Course detail
Applied Algebra for Engineers
FSI-0AA Acad. year: 2020/2021 Winter semester
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
2
Supervisor
Department
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.
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
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
The study programmes with the given course
Programme B3S-P: Engineering, Bachelor's
branch B-STI: Fundamentals of Mechanical Engineering, elective
Type of course unit
Lecture
26 hours, optionally
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.