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Mathematical Modeling and Simulation in Science and Engineering Education

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 June 2020) | Viewed by 62766

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Prof. Dr. J. Alberto Conejero

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Institute of Pure and Applied Mathematics (IUMPA-UPV), Polytechnic University of Valencia, E-46022 Valencia, Spain
Interests: applied mathematics; graph theory; data science; interdisciplinary applications of mathematics to computer science, engineering and biology
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Dear Colleagues,

There is longstanding quest in making scientific and engineering studies more attractive to potential students at all levels in order to increase the number of vocations. It seems that the labor opportunities that they offer in our present technological society are not sufficient for increasing the engagement of young people in science and engineering. Therefore, all efforts carried out in making the learning content more interesting are welcome. Nowadays, students can have access to a huge amount of computational and technological tools. However, the potential uses of these technologies depend, in great part, on their mathematical knowledge and skills. These competencies can be developed in different ways, such as the inclusion of mathematical modeling and simulation in the syllabus of educational programs.

Mathematical modeling enables us to describe the behavior of a broad range of phenomena and systems in nature and society. With simulations, they permit us to predict the evolution of those systems without actually testing them in the real world. This way is not only cheaper, safer, and faster, but also helps to develop critical and analytical thinking skills in students. After a preliminary model is generated, different scenarios can be easily considered by carrying out slight modifications to the model. In silicon experiments, students will obtain a better understanding of the real world and the consequences and implications of different decisions in the system. In this way, it also contributes to the development and use of assessment methods by students.

In this Special Issue we want to expose several state-of-the-art examples of how mathematical modeling and simulations can be incorporated by different disciplines and how they can increase the engagement and results of students in science and engineering courses.

Prof. Dr. J. Alberto Conejero
Guest Editor

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Keywords

Complex systems
Computational and numerical simulation
Engineering education
Engineering and environmental processes
Mathematical education
Mathematical modelling
Multiphysics processes

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Published Papers (12 papers)

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Research

20 pages, 2781 KiB

Open AccessArticle

Graph-Based Problem Explorer: A Software Tool to Support Algorithm Design Learning While Solving the Salesperson Problem

by Aura Hernández-Sabaté, Lluís Albarracín and F. Javier Sánchez

Mathematics 2020, 8(9), 1595; https://doi.org/10.3390/math8091595 - 16 Sep 2020

Cited by 4 | Viewed by 3885

Abstract

In this article, we present a sequence of activities in the form of a project in order to promote learning on design and analysis of algorithms. The project is based on the resolution of a real problem, the salesperson problem, and it is theoretically grounded on the fundamentals of mathematical modelling. In order to support the students’ work, a multimedia tool, called Graph-based Problem Explorer (GbPExplorer), has been designed and refined to promote the development of computer literacy in engineering and science university students. This tool incorporates several modules to allow coding different algorithmic techniques solving the salesman problem. Based on an educational design research along five years, we observe that working with GbPExplorer during the project provides students with the possibility of representing the situation to be studied in the form of graphs and analyze them from a computational point of view. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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20 pages, 3995 KiB

Open AccessArticle

Rational Design of a Genetic Finite State Machine: Combining Biology, Engineering, and Mathematics for Bio-Computer Research

by David Fuente, Óscar Garibo i Orts, J. Alberto Conejero and Javier F. Urchueguía

Mathematics 2020, 8(8), 1362; https://doi.org/10.3390/math8081362 - 14 Aug 2020

Cited by 1 | Viewed by 6890

Abstract

The recent success of biological engineering is due to a tremendous amount of research effort and the increasing number of market opportunities. Indeed, this has been partially possible due to the contribution of advanced mathematical tools and the application of engineering principles in genetic-circuit development. In this work, we use a rationally designed genetic circuit to show how models can support research and motivate students to apply mathematics in their future careers. A genetic four-state machine is analyzed using three frameworks: deterministic and stochastic modeling through differential and master equations, and a spatial approach via a cellular automaton. Each theoretical framework sheds light on the problem in a complementary way. It helps in understanding basic concepts of modeling and engineering, such as noise, robustness, and reaction–diffusion systems. The designed automaton could be part of a more complex system of modules conforming future bio-computers and it is a paradigmatic example of how models can assist teachers in multidisciplinary education. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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17 pages, 4068 KiB

Open AccessArticle

Backward Reasoning and Epistemic Actions in Discovering Processes of Strategic Games Problems

by Marta Barbero, Inés M. Gómez-Chacón and Ferdinando Arzarello

Mathematics 2020, 8(6), 989; https://doi.org/10.3390/math8060989 - 17 Jun 2020

Cited by 1 | Viewed by 3721

Abstract

The paper focuses on the cognitive and epistemic characterization of backward reasoning in strategy games resolution. It explores the use of abstraction in context (AiC) theory as a tool for the analysis of the epistemic actions involved in these processes. We follow a qualitative methodology based on design experiments, focusing on a study carried out with mathematics and engineering students. The analysis allowed us to combine the two models derived from the epistemology of mathematical backward reasoning and AiC theory in a unified framework that allowed us to focus both short-term and long-term processes in mathematical activities. Recurring patterns of epistemic actions were identified. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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16 pages, 1709 KiB

Open AccessArticle

Decision Trees for Evaluation of Mathematical Competencies in the Higher Education: A Case Study

by Atanas Ivanov

Mathematics 2020, 8(5), 748; https://doi.org/10.3390/math8050748 - 8 May 2020

Cited by 10 | Viewed by 7853

Abstract

The assessment of knowledge and skills acquired by the student at each academic stage is crucial for every educational process. This paper proposes and tests an approach based on a structured assessment test for mathematical competencies in higher education and methods for statistical evaluation of the test. A case study is presented for the assessment of knowledge and skills for solving linear algebra and analytic geometry problems by first-year university students. The test includes three main parts—a multiple-choice test with four selectable answers, a solution of two problems with and without the use of specialized mathematical software, and a survey with four questions for each problem. The processing of data is performed mainly by the classification and regression tree (CART) method. Comparative analysis, cross-tables, and reliability statistics were also used. Regression tree models are built to assess the achievements of students and classification tree models for competency assessment on a three-categorical scale. The influence of 31 variables and groups of them on the assessment of achievements and grading of competencies is determined. Regression models show over 94% fit with data and classification ones—up to 92% correct classifications. The models can be used to predict students’ grades and assess their mathematical competency. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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20 pages, 13907 KiB

Open AccessArticle

QMwebJS—An Open Source Software Tool to Visualize and Share Time-Evolving Three-Dimensional Wavefunctions

by Edgar Figueiras, David N. Olivieri, Angel Paredes and Humberto Michinel

Mathematics 2020, 8(3), 430; https://doi.org/10.3390/math8030430 - 16 Mar 2020

Cited by 5 | Viewed by 4000

Abstract

Numerical simulation experiments are of great importance for research and education in Physics. They can be greatly aided by proper graphical representations, especially for spatio-temporal dynamics. In this contribution, we describe and provide a novel Javascript-based library and cloud microservice—QMwebJS—for the visualization of the temporal evolution of three-dimensional distributions. It is an easy to use, web-based library for creating, editing, and exporting 3D models based on the particle sampling method. Accessible from any standard browser, it does not require downloads or installations. Users can directly share their work with other students, teachers or researchers by keeping their models in the cloud and allowing for interactive viewing of the spatio-temporal solutions. This software tool was developed to support quantum mechanics teaching at an undergraduate level by plotting the spatial probability density distribution given by the wavefunction, but it can be useful in different contexts including the study of nonlinear waves. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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16 pages, 1734 KiB

Open AccessArticle

Collaborative Learning Based on Harry Potter for Learning Geometric Figures in the Subject of Mathematics

by Antonio-José Moreno-Guerrero, Marina Rondón García, Nazaret Martínez Heredia and Antonio-Manuel Rodríguez-García

Mathematics 2020, 8(3), 369; https://doi.org/10.3390/math8030369 - 6 Mar 2020

Cited by 31 | Viewed by 8154

Abstract

Nowadays, education requires changes in the teaching and learning processes, through the implementation of innovative and motivating pedagogical actions, owing to the existing needs in society. Education, owing to the current needs of society, requires changes in the teaching and learning processes through the implementation of innovative and motivating pedagogical actions. The main objective of this study is to evaluate the effectiveness of the collaborative method, based on the Harry Potter theme, with respect to the traditional method in the first year of Obligatory Secondary Education for the learning of geometric figures in the subject of mathematics. For this purpose, a quasi-experimental, quantitative, descriptive, and correlational study has been designed, using a standardized questionnaire as a technique to collect information. The sample is composed of 236 students from the first year of Obligatory Secondary Education distributed in eight groups (four control and four experimental) from a public high school in the city of Cádiz (Spain). The tests carried out show that collaborative learning generates improvements in the attitudes and mathematical dimensions. Therefore, the collaborative method, developed by means of the Harry Potter theme for students in the first year of Compulsory Secondary Education in the subject of mathematics, causes a better attitude of the student towards the teaching and learning process. Furthermore, it facilitates the acquisition of mathematical contents related to geometry, which does not directly affect the students’ grades because, although those of the experimental group are better than those obtained by the control group, the differences between the two are minimal. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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14 pages, 302 KiB

Open AccessArticle

Secondary Education Students’ Beliefs about Mathematics and Their Repercussions on Motivation

by Vanesa Rojo Robas, José María Madariaga and José Domingo Villarroel

Mathematics 2020, 8(3), 368; https://doi.org/10.3390/math8030368 - 6 Mar 2020

Cited by 10 | Viewed by 6851

Abstract

This research analyses the role of the affective dimension in learning mathematics during secondary education. In particular, the evolution of motivation and beliefs according to the students’ academic level, as well as the relationship between these two factors. The sample consisted of 202 students from all four years of secondary education, whose motivation and beliefs about mathematics and learning mathematics were evaluated. Beliefs were grouped into three categories: related to the specific classroom context, to mathematics, and to oneself as a learner of this subject. The results obtained indicate lower motivation and less favourable beliefs in 3rd year. From the beliefs analysed, those regarding the classroom context, and more specifically the teachers, have obtained the largest effect size. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

13 pages, 253 KiB

Open AccessArticle

Fractions and Pythagorean Tuning—An Interdisciplinary Study in Secondary Education

by Rocío Chao-Fernández, Dorinda Mato-Vázquez and Aurelio Chao-Fernández

Mathematics 2019, 7(12), 1227; https://doi.org/10.3390/math7121227 - 12 Dec 2019

Cited by 2 | Viewed by 3376

Abstract

Formal education is experiencing a series of reforms that favor the integration of the contents of different areas in the teaching and learning of the different educational stages. The present study examined the use of an interdisciplinary music and mathematics experience in Secondary Education in Galicia (Spain) in the 2016/17 academic year. A descriptive–exploratory design was used, through a Likert questionnaire applied to 197 students with a diagnostic test and a reference test, and a study of multiple cases was carried out in which information was collected through classroom observations. The results show improvements in the understanding of mathematical and musical concepts, and attitudes and procedures so we can argue that the use of interdisciplinary activities have favored the development of teaching–learning opportunities in mathematical and musical training. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

18 pages, 7222 KiB

Open AccessArticle

Image Interpolation Using a Rational Bi-Cubic Ball

by Nur Atiqah Binti Zulkifli, Samsul Ariffin Abdul Karim, A’fza Binti Shafie, Muhammad Sarfraz, Abdul Ghaffar and Kottakkaran Sooppy Nisar

Mathematics 2019, 7(11), 1045; https://doi.org/10.3390/math7111045 - 3 Nov 2019

Cited by 28 | Viewed by 3059

Abstract

This study deals with the application of new rational bi-cubic Ball function with six parameters in image interpolation, especially for the grayscale image. These six free parameters can be modified to get better and quality image resolution, and refine the shape of the interpolating surface. This bivariate rational Ball function has been extended from univariate cases by using a tensor product approach. The proposed scheme is tested for image upscaling with factors of two and four through an efficient algorithm. The effectiveness of the proposed scheme is measured by using an image quality assessment (IQA), such as peak-signal-to-noise-ratio (PSNR), root mean square error (RMSE) or feature similarity (FSIM) index. Numerical and graphical results with comparisons against some existing scheme are presented by using MATLAB. The proposed scheme resulted in higher PSNR and FSIM, and smaller RMSE. Thus, the new rational bi-cubic Ball with six parameters is better than the existing scheme via an efficient algorithm. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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16 pages, 2903 KiB

Open AccessFeature PaperArticle

Undergraduate Students’ Solutions of Modeling Problems in Algorithmic Graph Theory

by Janka Medová, Kitti Páleníková, Ľubomír Rybanský and Zuzana Naštická

Mathematics 2019, 7(7), 572; https://doi.org/10.3390/math7070572 - 26 Jun 2019

Cited by 15 | Viewed by 5284

Abstract

Graphs can be considered as useful mathematical models. Graph algorithms are a common part of undergraduate courses in discrete mathematics. Even though they have been successfully implemented in secondary curricula, little research has been dedicated to the analysis of students’ work. Within a discrete mathematics course for university students, several graph algorithms were introduced via their applications. At the end of the course, the students took a test focused, inter alia, on applications of the algorithms. The mistakes that occurred in 127 students’ solutions of three problems (the Chinese postman problem, the shortest path problem, and the minimum spanning tree problem) were categorized and compared. Surprisingly, no mistakes were identified in the mathematization of situations or in the interpretation of results with respect to the wording of the problem. The categories of errors varied regardless of the problem types. Hierarchical cluster analysis grouped together the students’ solutions for the Chinese postman problem and the minimum spanning tree problem. By means of nonparametric item response theory analysis, the Chinese postman problem was identified as the most problematic for students. Possible sources of this difficulty are discussed in more detail herein. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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13 pages, 2237 KiB

Open AccessArticle

Modeling, Simulation, and Temperature Control of a Thermal Zone with Sliding Modes Strategy

by Frank Florez, Pedro Fernández de Córdoba, José Luis Higón, Gerard Olivar and John Taborda

Mathematics 2019, 7(6), 503; https://doi.org/10.3390/math7060503 - 2 Jun 2019

Cited by 10 | Viewed by 5211

Abstract

To reduce the energy consumption in buildings is necessary to analyze individual rooms and thermal zones, studying mathematical models and applying new control techniques. In this paper, the design, simulation and experimental evaluation of a sliding mode controller for regulating internal temperature in a thermal zone is presented. We propose an experiment with small physical dimensions, consisting of a closed wooden box with heat internal sources to stimulate temperature gradients through operating and shut down cycles. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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10 pages, 738 KiB

Open AccessArticle

Edge Irregular Reflexive Labeling for Disjoint Union of Generalized Petersen Graph

by Juan L. G. Guirao, Sarfraz Ahmad, Muhammad Kamran Siddiqui and Muhammad Ibrahim

Mathematics 2018, 6(12), 304; https://doi.org/10.3390/math6120304 - 5 Dec 2018

Cited by 13 | Viewed by 2588

Abstract

A graph labeling is the task of integers, generally spoken to by whole numbers, to the edges or vertices, or both of a graph. Formally, given a graph

G = (V, E)

a vertex labeling is a capacity from V [...] Read more.

A graph labeling is the task of integers, generally spoken to by whole numbers, to the edges or vertices, or both of a graph. Formally, given a graph

G = (V, E)

a vertex labeling is a capacity from V to an arrangement of integers. A graph with such a capacity characterized is known as a vertex-labeled graph. Similarly, an edge labeling is an element of E to an arrangement of labels. For this situation, the graph is called an edge-labeled graph. We examine an edge irregular reflexive k-labeling for the disjoint association of the cycle related graphs and decide the correct estimation of the reflexive edge strength for the disjoint association of s isomorphic duplicates of the cycle related graphs to be specific Generalized Peterson graphs. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)

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