Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Algebra (17.E213A)

Native organizations units: No data

Type of studies	Title
Undergraduate Academic Studies	Power Software Engineering (Godina: 1, Winter)
Undergraduate Academic Studies	Computing and Control Engineering (Godina: 1, Winter)
Undergraduate Academic Studies	Information Engineering (Godina: 1, Winter)

General information:

Category	Academic-general educative
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	9

Educational goal:

Enabling students to think abstractly and gain new knowledge in the field of elementary, general, abstract and linear algebra, as well as in the fundamentals of classic combinatorics. The aim is that the student adopts knowledge from selected areas of algebra and linear algebra that are necessary for understanding the material from other mathematical and professional subjects. Also, an important objective is that the student adopts a mathematical and theoretical basis of the relational and operating algebraic structures used in programming and other professional subjects. Also, students suggest in understanding other technical literature and using software that resolves problems in the field of algebra and linear algebra.

Educational outcome:

Acquired knowledge is used in further education and professional courses. Mathematical models are designed and solved in professional courses using the material from this course. By adopting theoretical knowledge and practical skills in the field of algebra and linear algebra, students are trained to model and resolve practical problems in professional subjects and other fields of implementation.

Course content:

Theoretical lectures: mathematical logic, relations, functions, Boolean algebras, groups, rings, fields, polynomials, complex numbers, finite fields, free vectors, analytical geometry in space, determinants, linear equation systems, vectoric spaces, matrices, linear transormations, eigen values and vectors. Exercises: examples of tasks and to theoretical lectures corresponding exercises which ilustrates lectures, and therefore exercises contribute to understanding theoretical lectures. It also puts the emphasis on methods and algorithms for solving the problems and tasks presented in class. Students are referred to the software tools and procedures for effective modeling and solving tasks in the field of applyed elementar and linear algebra in computer science and information technology.

Teaching methods:

The teaching methods are lectures, computer exercises and consultations. Lectures are performed dynamically and interactively. Theoretical part of the classes exposes the material accompanied by characteristic and representative examples for easier understanding of material. The exercises, which follow the lectures, work out specific tasks and exposes material from theoretical lectures. In addition to the lectures and exercises, regular consultations and group consultations are held. Maintenance the exam, parts of the material which constitutes an natural unit, can be put in two following modules. 1) First modul: relations, functions, Boolean algebras, groups, rings, fields, polyomials, complex numbers, finite fields. 2) Second modul: determinants, linear equation systems, free vectors, analytical geometry in space, vector spaces, matrices, linear transformations, eigen values and vectors. The theoretical part of exam is taken through a test and an oral presentation, and the practical

Literature:

Authors	Title	Year	Publisher	Language
Doroslovački, R.	Elementi opšte i linearne algebre	2006	Alfa-graf NS, Novi Sad	Serbian language
Doroslovački, R.	Principi algebre, opšte, diskretne i linearne	2015	Fakultet tehničkih nauka, Novi Sad	Serbian language
Doroslovački, R., Nedović, Lj.	Zbirka ispitnih zadataka iz diskretne matematike : 1985-2006	2006	ALFA-GRAF, Novi Sad	Serbian language
Doroslovački, R., Nedović, Lj.	Zbirka ispitnih zadataka iz diskretne matematike : 1985-2006	2006	ALFA-GRAF, Novi Sad	Serbian language
Klaus Jänich	Linear Algebra, Undergradute Text in Mathematics	1994	Springer-Verlag, New York	English
Seth Warner	Modern Algebra	1990	Dover Publications, INC., New York	English

Knowledge evaluation:

Course activity	Pre-examination	Obligations	Number of points
Theoretical part of the exam	No	Yes	40.00
Test	Yes	Yes	10.00
Test	Yes	Yes	10.00
Computer exercise attendance	Yes	Yes	5.00
Lecture attendance	Yes	Yes	5.00
Written part of the exam - tasks and theory	No	Yes	30.00