Tabakow I.G. Discrete mathematical structures. Part II. Algebraic Systems

Wrocław: Wrocław University of Science and Technology, 2022. — 52 p. — ISBN: 978-83-7493-221-9.Discrete mathematical structures, in particular, such as mathematical logic and set theory, algebraic systems, formal languages, automata theory, graphs, number theory, coding theory, combinatorial analysis, discrete probability theory, Petri nets, and so on, underpin a large amount of modern computer science.Discrete structures became a very large and dynamic science. Unfortunately, the speedy developments and knowledge in this area make impossible the presentation of all notions, definitions, and applications used here.This part is an extension of the previous one (i.e. a supplement / a separate work) and it is related to algebraic systems (considered as discrete mathematical structures).Some basic notions concerning: operations and algebraic systems, lattices, multiple-valued and fuzzy algebras, homomorphisms of algebraic systems (i.e. epimorphism, monomorphism, isomorphism, endomorphism, and automorphism), congruencies, quotient algebraic systems, finite direct products of algebraic systems and free algebraic systems, grammars and sequential machines, algorithms, computability, recursion, graph theory, and Petri nets, combinatorial analysis, probability theory, Markov’s chains, number theory, information, coding, and algorithm complexity, are briefly considered in this part.Several parts of this work were presented during my lectures at the Institute for Mechanical and Electrical Engineering in Sofia, now known as TU Sofia, Bulgaria, and also at the Wroclaw University of Technology in Wroclaw, Poland. A preliminary version of this study was realized by some research projects during my stay in Wroclaw.