Course detail

Applied Algebra for Engineers

FSI-0AAOptional (voluntary)Bachelor's (1st cycle)Acad. year: 2016/2017Winter semester2. year of study2  credits

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.

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

Prerequisites

Basics of linear algebra.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

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

Czech

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

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

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.