Applied Mathematics Research Articles

Fostering quantitative reasoning abilities in medical education for future healthcare professionals

Madam, Quantitative reasoning (QR) refers to quantitative skills that involve the use of mathematical and statistical reasoning within a real-world context and are essential for understanding and studying social reality.1 QR, a multidisciplinary approach that combines mathematical skills, knowledge application, logical reasoning, and real-world problem-solving, is crucial for practical and informed decision-making across various disciplines.2 There is an international consensus that quantitative skills are crucial for undergraduate students in the life sciences.3 In 2020, recognising the importance of quantitative reasoning (QR), Higher Education Commission (HEC) introduced a policy for undergraduate degrees. Dow University of Health Sciences (DUHS) has implemented Quantitative Reasoning as a key component of major health disciplines, including undergraduate medical programs. This initiative is part of the first module of the MBBS programme and was introduced in 2024. This was a significant step toward mobilising future healthcare professionals with essential analytical skills. However, this shift had not been without challenges. Integrating quantitative reasoning into the undergraduate MBBS curriculum has increased stress levels among medical students, who are already facing challenges in transitioning from intermediate studies to the rigorous demands of medical school. This change has added to an already heavy workload, as students are expected to master a wide range of medical subjects within a limited timeframe. The additional analytical requirements of quantitative reasoning, combined with clinical subjects, have made the adjustment particularly challenging, leaving students feeling overwhelmed. To alleviate concerns among medical students about quantitative reasoning and the challenges of an integrated curriculum, we should design modules that enhance skills in quantitative numeracy. Small group teaching will be effective for learning QR because it facilitates interaction and detailed explanations. 4 Additionally, integrating interactive whiteboards into sessions is a practical method for teaching test ordering and interpretation to undergraduate students.5 A hybrid learning model could be implemented by providing tutorials as additional student support. In conclusion, although integrating QR into medical education may present initial challenges, it ultimately provides students with essential tools for their professional development. By designing a thoughtful curriculum and employing supportive teaching strategies, we can help students overcome their apprehension about QR and transform it into a valuable skill set that will benefit them in their medical careers.

STEM-BASED BIOLOGY LEARNING AND ITS IMPACT ON STUDENTS LEARNING OUTCOMES

Science learning, especially Biology, requires an approach that can integrate various disciplines and utilize technology to improve students' understanding and critical thinking skills. In this context, the application of Science, Technology, Engineering and Mathematics (STEM)-based learning models is a strategic step to improve learning outcomes. This research will focus on efforts to overcome various kinds of problems that are thought to be the cause of the low critical thinking of students in science subjects, to be able to create a learning atmosphere that is fun, interesting, in this study Quizizz-based learning STEM model will be carried out. The approach in this study is a quantitative approach, with the research method Experiment One Group Pretest-Post test Design model. The sample used is a saturated sample, namely all VIIIA class students as many as 42 people. The instruments used in this study were multiple choice questions on the pretest. The results of data analysis using normality test and regression and correlation analysis showed a significant effect of the application of STEM-based biology learning with increased learning outcomes.

Report from the EMS Executive Committee meeting in Turin, 15–17 November 2024

The EMS Executive Committee (EC) usually holds two major meetings each year, plus regular shorter virtual meetings. The second major meeting of 2024 was held from 15 to 17 November at the Department of Mathematics of the University of Turin (Italy). The event was organized by EC member Susanna Terracini, with support from the Italian Mathematical Union (UMI) and the Italian Society for Applied and Industrial Mathematics (SIMAI). This report focuses on matters of direct interest to EMS members, particularly the Committee’s strategic objectives and positions on

The Opinions of Academics on the Usage of Artificial Intelligence Tools in Primary Schools

Within the scope of this research, it is aimed to obtain academician opinions on the use of artificial intelligence applications such as ChatGPT in the teaching-learning process and classroom applications in primary schools. In this research, the case study method, which is one of the qualitative research approaches, was used. The study group of the research consists of 10 academicians working in state and foundation universities. A semi-structured interview form prepared by the researchers was used as a data collection tool. The data obtained were analyzed by content analysis method. The findings reveal that artificial intelligence tools make significant contributions to the teaching-learning process in areas such as measurement and evaluation and material preparation; to teachers in terms of saving time and understanding the curriculum; to professional development in terms of following the literature and improving field knowledge; and to students in areas such as increasing motivation and supporting individual learning. However, negative aspects such as ethical and security issues, weakening of higher-order thinking skills in students, and mislearning were also pointed out. In addition, it was stated that artificial intelligence tools can be used effectively in various classroom applications in social studies, Turkish, mathematics and science courses. The study emphasizes the importance of balanced and conscious integration of artificial intelligence in education.

Analysis of Grade 11 Students’ Conceptual Understanding in Probability Concepts: A Perspective of Skemp Understanding Theory

This study investigates Grade 11 high school students' conceptual understanding of probability concepts through the framework of Skemp's understanding theory. Recognising the critical role of mathematics in everyday life and its application across various fields, this study emphasises the need for deep comprehension rather than mere memorisation. Utilising a qualitative descriptive methodology, the research analyses the scripts of eight (8) students in response to a cognitive ability test focused on probability, revealing distinct patterns of understanding categorised as relational and instrumental. The findings indicate that while some students exhibit relational understanding, demonstrating the ability to explain concepts and apply knowledge flexibly, many struggle with instrumental understanding, relying on rote memorisation and showing difficulty in problem-solving. The study identifies specific misconceptions and gaps in understanding, such as equiprobability bias, representativeness bias, belief bias and proportional reasoning. These misconceptions hinder the students' engagement with probability concepts. Ultimately, this research highlights the necessity for improved instructional strategies that promote relational understanding, fostering meaningful connections between mathematical concepts. The insights gained from this analysis aim to inform educators and curriculum developers, providing a foundation for targeted interventions that enhance students' mathematical comprehension and application in real-world scenarios

A Zykov algebra approach to clique propagation: Classifying clique complexes in graphs

This study applies the method of Clique Propagation ‘initially used in the context of medical imaging’ to characterize two types of clique complexes: those that exhibit ‘total clique propagation’, forming a single cohesive clique, and those that demonstrate ‘normal clique propagation’, where a coherent clique is not formed. We utilize Zykov Algebra, a graph-theoretic framework characterized by its overlay [Formula: see text], link (∗), and induction [Formula: see text] operations, and segmentation ‘sub-graphs of a graph’ to analyze these propagations through a system of clique equations. The aim is to algebraically determine whether a set of cliques conforms to one of the two propagation types. This study includes solving, graph construction, and computational applications to illustrate the practical use of this methodology. The algebraic formulations and graph equations presented reflect not only a novel approach to representing graphs but also hint at a deeper mathematical framework with broad applicability. We believe that this perspective opens new doors for theoretical and practical application in mathematics, computer science, and beyond.

Volume of n-dimensional Spheres

In this paper, we present two methods to derive the formula for the volume of n-dimensional spheres in Euclidean space and analyze its asymptotic behavior as n approaches infinity using Stirlings formula. We then establish a connection between the infinite sum of all even-dimensional spheres of radius r and the exponential function through a differential equation. Our findings highlight the decay characteristics of high-dimensional volumes and reveal a novel link between geometry and analysis. This work not only refines classical volume estimation techniques but also offers valuable insights into applications in higher-dimensional mathematics, contributing to fields such as statistical mechanics and theoretical physics.

Similarity Solutions of Partial Differential–Integral Equations from the Theory of Stochastic Processes

First-exit problems are studied for two-dimensional diffusion processes with jumps according to a Poisson process. The size of the jumps is distributed as an exponential random variable. We are interested in the random variable that denotes the first time that the sum of the two components of the process leaves a given interval. The function giving the probability that the process will leave the interval on its left-hand side satisfies a partial differential–integral equation. This equation is solved analytically in particular cases by making use of the method of similarity solutions. The problem of calculating the mean and the moment-generating function of the first-passage time random variable is also considered. The results obtained have applications in various fields, notably, financial mathematics and reliability theory.

PENGARUH PENERAPAN ALGORITMA TERHADAP PEMBELAJARAN PEMROGRAMAN KOMPUTER

The advancement of information and computer technology is currently increasingly advanced, all fields of science require computer skills, so for students an understanding of mathematical logic and computer learning is very important because the two are interrelated. Based on the experience of learning computer programming courses, there are still many students who have not mastered the course. To overcome this, research was conducted by applying mathematics in computer programming learning. This research can be a qualitative research that aims to see the effect of the application of mathematics on student learning outcomes in computer programming learning. The research sample was students of STKIP AMAL BAKTI Medan in the 2024/2025 academic year consisting of two classes (experimental class and control class). After conducting the research, the following results were obtained: 1) The learning outcomes of students after applying mathematics to each programming class were better than students who received normal learning in terms of students in general; 2) The learning outcomes of students after applying calculations to each program structure were much better than students who received normal learning in terms of KAM (high, medium, and young)

Corrigendum to “Urban growth stage analysis with fractal dimension logistic curve modeling and head/tail breaks method” [Applied Mathematical Modelling Volume 138, Part B (2025) 115813

Corrigendum to “Urban growth stage analysis with fractal dimension logistic curve modeling and head/tail breaks method” [Applied Mathematical Modelling Volume 138, Part B (2025) 115813

THE CREATION OF INTEGRATIVE PROJECTS WITH MATHEMATICAL APPLICATIONS AS A TEACHING METHOD FOR IMPROVING LEARNING AND STRENGTHENING IN THE AREA OF MATHEMATICS.

The following article, using a constructivist and action research approach, explores how the implementation of integrative projects with mathematical applications can strengthen learning in this subject. A methodology was developed for the creation of five integrative projects with mathematical applications for a group of 20 students taking a mathematical calculus course. The research was directed toward two research questions. Among the most significant findings was that 93% of the students better understood mathematical concepts while applying them in their projects. There is a significant relationship (r=.92) between learning from the application of integrative projects and learning mathematics in the mathematical reasoning course. Keywords: integrative projects, learning, mathematicsThe following article, using a constructivist and action research approach, explores how implementing integrative projects with mathematical applications can strengthen learning in this subject. A methodology was developed for the creation of five integrative projects with mathematical applications for a group of 20 students studying mathematical calculus. The research was conducted with two research questions. Among the most significant findings was that 93% of the students better understood mathematical concepts by applying them to their projects. There is a significant relationship (r=.92) between learning from the application of integrative projects and learning mathematics in the mathematical reasoning course.

Technology-Based Interactive Mathematics Learning: A Case Study of Community Service Activities at SMA PGRI Cicalengka

The This community service activity was conducted through collaboration between the Mathematics Study Program of the Republic of Indonesia National University and SMA PGRI Cicalengka, involving 80 participants consisting of 12th-grade students. The one-day program aimed to enhance students' understanding of mathematics applications in science and technology (IPTEK), including programming algorithm simulations, through interactive lectures. The sessions focused on developing logical thinking, strategic problem-solving skills, and awareness of mathematics' role in daily life. The event began with an opening ceremony attended by school representatives, faculty members, and university officials. Two main sessions were delivered: the first covered practical applications of mathematics in everyday contexts, while the second highlighted its role in advancing IPTEK through online gaming. Active participation was observed during Q&A sessions. The program concluded with a satisfaction survey, with results analyzed and published as part of the activity's outcomes. Overall, this initiative successfully introduced students to the interdisciplinary relevance of mathematics while fostering engagement through interactive learning. Follow-up evaluations will assess its impact on strengthening students' appreciation of mathematics in technological and real-world applications.

Factorizations and Accurate Computations with Min and Max Matrices

Min and max matrices are structured matrices that appear in diverse mathematical and computational applications. Their inherent structures facilitate highly accurate numerical solutions to algebraic problems. In this research, the total positivity of generalized Min and Max matrices is characterized, and their bidiagonal factorizations are derived. It is also demonstrated that these decompositions can be computed with high relative accuracy (HRA), enabling the precise computations of eigenvalues and singular values and the solution of linear systems. Notably, the discussed approach achieves relative errors on the order of the unit roundoff, even for large and ill-conditioned matrices. To illustrate the exceptional accuracy of this method, numerical experiments on quantum extensions of Min and L-Hilbert matrices are presented, showcasing their superior precisions compared to those of standard computational techniques.

Instructional Competence of Mathematics Teachers: Basis for a Training Program

GONZALO, RAHMAN S. (2025). INSTRUCTIONAL COMPETENCE OF MATHEMATICS TEACHERS: BASIS FOR A TRAINING PROGRAM Master of Arts in Education, major in Educational Management. Ilocos Sur Polytechnic State College, Graduate School. Sta. Maria, Ilocos Sur. Adviser: MARIA TERESA T. GARCIA, EdD Despite extensive research on mathematics instruction, gaps persisted in understanding the interplay between teaching strategies and teacher characteristics such as age, experience, gender, and technological integration. Limited studies also explored the impact of specific mathematical applications on student learning, the effect of multiple teaching preparations on instructional competence, and the competence differences between mathematics and non-mathematics teachers. Given these gaps, this study aimed to assess the pedagogical competence of secondary mathematics teachers in the Schools Division of Candon City, serving as a foundation for a targeted training program. Employing a descriptive-developmental quantitative design, the study involved secondary mathematics teachers and a representative sample of students. A structured questionnaire checklist, adapted from the DepEd Class Observation Tool (DepEd Memorandum No. 004, s. 2022) and Ragma’s (2017) pedagogical competence instrument, was used to assess instructional competence across teaching, management, guidance, and evaluation skills. Data analysis included frequency counts and percentages for respondent profiles, and weighted means for instructional competence levels, t-tests for group perception differences, and Pearson’s correlation and chi-square tests for relationships between teacher profiles and instructional competence. Findings identified strengths and weaknesses, which served as the basis for developing an evidence-based training program to enhance mathematics instruction. The results indicate that mathematics teachers are highly competent, with overall ratings of Excellent in Guidance, Management, and Evaluation Skills, and Teaching/Facilitating Skills. Teachers consistently rated themselves slightly higher than students did, but both groups acknowledged strong instructional abilities. The findings suggest that while teachers excel in classroom management, student guidance, and assessment, there is room to enhance teaching strategies for better student engagement. Moreover, it signifies that there is no significant relationship between mathematics teachers' profiles and their instructional competence across teaching/facilitating, guidance, management, and evaluation skills. The study highlights that mathematics teachers demonstrate a high level of instructional competence, with strong subject mastery, effective teaching skills, and the ability to integrate technology into their teaching. However, there is a need for continuous improvement in diversifying teaching methods, refining assessment strategies, and enhancing adaptability to different learning styles to further optimize student learning outcomes. To enhance Mathematics instruction, intensify teacher training programs, integrate technology through educational applications like Kahoot and Geogebra, and develop interactive slides catering to diverse learning styles. Additionally, invest in Continuous Professional Development (CPD) through regular workshops, mentorship programs, and collaborative learning communities to foster innovation and knowledge sharing among educators.

Some Properties of Bessel I_2-Δ_θ^n-Asymptotically Statistical Equivalent Double Sequence of Order ρ ˜

In the context of sequence spaces and summability theory, significant progress has been made in the theoretical foundations of classical concepts such as convergence and boundedness. However, the exploration of innovative convergence methods continues to emerge as a critical area of research. A notable gap in the literature is the integration of Bessel functions into these theoretical frameworks. This study aims to fill this gap by introducing the concepts of Bessel I_2-Δ_θ^n-asymptotically statistical equivalence of order ρ ˜ and strong Bessel I_2-Δ_θ^n-asymptotically equivalence of order ρ̃ for double sequences, examining the comprehensive interrelations of these concepts. The inclusion of Bessel functions in these theories not only extends the existing theoretical frameworks within mathematical analysis but also provides a solid foundation for further research and the solution of applied problems in the field. These innovative concepts contribute to a deeper understanding of sequence behavior related to Bessel functions and enhance their applicability in mathematical applications.

The Application of Mathematics in Logistics Distribution Optimization

The optimization of logistics delivery routes plays a crucial role in reducing transportation costs and improving delivery efficiency. This paper focuses on the problem of logistics delivery route optimization, taking 20 Hema Fresh stores in Pudong New Area, Shanghai as the research object. By analyzing factors such as vehicle load limits and variable costs generated during the delivery process, a suitable mathematical model is constructed. Subsequently, the greedy algorithm and the genetic algorithm are applied to solve the model respectively, aiming to find the optimal delivery routes. The performance differences of different algorithms in practical applications are compared in detail. The research results show that different algorithms have different effects on the optimization of logistics delivery routes and need to be selected according to the actual situation. This paper provides a feasible solution and useful reference for the logistics delivery route planning of Hema Fresh and other fresh - food e - commerce enterprises.

Combinatorial Approaches to Database Query Optimization: Enhancing Efficiency and Performance

Database query optimization plays a crucial role in the efficiency of database management systems (DBMS). As data complexity increases, optimizing query performance becomes even more critical. This paper investigates the application of combinatorial mathematics in query optimization, particularly focusing on the algorithms and techniques that aid in determining optimal query execution plans. The role of combinatorial algorithms in solving problems related to join ordering, query enumeration, and graph traversal is examined. By leveraging combinatory, database systems can process queries more efficiently, improving resource management, response time, and overall system performance.

An investigation of the mathematics applications in the Apple App Store: Do they contain benchmarks of educational quality?

Given the numerous mathematics applications marketed in the Apple App Store and the lack of quality control, it is critical to determine whether these digital learning tools are well-designed and if they are accurately marketed by developers. The present study evaluated the top math apps (n = 33) priced under $15, categorized into three age groups (i.e. <5, 6-8, and 9-11) in the App Store. It examined how well they incorporate five educational features or benchmarks in their apps, namely- scaffolding, feedback, learning theory, math subjects, and content integration (i.e. the connection between game and learning content). Furthermore, it assessed whether developers mentioned these benchmarks in their store descriptions and if the descriptions accurately reflected the app’s content. Most apps included more than three benchmarks. All apps contained feedback and learning theory and most provided some forms of scaffolding. The types and amount of math subjects, feedback, and scaffolding varied significantly across apps. Interestingly, these top apps contained more benchmarks and content than developers advertise in the App Store. The findings emphasize the importance of developers incorporating benchmarks into their apps and accurately communicating this to the public to help them navigate the sea of available apps.

A Probabilistic Formulation of Problem of Optimal Search for a Lost Person

This paper deals with a simple probabilistic description of some issues related to searching for a missing person. The questions solved are only a small part of a complex area of the search and rescue problems, but they nevertheless concern at least two interesting points of the application of mathematics in managerial decision-making. First, we propose the use of Bayes’ rule to recalculate the probability of a lost person’s location based on additional information. Next, the optimal ordering of searched areas is determined that minimizes the average (expected) search time. Finally, the proposed solutions will be illustrated with several artificial examples.

Review of «Mathematical modeling of ethanol kinetics» monograph by G.V. Nedugov

Main concepts of "Mathematical modeling of ethanol kinetics" monograph by G.V. Nedugov were analyzed in the article covering relevance, scientific and practical significance. It has been shown that comprehensive analysis of existing and proposed by the author mathematical models for assessing ethanol kinetics presented in the article is a significant contribution to the scientific and practical base of forensic medicine. The possibilities of mathematical models' effective application as a practical solution of forensic medical tasks based on objective mathematical methods were noted. Undoubtedly, the monograph is interesting not only for forensic doctors but also for other specialists of medical and biological sphere.