Algebra and Discrete Mathematics for Economics
Description
Algebra and Discrete Mathematics are essential tools also for economists.
Globalization makes that goods and services are exchanged worldwide. Input-output analysis uses the advantage of a relatively stable flow of commodities and services. The essential principles can be described by input-output tables. Such tables correspond to systems of linear equations, written as single equations consisting of matrices whose entries are non-negative rational numbers. The flow itself can be described by a directed edge-valued graph where the sets of values consist of positive rational numbers. Therefore numbers, especially non-negative rational numbers, multiple-partite graphs and matrices with non-negative rational entries play an important role in input-output analysis. Thus knowledge from Algebra and Discrete Mathematics becomes more and more useful in this area.
We will consider a particular set of graphs, the so-called input-output graphs and a particular set of matrices, the input-output matrices, define a partial binary operation on each of these sets and prove that we obtain weakly isomorphic weakly partial semigroups. The result of considering this situation can be applied to multiple-step production processes, to material reqirements planning and to internal cost allocation of a business.
The results show that Algebra and Discrete Mathematics are quite useful for mathematical modeling in Economy.
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Klaus Denecke was born in 1944 in Thale (Harz). He studied Mathematics and Physics at universities in Halle and Potsdam. After undertaking research on the borderline between Universal Algebra and Mathematical Logic with Hans-Jürgen Hoehnke from the Academy of Sciences in Berlin he got his Ph.D. in 1979 and his habilitation in 1983. From 2015 to 2017 he studied at the Freie Journalistenschule in Berlin to get a Diploma as a Journalist. From 2017 to 2023, after his retirement from Potsdam University, he worked as editor of the monthly magazine "Der Uhu". From 2023 to 2024 he studied Economy at the Fernuniversity Hagen.
He began his professional life as a high school teacher. From 1981 until 1984 he worked as a mathematician at plant breeding institute and at teacher's trainings college in Quedlinburg (Harz).
1984 he became full professor of Mathematics at University of Potsdam. His research interests are in General Algebra, Theoretical Computer Science, in Mathematical Logic and in Theoretical Economy. He belonged to the organizers of the series of conferences "Arbeitstagungen Allgemeine Algebra", was guest professor at several universities around the world and is Dr. honoris causa of the Bulgarian South-West University.