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JTAM (Jurnal Teori dan Aplikasi Matematika)
Published by Universitas Muhammadiyah Mataram
ISSN : 25977512     EISSN : 26141175     DOI : 10.31764/jtam
Core Subject : Education,
Mathematics
Jurnal Teori dan Aplikasi Matematika (JTAM) dikelola oleh Program Studi Pendidikan Matematika FKIP Universitas Muhammadiyah Mataram dengan ISSN (Cetak) 2597-7512 dan ISSN (Online) 2614-1175. Tim Redaksi menerima hasil penelitian, pemikiran, dan kajian tentang (1) Pengembangan metode atau model pembelajaran matematika di sekolah dasar sampai perguruan tinggi berbasis pendekatan konstruktivis (PMRI/RME, PBL, CTL, dan sebagainya), (2) Pengembangan media pembelajaran matematika berbasis ICT dan Non-ICT, dan (3) Penelitian atau pengembangan/design research di bidang pendidikan matematika, statistika, analisis matematika, komputasi matematika, dan matematika terapan.
Arjuna Subject : -
Articles 540 Documents
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Dynamical Analysis of Discrete-Time Modified Leslie-Gower Predator-Prey with Fear Effect Purnomo, Anna Silvia; Darti, Isnani; Suryanto, Agus; Kusumawinahyu, Wuryansari Muharini
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26515

Abstract

It has been studied that fear plays a significant role in establishing ecological communities, influencing biodiversity, and preserving ecological balance in predator-prey interactions. In this study, it is proposed a discrete-time predator-prey model that takes the fear effect into account that is derived by using Euler method. Objective of this study is analyzing the model by linearization. Similar to the continuous model properties, the trivial fixed point and the predator-free fixed point are both unstable. The discrete model differs from the continuous model in that the stability of the interior fixed point and the free prey fixed point is affected by the time step size. Using numerical methods, we examine period-doubling bifurcations related to interior fixed point and prey-free point that are impacted by time step size.
A Posteriori Premium Rate Calculation using Poisson-Gamma Hierarchical Generalized Linear Model for Vehicle Insurance Novkaniza, Fevi; Putri, Irene Devina; Kafi, Rahmat Al; Devila, Sindy
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27837

Abstract

This study develops and applies the Poisson-Gamma Hierarchical Generalized Linear Model (PGHGLM) to address the challenge of determining accurate and fair premium rates in vehicle insurance. The PGHGLM models a mixture distribution for the response variable, influenced by random effects, and employs a logarithmic link function. Parameter estimation is conducted using the maximum likelihood method. However, since analytical estimation is not feasible, the numerical conjugate gradient method, specifically the Fletcher-Reeves algorithm, is utilized. The implementation of the PGHGLM uses the longitudinal Claimslong dataset, incorporating driver age as a covariate. The main contribution of this research lies in integrating a priori risk classification with a posteriori adjustment based on longitudinal claim frequency data. For datasets without covariates, trend parameters are incorporated into the model. For datasets with covariates, such as driver age, the average claim frequency is computed for each age category. Results show that posteriori premium rates increase with rising claim frequency from the previous year, with higher claim frequencies leading to larger rate adjustments in the subsequent year. Through the PGHGLM, a posteriori premium rate estimates are obtained for each age group of vehicle insurance policyholders. This study demonstrates the practical application of the PGHGLM in calculating precise premium rates. By analyzing a longitudinal vehicle insurance dataset, the model generates annual a posteriori premium rates tailored to age groups. These findings underscore the PGHGLM’s robust methodological framework and its potential to enhance premium fairness, enable risk-adjusted pricing, and better tailor insurance products to diverse policyholder profiles. 
Trace of the Positive Integer Powers (n-1)-Tridiagonal Toeplitz Matrix n×n Aryani, Fitri; Wati, Fitri Ambar; Marzuki, Corry Corazon; Zukrianto, Zukrianto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27387

Abstract

The trace of a matrix is obtained by summing the elements along the main diagonal of a square matrix. The matrix used in this study is a Toeplitz (n-1)-tridiagonal matrix of order n×n. The aim of this research is to determine the general form or formula for the trace of a Toeplitz (n-1)-tridiagonal matrix of order n×n raised to a positive integer power. This research is quantitative, with the research instrument being the collection of data from the multiplication of Toeplitz (n-1)-tridiagonal matrices starting from order 3×3 from powers 2 through 10. This process continues up to order 6×6 from powers 2 through 10, until the pattern becomes apparent. The results of the research are two general forms of the powers of the Toeplitz (n-1)-tridiagonal matrix of order n×n: one for odd positive integer powers and another for even positive integer powers, both of which have been proven using mathematical induction. Furthermore, by using the definition of the trace of a matrix obtained two general forms for the trace of the Toeplitz (n-1)-tridiagonal matrix of order n×n are also derived: one for odd positive integer powers and another for even positive integer powers from the general form of the matrix power. Given the application of these two general forms in example problems with the order 8x8 for powers 12 and 21.
Effectiveness of Mathematics Learning using the Google Sites Application at Junior High School Fauziyah, Nur; Martiningsih, Raden Roro
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.28167

Abstract

Building innovative learning can be achieved by utilizing the Google Sites application in learning the topic of value comparison in grade VII of junior high school. The purpose of this study was to determine the effectiveness of using Google Sites in value comparison learning at SMP Muhammadiyah 1 Surabaya. This study used an experimental research design to compare the mathematics learning achievements of grade VII students at SMP Muhammadiyah 1 Surabaya who utilized Google Sites and those who did not. The treatment provided was the use of Google Sites in value comparison learning, referred to as the experimental class, consisting of 24 students. Meanwhile, learning in the class that did not use Google Sites was called the control class, consisting of 22 students. Both the experimental and control classes had the same mathematical abilities, based on the results of the homogeneity test using the summative scores from the previous semester. The research instrument was substantively validated by experts. Through Google Sites, students can access content such as texts, instructional videos, and quizzes organized on a site that is easily accessible to them anytime and anywhere. Google Sites allows students to learn independently, offering visual explanations of math concepts and providing immediate feedback through online quizzes. The results of this study showed that the average difference in the learning achievement of value comparison between students who utilized Google Sites was 8.125, while the group of students who did not utilize it was 6.00. The results of the t-test showed a significance value of 0.007, with a significance level of 0.05, indicating a significant difference in the learning achievement of value comparison between students who utilized and those who did not utilize Google Sites. Therefore, it can be concluded that learning with Google Sites in the topic of value comparison has a significant effect on students' learning achievement.
Analysis of Rainbow Vertex Antimagic Coloring and its Application to Cryptographic Secret Sharing with Affine Cipher Technique Dafik, Dafik; Firdausiyah, Iftitahul; Adawiyah, Robiatul; Agustin, Ika Hesti; Mursyidah, Indah Lutfiyatul; Marsidi, Marsidi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.28037

Abstract

Rainbow vertex antimagic coloring is a novel concept in graph theory that combines rainbow vertex connection with antimagic labeling. Rainbow vertex connection is a vertex coloring where each vertex in a simple connected graph G=(V,E) is connected by a path such that all interior vertices have distinct colors. The antimagic labeling assigns a bijective function f:E(G)→ {1,2,3,...,|E(G)|} to the edges, and the vertex weight w_f(v) = ∑_(e∈ E(v))▒〖f(e)〗, where E(v) is the set of edges adjacent to vertex ?. A graph ? achieves rainbow vertex antimagic coloring if all its internal vertices have unique vertex weights. This research investigates the application of rainbow vertex antimagic coloring to Shadow D_2 (S_n) graphs and Amal(V_n,v,m) graphs in cryptographic secret sharing and encryption using the affine cipher technique. The study employs mathematical modeling, graph visualization tools, and cryptographic software to ensure methodological rigor. The encryption and decryption processes are evaluated based on effectiveness, including brute force test resistance, encryption time, and encryption size. The results demonstrate that rainbow vertex antimagic coloring is an effective method for dividing cryptographic keys into segments during the secret sharing stage and serves as a robust key in the affine cipher technique. The method offers significant advantages, including faster encryption times for Shadow D_2 (S_n) graphs compared to Amal(V_n,v,m) graphs and reduced encryption size for Amal(V_n,v,m) graphs. Both graphs exhibited strong resistance to brute force attacks. In conclusion, this study highlights the relevance of rainbow vertex antimagic coloring in advancing graph theory applications and its utility in developing secure and efficient cryptographic systems. These findings contribute to bridging theoretical graph concepts with practical cryptographic implementations.
A Comparative Analysis of First-Difference GMM and System GMM Approaches on Economic Growth Hendayanti, Ni Putu Nanik; Nurhidayati, Maulida; Soraya, Siti; Sufahani, Suliadi Firdaus; Ismoen, Muhaimin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27620

Abstract

One of the critical causes of Indonesia's economic growth is the presence of the Covid-19 Pandemic which has resulted in a decline in public consumption and investment interest at the household level in each region. One of the areas with a decrease in the number of affected tourist visits is Bali Province. This is because Bali is an icon of Indonesia and is the best tourist destination. The purpose of this study is to obtain the most suitable model to model economic growth with the FD-GMM and Sys-GMM approach meeting the criteria of validity, consistency, and unbiased. This type of research is quantitative research with data sourced from the central statistical agency of Bali Province. The method used in this study is to compare the First-Difference Generalized Method of Moment (FD-GMM) and System Generalized Method of Moment (Sys-GMM) on economic growth data in Bali Province. The result of this study is the estimation of model parameters with the approach FD- GMM meets valid, consistent, and unbiased criteria. In contrast, the estimation of model parameters with the Sys-GMM meets validity and consistency criteria. However, the unbiased criteria are not met because the resulting model has a biased coefficient. The best model used to model Bali's economic growth data is the FD-GMM model. The above results imply that the existence of the population categorized as poor and the existence of the workforce are still a special concern. So, the suggestion in this study is that it is necessary to conduct a policy analysis from the Bali Provincial Government in dealing with poverty rates. Furthermore, employment management in Bali will be reorganized to be more directed and measurable in increasing the economic growth of Bali Province. 
Forecasting the Number of Dropout Student in Indonesia using ARIMA Model Az-Zahra, Aisyah Dhifa; Fajriati, Luthfia Azzahra; Sari, Sherlyana Devita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.31625

Abstract

The high rate of dropout students in Indonesia remains a matter of considerable concern, as it erodes the quality of education and hinders the long-term development of human capital. The government of Indonesia has endeavored to address the issue of high dropout rates among students by implementing a range of initiatives. To demonstrate the effectiveness of this program, forecasting is necessary to measure and predict its outcomes. The purpose of this study is to utilize a time series approach, specifically the Autoregressive Integrated Moving Average (ARIMA) model, to predict the number of dropout students in the forthcoming years. This study employs a quantitative analysis using secondary data obtained from Statistics Indonesia (BPS) for the period 1970-2023. The ARIMA method is a statistical technique used to determine the most suitable forecasting model from historical data. This method has gained widespread popularity in the field of time series analysis due to its ability to manage non-stationary data effectively. The result shows that ARIMA (0,2,1) has the smallest AIC and meets the significant criteria model, also having the lowest MAPE value of 1.9%, indicating excellent forecasting accuracy. The plot of the result indicates a downward trend in the number of dropout students over the coming years. This downward trend aligns with the timeline of government interventions, suggesting a potential causal relationship between the implementation of educational support programs and the declining dropout rates. Thus, the prediction supports the effectiveness of these initiatives in mitigating dropout student in Indonesia.
Control Strategies for HIV/AIDS-Hepatitis B Coinfection using Optimal Control Approach and Cost-Effectiveness Analysis Annisa, Winda Nur; Bakhtiar, Toni; Silalahi, Bib Paruhum
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29601

Abstract

HIV/AIDS and Hepatitis B are infectious diseases caused by viruses, sharing similar transmission mechanisms. This study seeks to determine the most effective and cost-efficient strategies for controlling the spread of these diseases by utilizing a modified HIV/AIDS-Hepatitis B coinfection model with various control variables. The model divides the total population into nine subpopulations, each representing a specific disease state. Based on these classifications, the model incorporates four key control variables, namely Hepatitis B vaccination program, Hepatitis B treatment, HIV/AIDS treatment, and public health education program. The research employs optimal control theory and the Pontryagin Maximum Principle to address the optimal control problem to minimize infection rates and implementation costs over a specific periode. The Hamilton function integritas the dynamic system and cost function. The model is analyzed through simulations using parameter values from previous studies, then optimizing control variables to generate a numerically solved system of differential equations that uses Scilab 2024 software. Simulation result show that the optimal combination of four control strategies reduces HIV/AIDS-Hepatitis B infection by 79,2% in under ten years. Furthermore, the cost-effectiveness of different strategies is evaluated using the Average Cost-Effectiveness Ratio (ACER) and Incremental Cost-Effectiveness Ratio (ICER) indicates that single control strategies are more cost-efficient, while combining all four strategies is more expensive. However, successful implementation depends on financial constraints (limited vaccination and ARV treatment), healthcare infrastructure (availability of testing facilities), and public compliance with health education programs. Consequently, the proposed strategies are recommended for policymakers, with consideration of associated costs to ensure feasibility.
Exploring Technology, Role, and Components of Computational Thinking in Mathematics Learning: A Systematic Literature Review Andriatna, Riki; Turmudi, Turmudi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.30440

Abstract

Computational thinking as a 21st century skill has attracted the attention of researchers, including in mathematics education. This research identifies the use of technology, the role and components of computational thinking in mathematics learning. This study uses a sysematic literature review with procedure consisting of planning the review, conducting the review, and reporting the review. The articles used came from the Scopus database in the 2010-2024 publication time range. Based on the PRISMA protocol involving criteria such as type of publication, language, field of study, publication stage, and accessibility to the article, 11 articles were obtained with the most research conducted in Spain. The research conducted involved many students and teachers as the object of research, including pre-service teachers. The reviewed studies also revealed that most of the computational thinking research used qualitative methods where the role of computational thinking in the research was mostly as a process or activity or tools used in learning, either using technological devices or in the form of unplugged activites. In addition, the results of the review of selected articles also reveal that the components of decomposition, pattern recognition, abstraction, and algorithm are still dominating as the main components studied in computational thinking.
Spatio-Temporal Median Polish Kriging with ARIMA Integration for Monthly Precipitation Interpolation in East Kalimantan Jannah, Friendtika Miftaqul; Fitriani, Rahma; Pramoedyo, Henny
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29570

Abstract

Precipitation can lead to disasters like droughts and floods, necessitating accurate interpolation methods. Traditional spatio-temporal kriging often struggles with outliers, which can reduce estimation reliability. This study develops spatio-temporal median polish kriging, which separates spatial and temporal components to improve interpolation accuracy, particularly in handling outliers. Unlike conventional kriging, this method integrates median polish kriging for robust spatial interpolation and ARIMA for capturing temporal trends, making it more effective in dynamic precipitation pattern estimation. The study utilizes precipitation data from seven observation posts in East Kalimantan (2021–2023). The data is processed using a combination of spatial, temporal, and spatial-temporal modeling approaches to capture precipitation variations accurately. For spatial interpolation, the study applies kriging in median polish spatial effects. The best semivariogram model for spatial effects is exponential, which is used to characterize spatial dependencies. To capture temporal effects of median polish, the study employs ARIMA(1,2,0), which models precipitation trends over time and helps manage temporal fluctuations. For residuals of median polish interpolation, the study applies spatio-temporal kriging, using a simple sum-metric model as the best approach to integrate both spatial and temporal dependencies. The semivariograms selected for spatial, temporal, and joint dependencies follow a gaussian structure. The interpolation results reveal that precipitation increases toward the west, with precipitation patterns also showing an increasing trend over time. These findings demonstrate the model’s capability in capturing spatial and temporal precipitation variations while addressing potential outliers through the median polish approach. By utilizing a robust statistical framework, the model reduces the influence of extreme values, leading to more reliable precipitation estimates. However, this study utilizes only seven observation posts. The limited number of observation posts may introduce uncertainty in regions distant from measurement stations and affect the model's accuracy. Therefore, further research should test this model by applying it to different geographical regions with a more extensive dataset.

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