Applied Algebra for Engineers (FSI-0AA)

Academic year 2018/2019
Supervisor: doc. Mgr. Jaroslav Hrdina, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
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.
Learning outcomes and competences:
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.
Course contents:
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.
Teaching methods and criteria:
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
Controlled participation in lessons:
Lectures: recommended
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
Course curriculum:
    Lecture 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.
Literature - fundamental:
1. Bogopolski, O., Introduction to Group Theory, EMS 2008
2. Leon, S.J., Linear Algebra with Applications, Prentice Hall 2006
3. Rousseau Ch., Mathematics and Technology, Springer Undergraduate Texts in Mathematics and Technology Springer 2008
4. Motl, L., Zahradník, M., Pěstujeme lineární algebru, Univerzita Karlova v Praze, Karolinum, 2002
5. Nešetřil, J., Teorie grafů, SNTL, Praha 1979
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B3S-P full-time study B-STI Fundamentals of Mechanical Engineering -- Cr 0 Elective (voluntary) 1 2 W