Course detail

Applied Algebra for Engineers

FSI-0AAAcad. year: 2017/2018

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.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. RNDr. Miroslav Kureš, Ph.D.

Department

Institute of Mathematics (ÚM)

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.

Prerequisites

Basics of linear algebra.

Co-requisites

Not applicable.

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

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

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

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Bogopolski, O., Introduction to Group Theory, EMS 2008
Leon, S.J., Linear Algebra with Applications, Prentice Hall 2006
Motl, L., Zahradník, M., Pěstujeme lineární algebru, Univerzita Karlova v Praze, Karolinum, 2002
Nešetřil, J., Teorie grafů, SNTL, Praha 1979
Rousseau Ch., Mathematics and Technology, Springer Undergraduate Texts in Mathematics and Technology Springer 2008

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B3S-P Bachelor's

    branch B-STI , 2 year of study, winter semester, elective (voluntary)

Type of course unit

 

Lecture

26 hod., 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.