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Course detail

Applied Algebra for Engineers

Course unit code: FSI-0AA
Academic year: 2016/2017
Type of course unit: optional (voluntary)
Level of course unit: Bachelor's (1st cycle)
Year of study: 2
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
The course makes access to mastering in a wide range of results of algebra. Students will apply the results while solving technical problems.
Mode of delivery:
90 % face-to-face, 10 % distance learning
Basics of linear algebra.
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
In the course Applied Algebra for Engineers, students are familiarised with selected topics of algebra. The acquired knowledge is a starting point not only for further study of algebra and other mathematical disciplines, but also a necessary assumption for a use of algebraic methods in a practical solving of problems in technologies.
Recommended or required reading:
Bogopolski, O., Introduction to Group Theory, EMS 2008
Leon, S.J., Linear Algebra with Applications, Prentice Hall 2006
Rousseau Ch., Mathematics and Technology, Springer Undergraduate Texts in Mathematics and Technology Springer 2008
Motl, L., Zahradník, M., Pěstujeme lineární algebru, Univerzita Karlova v Praze, Karolinum, 2002
Nešetřil, J., Teorie grafů, SNTL, Praha 1979
Planned learning activities and teaching methods:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
Course credit: the attendance, satisfactory solutions of homeworks
Language of instruction:
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Students will be made familiar with fundaments of algebra, linear algebra, graph theory and geometry. They will be able to apply it in various engineering tasks.
Specification of controlled education, way of implementation and compensation for absences:
Lectures: recommended

Type of course unit:

Lecture: 26 hours, optionally
Teacher / Lecturer: doc. RNDr. Miroslav Kureš, Ph.D.
Syllabus: 1. Vector spaces, basis, the group SO(3). Application: Rotation of the Euclidean space.
2. Change of basis matrix, moving frame method. Application: The robotic manipulator.
3. Universal covering, matrix eponential, Pauli matrix, the group SU(2). Application: Spin of particles.
4. Permutation groups, Young tableaux. Application: Particle physics, representations of groups.
5. Homotopy, the fundamental group. Application: Knots in chemistry and molekular biology.
6. Polynomial algebras, Gröbner basis, polynomial morphisms. Application: Nonlinear systems, implicitization, multivariable cryptosystems.
7. Graphs, skeletons of graphs, minimal skeletons. Application: Design of an electrical network.
8. Directed graphs, flow networks. Application: Transport,
9. Linear programming, duality, simplex method. Application: Ratios of alloy materials.
10. Applications of linear programming in game theory.
11. Integer programming, circular covers. Application: Knapsack problem.
12: A reserve.

The study programmes with the given course