Applied Mathematics Research Articles

The Application of Mathematics in Geophysical Image Processing and Analysis

With the widespread application of big data technology across various industries, cultivating big data analysis capabilities in accounting-related majors has become a crucial direction in higher education. This study aims to explore the construction of a practical training base for big data analysis in accounting majors in the "intelligent" era. By analyzing the current application status of big data technology in the accounting field and combining it with educational and teaching needs, a systematic and scientific training base construction plan is proposed. The research results show that building a big data analysis training base can not only enhance students' data analysis capabilities and practical skills but also provide strong support for the teaching reform of accounting majors in colleges and universities.

Needs Analysis in English for Moroccan Applied Mathematics Graduate Students at Ibn Zohr University

This study examined the English academic needs of students in the Applied Mathematics in the Science of Engineering (AMSE) master program at the Faculty of Sciences, Ibn Zohr University, Morocco. It aimed at determining the gap between students' language needs and their actual competencies and identifying learners’ perceptions of their linguistic needs and their linguistic difficulties. The study was conducted based on a mixed-methods design approach with multiple data collection instruments. As a research framework, the Dudley-Evans and St John's (1998) needs analysis model was used. The results showed that participants attach different values to the importance and competence of macro- and micro-language skills. Students and teachers placed a high value on grammatical knowledge. Students valued grammar, speaking, and writing highly, while subject matter teachers valued grammar, speaking, and writing highly, but listening and pronunciation skills were valued as less important. The study showed that learners' English proficiency level is average. Their average English levels then influenced their academic achievement. Based on the aforementioned results, the researchers proposed that syllabus designers should address the macro- and micro-skills regarding academic studies when developing and redesigning course syllabus and its objectives in the ESP context.

Preface: 3rd International Conference on Applied Mathematics, Modeling Simulation and Automatic Control (AMMSAC 2024)

Preface: 3rd International Conference on Applied Mathematics, Modeling Simulation and Automatic Control (AMMSAC 2024)

Mapping Ethnomathematical Research Directions and Trends in the Scopus Database: A Bibliometric Analysis

<p style="text-align:justify">Although research on ethnomathematics has been widely carried out, there is still little empirical evidence reporting the mapping and trends of ethnomathematical research in Scopus-indexed journals. The purpose of writing this article is to map trends in ethnomathematical research in Scopus-indexed journals in the range from 1986 to 2022. The fundamental tenet of ethnomathematics is to study, appreciate, and exclusively take into account the application of mathematics by ethnic groups. In other words, in understanding mathematics to look attractive, it is necessary to make a connection between everyday life and the realm of abstract mathematics. Scopus is a resource for further research, identifying scientific uniqueness and gaps. This study uses bibliometric analysis methods using VOSviewer, article searches using Publish or Perish (version 8), and SEforRA applications. Bibliometric research provides a reliable and impartial way to gauge the contribution of an article to knowledge advancement and is a tool that is often used to analyze trends and performance on certain subjects. These findings reveal an increasing trend in ethnomathematical research and identify some topics or keywords that could form the basis for additional studies. In conclusion, for future studies, bibliometric analysis will provide information and knowledge about the evolution of ethnomathematical research.</p>

An Example of Using Advanced Excel Applications Within the Scope of Financial Mathematics Calculations: Modelling of Calculations Related to Annuities in Microsoft Excel Program

Financial mathematics applications, form the mathematical basis for rational financial decisions within the scope of financial management. Carrying out financial management in line with the scientific rules is of vital importance for businesses to sustain their existence and carry out their activities effectively and efficiently. In this context, the ability to carry out financial management rationally is only based on the correct determination of the mathematical datas (etc. time value of money) that forms the basis for decisions. The use of technology in this area is very important and technology level in this area has evolved from financial calculators to computer programs and MS. Excel program is perhaps the most important application tool in this field according to its mathematical calculation capacity and capability. In this regard, the study reveals how to perform complex calculations regarding the present and future values of different annuity types in Excel. The calculation of all variables related to annuity calculations and the mathematical relationships between variables are discussed separately according to different annuity types is examined with a model which developed in Excel program within the scope of the purpose of the study. The study will provide guidance to academics related to the field and professionals working in the field of financial management by combining theoretical knowledge and practical applications.

Skew-Normal Inflated Models: Mathematical Characterization and Applications to Medical Data with Excess of Zeros and Ones

The modeling of data involving proportions, confined to a unit interval, is crucial in diverse research fields. Such data, expressing part-to-whole relationships, span from the proportion of individuals affected by diseases to the allocation of resources in economic sectors and the survival rates of species in ecology. However, modeling these data and interpreting information obtained from them present challenges, particularly when there is high zero–one inflation at the extremes of the unit interval, which indicates the complete absence or full occurrence of a characteristic or event. This inflation limits traditional statistical models, which often fail to capture the underlying distribution, leading to biased or imprecise statistical inferences. To address these challenges, we propose and derive the skew-normal zero–one inflated (SNZOI) models, a novel class of asymmetric regression models specifically designed to accommodate zero–one inflation presented in the data. By integrating a continuous-discrete mixture distribution with covariates in both continuous and discrete parts, SNZOI models exhibit superior capability compared to traditional models when describing these complex data structures. The applicability and effectiveness of the proposed models are demonstrated through case studies, including the analysis of medical data. Precise modeling of inflated proportion data unveils insights representing advancements in the statistical analysis of such studies. The present investigation highlights the limitations of existing models and shows the potential of SNZOI models to provide more accurate and precise inferences in the presence of zero–one inflation.

THE URGENCY OF CRITICAL THINKING DISPOSITION IN MATHEMATICS LEARNING IN THE INDEPENDENT CURRICULUM

The purpose of this article is to describe the definition and characteristics of critical thinking disposition, mathematics learning in the independent curriculum, and to analyze the urgency of critical thinking disposition in mathematics learning, especially in the application of mathematics learning in the independent curriculum. This research is descriptive research using the systematic literature review method through searching for accurate and relevant references, namely articles, books, and other relevant sources. From the results of the analysis, it is concluded that the urgency of critical thinking disposition in mathematics learning in the independent curriculum can be seen from several dimensions of the Pancasila student profile, especially the critical reasoning dimension which involves critical thinking disposition and needs to be built optimally and balanced in mathematics learning; the things that are emphasized in mathematics learning in the independent curriculum and involve critical thinking disposition include mathematical problem solving activities, student independence in understanding the mathematics material, and discussion and collaboration activities; mathematics learning models in the independent curriculum that direct students to involve critical thinking disposition; and projects to strengthen the Pancasila student profile in mathematics learning which involve critical thinking disposition in activities and their assessments

Pengembangan Aplikasi Android Guizzer sebagai Media Pembelajaran Matematika untuk Siswa Kelas V Sekolah Dasar

Purpose – This research aims to determine the feasibility of the Android-based "guizzer" application in mathematics learning for fifth grade elementary school. The lack of teacher innovation in the use of learning media, especially mathematics, makes students less enthusiastic. Therefore, researchers developed an Android-based Guizzer application to improve the quality of fifth grade elementary school mathematics learning.Method – This research uses Research and Development (R&D) research with the ADDIE development model including the Analyze, Design, Development, Implement and Evaluate stages. This research was carried out at Waturoyo State Elementary School with the research subject being class V. Data collection techniques used included observation, interviews and questionnaires. The data analysis used is in the form of validity.Findings – The research results show that the results of media validation by validator 1 were 78.3% and validator 2 were 85%, resulting in an average of 81.65% (very feasible). The results of material validation by validator 1 obtained a percentage of 83.3% and validator 2 of 81.7%, so an average of 82.5% was obtained (very feasible). The results of the trial, namely student responses, obtained a percentage of 97.1% (very feasible). It can be concluded that the "guizzer" application is very suitable for use in the learning process. Research Implications – Based on the research results, the Android application "Guizzer" is suitable for use in the fifth grade elementary school mathematics learning process. The implication is that students are interested and enthusiastic in the learning process, thereby making a positive contribution to achieving learning goals.

Exploring the relationship between students' attitudes and fraction sense proficiency across lower secondary grades

Understanding fractions is a critical mathematical skill necessary for more advanced mathematical concepts and applications. However, many students struggle with fraction sense, which is the foundational understanding and flexible use of fractions. This study aims to explore the relationship between students' attitudes toward learning fractions and their proficiency in fraction sense in lower secondary grades. Using a descriptive-correlational design, data were collected from 296 students aged 13 to 15 using the Fraction Sense Test (FST) and the Attitudes Towards Learning Fractions Questionnaire (ATLF). The study found that students consistently struggled with fractional concepts, achieving low scores across all grades. Nevertheless, a significant, though diminishing, relationship was observed between positive attitudes towards fractions and fraction sense proficiency from Secondary One to Secondary Three. These findings suggest the need to integrate meaningful fraction learning approaches to maintain students' positive attitudes, thereby improving their overall mathematical competence.

A reliable neural network procedure for the novel sixth-order nonlinear singular pantograph differential model

An innovative singular nonlinear sixth-order (SNSO) pantograph differential model (PDM), known as the SNSO-PDM, is the subject of this novel study along with its numerical investigation. The concepts of pantograph and conventional Emden-Fowler have been presented in the design of the novel SNSO-PDM. The models based on Emden–Fowler have huge applications in mathematics and engineering and are always difficult to solve due to singularity. For each class of the innovative SNSO-PDM, the singularity, shape and pantograph factors are described. A reliable stochastic Levenberg-Marquardt backpropagation neural network (LMBPNN) procedure is designed for the SNSO-PDM. The correctness of the SNSOs-PDM is observed through the comparison performances of the achieved and reference outputs. The obtained results of the SNSO-PDM are considered by applying the process of training, certification, and testing to reduce the mean square error. To authenticate the efficacy of the innovative SNSO-PDM, the numerical performances of the solutions are depicted in the sense of regression, error histograms and correlation.

Applications of Fourier transforms in engineering

The Fourier transform was proposed by Fourier in 1807. Fourier transform is a method of analyzing signals, which can analyze the components of the signal or synthesize the signal using these components. Many waveforms can be used as signal components, such as sine waves, square waves, sawtooth waves, etc. The Fourier transform uses sine waves as components of the signal. Due to its excellent properties, the Fourier transform has a wide range of applications in physics, number theory, combinatorial mathematics, signal processing, probability, statistics, cryptography, acoustics, optics, and other fields. This paper focuses on the study of fractional-order Fourier transform in the engineering field, for the equipment of the tiny fault diagnosis method, and according to some existing diagnostic methods, put forward the idea of diagnostic method enhancement.

Mini-Workshop: Felix Klein’s Foreign Students: Opening Up the Way for Transnational Mathematics

Extending existing analyses of the topic, the workshop aimed to investigate the influence of Felix Klein on the development of mathematics (especially number theory, algebra, geometry, analysis, applications of mathematics in scientific and technical fields as well as in mathematics education) in countries other than Germany. The goal of the workshop was to take a look at mathematicians of foreign origin who studied with Klein that have received little attention so far (including Czech, Greek, Hungarian, Japanese, Polish, Russian, and Ukrainian mathematicians) and uncover how Klein guided them through his lectures and seminars. The protocols of the lectures held in Klein’s seminars (from 1872 to 1912 in Göttingen, Erlangen, and Leipzig), which are a unique and so far largely unexplored source, were the basis for the workshop.

Preface of the proceedings: mathematical analysis and applications

Preface of the proceedings: mathematical analysis and applications

About properties and the monomiality principle of Bell-based Apostol-Bernoulli-type polynomials

This article investigates the properties and monomiality principle within Bell-based Apostol-Bernoulli-type polynomials. Beginning with the establishment of a generating function, the study proceeds to derive explicit expressions for these polynomials, providing insight into their structural characteristics. Summation formulae are then derived, facilitating efficient computation and manipulation. Implicit formulae are also examined, revealing underlying patterns and relationships. Through the lens of the monomiality principle, connections between various polynomial aspects are elucidated, uncovering hidden symmetries and algebraic properties. Moreover, connection formulae are derived, enabling seamless transitions between different polynomial representations. This analysis contributes to a comprehensive understanding of Bell-based Apostol-Bernoulli-type polynomials, offering valuable insights into their mathematical nature and applications.

Comparing Ninth-Grade Students’ Approaches to Trigonometric Ratio Problems Through Real-World and Symbolic Contexts

This study investigates the problem-solving strategies employed by ninth-grade students when addressing symbolic and real-world contextual problems involving trigonometric ratios. Conducted with 46 ninth-grade students from a Turkish public high school, this research employed a worksheet consisting of six problems aligned with the Turkish ninth-grade mathematics curriculum. Three of these problems were based on real-world contexts, while the other three were conventional symbolic problems. The findings indicate that students exhibited proficiency in identifying similarity ratios using side length ratios. Additionally, the results revealed that students were more adept at solving real-world mathematical scenarios compared to purely symbolic tasks. This study offers significant insights into the problem-solving strategies of ninth-grade students when confronted with trigonometric ratio problems. It underscores crucial implications for mathematics curricula and pedagogy, highlighting the importance of preparing ninth-grade students for success in their future academic and professional endeavors. The study emphasizes the necessity for a balanced approach in teaching, integrating both real-world and symbolic problem-solving tasks to enhance students’ mathematical understanding and application. By identifying the strengths and areas for improvement in students’ problem-solving strategies, this research contributes to the development of more effective educational practices that address the diverse needs of learners.

Using ChatGPT as a Tutor to learn Mathematics Application Program

The ability of ChatGPT to understand conversational context and provide relevant responses makes it very useful in human-computer interactions. ChatGPT can be a very useful tool for mathematics teachers in their role as tutors to learn and teach various applications related to mathematics. In this digital era, mathematical applications and software like GeoGebra, Matlab, Augmented Reality, and SPSS are becoming increasingly important in teaching and learning mathematics. ChatGPT can help teachers understand how to use these tools by providing detailed explanations, tutorials, and examples of their application in teaching. This research aims to determine the effectiveness and efficiency of ChatGPT in helping teachers understand and apply technologies such as GeoGebra, Matlab, Augmented Reality, and SPSS. Participants in this case study research consisted of 5 teachers. The categories of participant questions asked to ChatGPT included (1) General explanation of the application, (2) How to download the application, (3) Equipment specifications required, (4) General use of the application, and (5) Requesting sample commands in the application. The results of this study indicate that participants will successfully use ChatGPT as a tutor for learning Mathematics Application Programs if they have the necessary equipment specifications required by the applications and are able to download the applications.

Learning by Doing: The Industrial and Applied Mathematics Program at Eindhoven University of Technology

Learning by Doing: The Industrial and Applied Mathematics Program at Eindhoven University of Technology

An introduction to mathematical algorithms and Artificial Intelligence

Artificial Intelligence (AI), as a hot topic in today's science and technology, has penetrated into every aspect of our lives. The relationship between AI and mathematics and algorithms has become increasingly close. Mathematics, as a basic science, provides the theoretical basis for AI algorithms and models and is an essential part of the development of AI. The algorithm is an element that acts as a bridge between mathematics and AI and is a series of steps taken to solve a particular problem or reach a clear result [1]. The purpose of this paper is to explore the application and impact of mathematics and algorithms in the field of AI, and to explore how AI can bring about far-reaching changes in our society and human development.

Vedic mathematics for sustainable knowledge: a systematic literature review

PurposeThis research lies in the domain of Vedic mathematics, and it explores the application of the related Vedic sutras in different branches of mathematics, science, education, and engineering across Asia and Europe.Design/methodology/approachThe study embraced a qualitative research design followed by a systematic literature review (SLR) approach which describes the significance of Vedic mathematics. The study made use of purposive sampling through which the data were collected from 102 articles by using inclusion and exclusion criteria. It includes publication years, the types of research methods, and uses of Vedic mathematics sutras in different branches of knowledge stated by the researchers. Its goal is to offer a more thorough explanation and an evaluation of how the inquiry affected the conclusions. The articles examined in this review included all the journal articles and doctoral theses from the databases of Google Scholar, Science Direct, Scopus, and Sodhganga which were published during the period 2010–2022.FindingsThe research found that the application of the sutras of Vedic mathematics has been increasing immensely in India. The researchers in this area are fond of qualitative research methods. This research has shown that sutras of Vedic mathematics especially “Urdhvatiryakbhyam” and “Nikhilam Navatascaramana Dasastah” have been frequently used in mathematics and engineering in technical higher education. The impact of other sutras has been quite useful, which augments that in many disciplines where the applications of Vedic mathematics are prevalent, it can be functional. The study concludes by reprising the result, its limitations, and the use of Vedic mathematics as a sustainable source of knowledge.Research limitations/implicationsVedic mathematics is an area where a lot of potential applications are created in science, mathematics, engineering, and education. Even with the latest technological advancements like learning analytics, artificial intelligence has its connection with this branch of learning, which is the greatest treasure of the Indian knowledge system. The research in this area is not reported in any databases or any standard format so researchers find it difficult to locate and study this broad conceptual domain.Practical implicationsIt will help the reader and other academic stakeholders to widen their view on the new and innovative techniques of Vedic mathematics. It is advised that additional studies would look at and evaluate papers published after this time so that readers may get a wider view of the concept of Vedic mathematics.Social implicationsIt will help society to know the essence of Vedic mathematics that how useful it is. Vedic mathematics helps learners to learn in a very factual and accurate manner especially while dealing with mathematical calculations. It will enhance the problem-solving skills among learners. It will be beneficial for all types of learners which will help them to become better individuals for a nation.Originality/valueThe paper enriches understanding of the potential applications of different sutras from Vedic literature in different fields of knowledge. The outcome of the research encourages educationists and policymakers to include Vedic mathematics in the curriculum to foster quantitative reasoning and problem-solving at varied levels of learning.

Preface to the Special Issue “State-of-the-Art Mathematical Applications in Europe”

This book collects under one cover twelve original research papers and one review paper submitted to the Special Issue “State-of-the-Art Mathematical Applications in Europe” and published in the MDPI journal Mathematics from December 2021 to January 2023 [...]