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.
Literature:
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Required Literature |
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No. |
Author |
Title |
Publisher |
Year |
|
1 |
W. Gilbert and W.K. Nicholson | Modern Algebra with Applications | WILEY | 2003 |
|
2 |
D. Joyner, R. Kreminski and J. Turisco | applied abstract algebra | The Johns Hopkins University Press | 2004 |
