Applied Algebra for Engineers
FSI-0AAAcad. year: 2020/2021
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.
Basics of linear algebra.
Recommended optional programme components
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
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
Type of course unit
26 hours, optionally
Teacher / Lecturer
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.