![[Alg] Algebra](https://www.kis.fri.uniza.sk/wp-content/themes/Divi-child/imgs/KIS-subject-default.png)
Main objectives of the course:
Studying the course student will get basic knowledge of the theory of linear algebra and the theory of abstract algebraic structures, which enable their use in solving technical problems in engineering practice but also an understanding of advanced methods of modern algebra.
After completing the course the student:
– Knows the basic concepts, arguments and methods of modern algebra,
– Can identify algebraic problem
– Has the ability to apply acquired knowledge to solve practical problems.
| Course information sheet | |||||||||||||
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| University: University of Žilina | |||||||||||||
| Faculty: Faculty of Management Science and Informatics | |||||||||||||
| Course ID: 5BF101 | Course name: Algebra (Alg) | ||||||||||||
| Form, extent and method of teaching activities: | |||||||||||||
| Number of classes per week in the form of lectures, laboratory exercises, seminars or clinical practice | Lectures: 2.0 Seminars: 2.0 Lab.exercises: 0.0 | ||||||||||||
| Methods by which the educational activity is delivered | Present form of education | ||||||||||||
| Applied educational activities and methods suitable for achieving learning outcomes | |||||||||||||
| Number of credits: 5.0 | |||||||||||||
| Study workload: hours Specification of the study workload: | |||||||||||||
| Recommended term of study: 1. year, winter semester | |||||||||||||
| Study degree: 1. | |||||||||||||
| Required subsidiary courses: Prerequisites: Co-requisites: | |||||||||||||
| Course requirements: Continuous assessment / evaluation: The condition for the successful completion of exercises on the subject is systematic work on exercises assessing compliance with the following criteria: - Passing the first written test at 6 weeks of the semester ( max. 30 points) - Passing the second written test at 12 weeks semester ( max. 30 points) - Active exercises (eg. Address specific tasks) Students can refer to test if for work during the semester obtained at least 30 points. Final assessment /evaluation: The condition for the successful completion of the course is to obtain at least 60 out of 100 points for the semester work and passing the examination of the subject. The test is will focus only on practical problem solving and to demonstrate theoretical knowledge in broken 20 + 20 points. Credit will not be awarded to a student who all parts of the test did not receive at least 10 points. The final assessment of the subject: 100-92 A 91-84 B 83-76 C 75-68 D 67-61 E To enroll for an exam student must have 30 points. | |||||||||||||
| Course outcomes: Studying the course student will get basic knowledge of the theory of linear algebra and the theory of abstract algebraic structures, which enable their use in solving technical problems in engineering practice but also an understanding of advanced methods of modern algebra. After completing the course the student: - Knows the basic concepts, arguments and methods of modern algebra, - Can identify algebraic problem - Has the ability to apply acquired knowledge to solve practical problems. | |||||||||||||
| Course scheme: 1. Vector spaces - the introduction of the concept, the arithmetic vector spaces, linear dependence and independence. 2. Basis and dimension of a vector space, the coordinates of the vector with respect to a given base, dimension of vector space. Coordinates in view of the different bases. 3. Scalar and vector product of vectors, geometric interpretation - perpendicular vectors, angle vectors. 4. Matrices, operations with matrices, determinant of a matrix and its properties, methods of calculating the determinant of a matrix. 5. Line equivalence of matrices, rank matrix, regular and singular matrix, inverse matrix. Gaussian elimination, Jordan elimination method. 6. Systems of linear equations, solvability of homogeneous and non-homogeneous system of linear equations - Frobenius theorem. 7. Eigenvalues and eigenvectors, geometric interpretation. 8. Polynomials - operations with polynomials, Horner's scheme, the roots of the polynomial. 9. The fundamental theorem of algebra, rational roots, complex roots, reducible, irreducible polynomials. 10. The notion of algebraic structures with one binary operation. Neutral and inverse binary operation and characteristics groupoid, group and subgroup. 11. The concept of algebraic structures with two binary operations 12. The finite fields. Galois field and its applications in computer science. | |||||||||||||
| Literature: Basic: S. Palúch, I Stankovianska: Algebra and its engineering applications, University of Zilina, 2009 J. Elias, J. Horváth, J. Kajan: Collection of tasks from higher mathematics, Bratislava 1985 E. Špániková, E. Wisztová: Collection of problems from algebra, Mechanical Engineering Faculty, University 2003 A. Klaudinyová, I.Stankovianska: Algebra in examples and tasks, University of Zilina, 2009 P. Czimmermann: Algebra and its use in graph theory, University of Zilina, 2020 Recommended: P. Zlatoš: Linear Algebra and Geometry, Out of the three dimensions of cross related disciplines, Merenčin PT, ISBN 978-80-8114-111-9, 2011 | |||||||||||||
| Instruction language: slovak | |||||||||||||
| Notes: | |||||||||||||
| Course evaluation:: Total number of evaluated students: 314
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| A | B | C | D | E | FX | ||||||||
| 16.56 % | 9.55 % | 14.97 % | 18.79 % | 24.20 % | 15.92 % | ||||||||
| Course teachers: Lecture: Mgr. Peter Czimmermann, PhD. Lecture: RNDr. Ida Stankovianska, CSc. Seminar: Mgr. Peter Czimmermann, PhD. Seminar: doc. PaedDr. Dalibor Gonda, PhD. Seminar: Ing. Maroš Janovec, PhD. Seminar: RNDr. Alžbeta Klaudinyová Seminar: doc. RNDr. Štefan Peško, CSc. Seminar: RNDr. Ida Stankovianska, CSc. | |||||||||||||
| Last updated: 2021-12-13 08:17:12.000 | |||||||||||||
| The person responsible for the course: doc. PaedDr. Dalibor Gonda, PhD. | |||||||||||||
| Approved by: prof. Ing. Pavel Segeč, PhD. | |||||||||||||