Applied Algebra

Course: Applied Algebra

Code: 3ФЕИТ08025

ECTS points: 6 ECTS

Number of classes per week: 3+0+0+3

Lecturer: Prof. Dr. Biljana Jolevska - Tuneska

Course Goals (acquired competencies): Upon completion of the course, the student demonstrates understanding and knowledge of several types of algebraic structures. Also, the student is trained in the application of the adopted algebraic structures in modeling various problems from the technique.

Course Syllabus: Introduction. A set algebra. Boolean algebras. Elements of logic. Apply in logical circuits. Normal forms and application. Groups and symmetries. Cyclic and dihedral groups. Morphisms. Groups of permutation. Factor groups. Equivalence relations. Ideal and Lagrange's theorem. Direct products. Symmetric groups in three dimensions: translation and Euclidean groups; groups of matrices; finite groups in two and three dimensions; groups of crystals. Polya-Burnside numbering method. The Burnside theorem and application. Monoids and machines.

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