Research Article
Investigation and Analysis on the Interactions Between Mathematics Literacy Skills Using Mathematical Modeling
Nkuturum Christiana*
,
Nwagor Peters
Issue:
Volume 10, Issue 2, June 2024
Pages:
12-18
Received:
18 July 2024
Accepted:
8 August 2024
Published:
27 August 2024
DOI:
10.11648/j.ml.20241002.11
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Abstract: This study investigated and analyzed the interactions between mathematics literacy skills using mathematical modeling. The study used an ASMD model to represent the population of individuals who have skills on addition (A), subtraction (S), multiplication (M) and division (D). The objectives achieved were that the recruitment parameter and coefficient of leaving any compartments significantly influence the system based on the free-equilibrium analysis of mathematics literacy skills. The study showed that system has direct and indirect dynamics in the three states: subtraction, multiplication and division. It also revealed that addition skill is easier to learn than others. Subtraction and multiplication do not interact and have no inter coefficient. The system showcased that good number of individuals are not efficient and effective in the utilization of these skills from the endemic equilibrium of the model showed that En>1 (asymptotically unstable). Finally, this study discovered that these elementary skills in mathematics is fundamental to learners, educated and uneducated, support continued inclusive, workable economic growth, full creative employment, decent work and improve academic performance for all at all levels and in the world at large. The study recommends that curriculum planners should give more time to study these skills thoroughly say one academic session, discourage the use of calculator at early stage, student and teacher factors should be taken into considerations and so on.
Abstract: This study investigated and analyzed the interactions between mathematics literacy skills using mathematical modeling. The study used an ASMD model to represent the population of individuals who have skills on addition (A), subtraction (S), multiplication (M) and division (D). The objectives achieved were that the recruitment parameter and coeffici...
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Research Article
On the Polya Permanent Problem over Finite Commutative Rings
Abrantes Malaquias Belo Caiúve*
Issue:
Volume 10, Issue 2, June 2024
Pages:
19-23
Received:
24 September 2024
Accepted:
16 October 2024
Published:
18 November 2024
Abstract: In this paper we address the Polya permanent problem that was first raised in the second decade of the last century. Despite this, it continues to be treated in several surveys, of which we highlight the studies that point out Polya’s permanent problem over finite fields. Unlike previous papers, we focus on finite commutative rings, and to this end, we start by considering a commutative ring with identity R and its decomposition into a direct sum of finite local rings. Next we suppose that the characteristic of each residue field Fiis different from two, and we proof that if n is greater than or equal to 3, then no bijective map Φ from Mn(R) to Mn(R) transforms the permanent into a determinant. We developed this technique to estimate the order of the general linear group of degree n over a finite commutative ring with identity. The paper begins with the introduction where we present the title, the preliminaries that help the understanding of the following subject, then we talk about the unit permanent and unit determinant in Mn(R), we demonstrate the main result and conclusions. Regarding the methodology, we use the previous results on finite fields and the structure of finite commutative rings and also radical theory of rings.
Abstract: In this paper we address the Polya permanent problem that was first raised in the second decade of the last century. Despite this, it continues to be treated in several surveys, of which we highlight the studies that point out Polya’s permanent problem over finite fields. Unlike previous papers, we focus on finite commutative rings, and to this end...
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