlag	English
Petar Đapić, Rozalia Sz. Madarasz, Petar Marković	Zbirka zadataka iz univerzalne algebre	2014	Univerzitet u Novom Sadu	Serbian language
Lidl, R., Pilz, G.	Applied abstract algebra	1998	Springer-Verlag, New York	English