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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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Robust Continuum Regression Study of LASSO Selection and WLAD LASSO on High-Dimensional Data Containing Outliers Daulay, Nurmai Syaroh; Erfiani, Erfiani; Soleh, Agus M
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.23123

Abstract

In research, we often encounter problems of multicollinearity and outliers, which can cause coefficients to become unstable and reduce model performance. Robust Continuum Regression (RCR) overcomes the problem of multicollinearity by reducing the number of independent variables, namely compressing the data into new variables (latent variables) that are independent of each other and whose dimensions are much smaller and applying robust regression techniques so that the complexity of the regression model can be reduced without losing essential information from data and provide more stable parameter estimates. However, it is hampered in the computational aspect if the data has very high dimensions (p>>n). In the initial stage, it is necessary to reduce dimensions by selecting variables. The Least Absolute Shrinkage and Selection Operator (LASSO) can overcome this but is sensitive to the presence of outliers, which can result in errors in selecting significant variables. Therefore, we need a method that is robust to outliers in selecting explanatory variables such as Weighted Least Absolute Deviations with LASSO penalty (WLAD LASSO) in selecting variables by considering the absolute deviation of the residuals. This method aims to overcome the problem of multicollinearity and model instability in high-dimensional data by paying attention to resistance to outliers. Leverages the outlier resistant RCR and variable selection capabilities of LASSO and WLAD LASSO to provide a more reliable and efficient solution for complex data analysis. Measure the performance of RKR-LASSO and RKR-WLAD LASSO; simulations were carried out using low-dimensional data and high-dimensional data with two scenarios, namely without outliers (δ= 0%) and with outliers (δ= 10%, 20%, 30%) with a level of correlation (ρ = 0.1,0.5,0.9). The analysis stage uses RStudio version 4.1.3 software using the "MASS" package to generate data that has a multivariate normal distribution, the "glmnet" package for LASSO variable selection, the "MTE" package for WLAD LASSO variable selection. The simulation results show the performance of RKR-LASSO tends to be superior in terms of model goodness of fit compared to RKR-WLAD LASSO. However, the performance of RKR-LASSO tends to decrease as outliers and correlations increase. RKR-LASSO tends to be looser in selecting relevant variables, resulting in a simpler model, but the variables chosen by LASSO are only marginally significant. RKR-WLAD LASSO is stricter in variable selection and only selects significant variables but ignores several variables that have a small but significant impact on the model.
The Value at Risk Analysis using Heavy-Tailed Distribution on the Insurance Claims Data Mukhaiyar, Utriweni; Dianpermatasari, Aprilia; Dzakiya, Azizah; Widyani, Sasqia Bunga; Syam, Husnul Khatimah
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.25053

Abstract

The insurance has often been involved to minimize financial losses. As the product providers, the insurance companies must effectively manage risks to prevent errors in risk measurement. The amount of risk or loss experienced by the policyholder refers to the claim amount. The Value at Risk (VaR) is commonly used to measure risk. The VaR is calculated from the probability function, which can be obtained by evaluating the distribution of claims data. Most claim frequencies are small, but occasionally, huge claims appear. Therefore, the appropriate distribution would be characterized by a heavy-tailed. Thus, this research aims to model and evaluate insurance claims data using exponential, Weibull, Pareto, and lognormal distributions to assess financial risk through VaR. The insurance claims data were collected from a single insurance company and include 1,326 claims. This research specifically examines variables such as gender, diabetic status, smoking status, the number of claims, and the level of confidence. The data were analysed using descriptive statistics, Maximum Likelihood Estimation for parameter estimation, and Goodness of Fit tests to determine the best-fitting distribution, along with VaR calculations based on the results. The suitability of the distribution model is assessed through the VaR and is analysed based on the appropriate distribution of insurance claims data. It is obtained that the Weibull and lognormal distributions appropriately model insurance claims data. The highest VaR is observed in the claim data for female non-diabetic smokers, with a level of confidence of 99.5%. The lowest VaR is obtained from the claim data for male diabetic non-smokers, with a level of confidence of 90%. This approach enhances the prediction of large potential losses for specific demographic groups, aiding more informed decision-making in premium pricing and risk management. The integration of heavy-tailed distributions in risk assessment, with a particular focus on demographic specificity, constitutes a substantial and novel contribution to this research.
Game Chromatic Number of Tadpole Graph, Broom Graph, and Tribune Graph Fran, Fransiskus; Abdurahman, M Luthfi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.25817

Abstract

Graph coloring game is one of application in graph theory. The goal in this article is determine game chromatic number of tadpole graph, broom graph, and tribune graph. The graphs are simple, connected, and undirected and thus eligible for playing graph coloring game. Given two players with the first player is called A and second player is called B coloring vertex of graph G with a set of colors C={c_1,c_2,c_3, ..., c_k}. A must to make sure that all vertex of G has colored and B must try to prevent A coloring of all vertex. The first step was taken by A as first player, two players take turns coloring vertex of graph G, with rule that every vertex have different color from the neighbourhood. If all vertex of graph G have been colored, then A win or B win if some vertex hasn’t colored. The smallest number of k if A has a strategy to win at graph G with k color, then k called game chromatic number which is denoted by χ_g (G). The strategy to win this game is coloring the biggest degree of vertex in graph first. The result obtained from this paper is A win the game with the strategy of first coloring the largest degrees of vertex. So, exact of game chromatic number of tadpole graph is 3, broom graph is 2 or 3 with several conditions, and tribune graph is 3 or 4 with several conditions.
Augmented Reality Learning Media with Ethnomathematic Approach to Grow Students' Mathematics Learning Motivation Rohim, Dhina Cahya; Hana, Fida Maisa; Manggalastawa, Manggalastawa; Saharani, Safira; Himayati, Ade Ima Afifa
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.25740

Abstract

The efforts that can be made to increase learning motivation are through the use of learning media integrated with current technology with a culture-based approach that students often find in everyday life. The purpose of this study was to describe the importance of AR in mathematics learning, the use of technology in ethnomathematics, and the effects of AR in fostering student learning motivation. This research method is Systematic Literature Review (SLR) with the PRISMA (Preferred Recording Items for Systematic Review and Meta-analysis) technique. The article search process uses a database from international journals indexed by Scopus and found 287 articles. Then a feasibility study was carried out according to the specified criteria so that 18 final articles were obtained. The results of the study showed that: (1) the use of AR in mathematics learning is very important because it has a positive impact such as improving learning outcomes, increasing learning motivation, improving the quality of learning, creating fun learning, improving learning experiences and improving creative thinking skills; (2) Cultural integration combined with technology provides benefits, namely learning becomes interesting so that it can foster student learning motivation, the form of integration between AR technology and ethnomathematics can be in the form of developing interactive learning media, modules or android-based media; and (3) Several studies using AR-based learning media have provided significant results in increasing students' learning motivation. 
Analysis Stability of the Model SEI_1 I_2 I_3 R on the Spread of TikTok User Bahri, Susila; Afdianti, Sri; Zulakmal, Zulakmal
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.25762

Abstract

TikTok addicts, namely content creators (I_1), people who shop (I_2), and people who watch TikTok content (I_3) in Indonesia, continue to increase from year to year. The dynamics of TikTok addicts are analogous to cases of disease transmission. This can be done because TikTok users (S) can gradually increase to become account owners (E), then because there is interaction between account owners and groups of TikTok addicts, TikTok addicts increase, increase or spread. However, TikTok addicts can recover (R) and become vulnerable again over time. Each TikTok addict can have different negative impacts, such as wasting time, getting inaccurate information that can spread people, being deceived, and can disrupt mental health such as depression. Therefore, it is necessary to know which group of TikTok addicts has the greatest influence on the increase in TikTok users in Indonesia so that the government can take action to reduce the increase in TikTok users. In this research, the mathematical dynamics model (〖SEI〗_1 I_2 I_3 R)was first constructed. Analysis of the stability of the model's equilibrium point is carried out by determining the eigenvalues and the Jacobian matrix to obtain an equilibrium point that is free from the influence of Tik Tok addicts, asymptotically stable if R_0=0.941019<1. This means that the influence of TikTok addicts on increasing TikTok users is slowly decreasing and will disappear from the population as time goes by. The endemic equilibrium point is asymptotically stable if R_0=1.011756>1. This means that the influence of TikTok addicts on the increase in TikTok users will remain in the population and will increase over time. Numerical simulations were carried out using MAPLE software.  
A Mathematical Model Analysis of COVID-19 Transmission with Vaccination in Caputo Fractional Derivatives: Case Study in Indonesia Nisardi, Muhammad Rifki; Kasbawati, Kasbawati; Khaeruddin, Khaeruddin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.24711

Abstract

This study aims to investigate a fractional-order mathematical model of COVID-19 transmission using the Caputo derivative definition which suitable to epidemiological cases by its advantage to explain memory effects. The model incorporates compartments for asymptomatic infections and includes a vaccination strategy aimed at mitigating the spread of COVID-19. We derived the disease-free and endemic equilibrium points for the fractional model and computed the basic reproduction number (R_0 )  using the Next-generation Matrix method. Additionally, we conducted sensitivity analyses of parameters affecting R_0. The stability of the fractional model requires specific conditions to be met by the model parameters. To approximate active COVID-19 cases in Indonesia, we utilized the Explicit Grunwald-Letnikov method which well fit with Caputo fractional differential system. Simulation results demonstrate that the fractional-order model offers a flexible approach for modelling active COVID-19 cases in these regions. We found that fractional order for active cases COVID-19 in Indonesia is α=0.9856. The simulation showed that decreasing the vaccination rate and the efficacy of the vaccine would affect the reduction of COVID-19 transmission.
Identifying Poverty Vulnerability Patterns in Indonesia using Cheng and Chruch’s Algorithm Afnan, Irsyifa Mayzela; Wijayanto, Hari; Wigena, Aji Hamim
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.25790

Abstract

Poverty remains a significant issue in developing countries, including Indonesia, where in 2022, the number of people living in poverty reached 26.36 million, with a poverty rate of 9.57%. The Central Statistics Agency (BPS) measures poverty using a basic needs approach, defined as the inability to meet essential food and non-food needs through expenditure. Individuals are considered poor if their average monthly per capita expenditure is below the poverty line. Research on poverty has evolved into a more multidimensional understanding, The Multidimensional Poverty Index (MPI), which identifies deprivation across three key dimensions: health, education, and living standards. This study aims to identify patterns of poverty vulnerability by applying the Cheng and Church (CC) algorithm through a biclustering approach using data from BPS. This quantitative method utilizes 13 multidimensional poverty indicators across 34 provinces. The CC algorithm begins by setting a threshold, followed by removing rows and columns with the largest residuals, adding qualifying rows and columns, and substituting elements to prevent overlap. The quality of the bicluster is then evaluated based on the Mean Squared Residue (MSR) value until optimal groups are formed. The results indicate that a threshold of ? = 0.01 generates seven biclusters with the lowest mean squared residual (0.0065), signifying optimal bicluster quality. Further validation using the Liu and Wang index reveals less than 50% similarity with other thresholds, reinforcing the uniqueness of these findings. MSR serves as a measure of homogeneity within the bicluster, similar to how uniform the level of poverty is within a region. If families have similar expenditures and are below the poverty line, they face similar challenges, resulting in a low MSR value. In contrast, the Liu and Wang index compares regions with different poverty alleviation strategies. These findings provide valuable insights for policymakers. For example, in bicluster 7, where specific interventions are needed in Papua and West Kalimantan, which face local challenges such as reliance on agriculture, low education levels, and limited access to sanitation and clean water.
Promoting Computational Thinking through Programming Trends, Tools, and Educational Approaches: a Systematic Review Irawan, Edi; Rosjanuardi, Rizky; Prabawanto, Sufyani
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.26407

Abstract

This systematic research aims to provide a comprehensive overview of the development of analysis related to the use of programming in the development of Computational Thinking (CT), especially in the context of education from primary to tertiary levels. This study analyzed 88 articles from empirical studies related to the use of programming to develop CT sourced from the Scopus database. The analysis process followed the PRISMA 2020 guidelines and consisted of three stages: search, selection, and data analysis. Descriptive and thematic statistical approaches were used for data analysis. Instruments used in the selection of articles included Rayyan for screening based on inclusion criteria, as well as Microsoft Excel for coding and thematic analysis. The results showed that articles related to the use of programming to promote CT have appeared since 2011 but have increased significantly since 2016, with an annual growth rate of 17.6%. Most studies used quantitative approaches, followed by qualitative and mixed methods. Overall, 270 authors from 27 countries contributed to the study, with the United States having the highest number of publications. A total of 33 programming tools were identified, with Scratch being the most widely used tool, followed by Blockly, LEGO, Scratch Jr., Code.org, Python, Alice, App Inventor, Kodu, R, MakeCode, and Arduino. Scratch Jr. is most commonly used at the early childhood education level, while programming languages such as Python, R, and MATLAB are more commonly used in higher education. The implications of these findings suggest that the trend of using programming tools such as Scratch and Blockly has the potential to influence CT teaching strategies in the classroom, as well as the importance of using varied programming tools in efforts to integrate CT into the education curriculum.
Analysis of Factor Affecting Tuberculosis Cases in West Java Province Using Panel Data Regression Approach Saifudin, Toha; Aisyah, Arlisya Shafwan; Indrasta, Irma Ayu; Amelia, Dita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.24795

Abstract

Tuberculosis (TB) is a disease that can cause death with the largest number of sufferers after COVID-19. In Indonesia, the number of TB cases reached 724.309 cases in 2022 with the highest number 184.406 cases in West Java Province. Given this situation, Indonesia must try to achieve the health target from SDGs, namely ending the TB epidemic by 2030. Therefore, this research aims to analyze the factors that have a significant influence on the incidence of TB in Indonesia, especially in West Java Province. The research focuses on four variables: percentage of poverty, number of diabetics, number of HIV/AIDS patients, and population density. To provide a more informative analysis, this research uses a combination of cross-section and time series data from 27 regions between 2020 and 2022. So, the method used according to the type of data is panel data regression including common effect, fixed effect, and random effect models. Based on statistical tests, namely through the chow test, hausman test, and lagrange multiplier test, it was found that the best model was fixed effect with an R-squared value of 90%. The research revealed that all the studied factors significantly influence the incidence of TB cases in West Java. The results of this study are expected to help the West Java government in an effort to reduce the number of TB cases and formulate policies by reducing the percentage of poverty and population density in West Java. By ensuring the availability of health facilities such as establishing health centers in densely populated areas and counseling programs also need to be conducted to underscore the importance of TB control in West Java.
Modeling Predator-Prey Interactions Barramundi in Dogamit Swamp Wasur National Park Merauke Pratama, Rian Ade; Ruslau, Maria F V; Suryani, Dessy Rizki; Nurhayati, Nurhayati; Meirista, Etriana
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.25563

Abstract

Dogamit, which serves as a habitat for fish species growth, has drawn attention due to its location within a national park and the practice of 'sasi' by the local community as a way to preserve the ecosystem and the species that interact within it. In this research, mathematical modeling variables are explained to describe species' life based on direct observation. As the ecosystem’s inhabitants, the dominant predator species in the ecosystem is the Barramundi fish. Historically, this predator species has migrated from the waters of Australia. The aim of this research is to determine the locally stable equilibrium point and analyze the growth trajectories of the species. The testing is conducted based on equilibrium point analysis. There are three equilibrium points, but only one is a non-negative and realistic point for stability testing. This equilibrium point is then tested using the Routh-Hurwitz criteria. Stability is analyzed using the Jacobian matrix to obtain the eigenvalues. All eigenvalues are negative, thus it can be concluded that the model tested is locally stable. A numerical simulation analysis is also provided, involving parameters that support the mathematical model. The parameters are derived from previous relevant studies and realistic assumptions. The numerical simulation analysis method is used to observe the population growth trajectories. The trajectories that appear show similar conditions for both populations. Both populations experience significant fluctuations with an average growth rate of 67%. It takes 3/5 of the species' lifespan for both populations to stabilize again within the ecosystem. The predator-prey populations also demonstrate resilience during fluctuations, indicating that both populations are highly robust in maintaining survival. The characteristics and findings of this research are commonly found only in endemic species populations. Endemic species tend to have long-term survival and endurance, allowing them to dominate their surrounding geographic habitat and maintain ecosystem balance. 

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