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INDONESIA
Jurnal Pendidikan Matematika
Published by Indonesian Journal Publisher
ISSN : -     EISSN : 30309263     DOI : https://doi.org/10.47134/ppm
Core Subject : Education,
Education Mathematics Other
Jurnal Pendidikan Matematika ISSN 3030-9263 is a scientific journal published by Indonesian Journal Publisher. This journal publishes four issues annually in the months of November, February, May, and August. This journal only accepts original scientific research works (not a review) that have not been published by other media. The focus and scope of Jurnal Pendidikan Matematika include mathematics learning strategies, mathematics learning design, development of mathematics learning tools, analysis in the field of mathematics education, and various things related to mathematics learning from elementary school to college level.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 57 Documents
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Statistical Challenges in Spatial Data Analysis: The Role of Kriging Models Ammar Ali Farhan
Jurnal Pendidikan Matematika Vol. 3 No. 1 (2025): November
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v3i1.2077

Abstract

Using Kriging models, a complex geostatistical technique for extrapolating and forecasting unknown spatial values based on known data, this study investigates spatial data analysis. Traditional statistical techniques that suppose observations to be independent are considerably challenged by spatial autocorrelation—the tendency for nearby spatial points to show comparable features. The research highlights the application of Kriging to environmental data, especially air quality measurements like PM2.5 concentrations, in order to better comprehend and forecast pollution patterns over several geographical areas. Using both Ordinary and Universal Kriging approaches, the research shows how these methods can efficiently address spatial dependencies, nonstationarity (where data characteristics change across space), and anisotropy (directional spatial variability). Moreover, the research combines Kriging with machine learning algorithms to record more sophisticated spatial interactions, therefore enhancing prediction accuracy. Methods of crossvalidation are used to thoroughly evaluate the models' performance. The study emphasizes how Kriging enables precise spatial predictions, hence giving important information for environmental monitoring and well-informed decision-making
Cross-Validated Regularization for Robust Mahalanobis Metric Learning Mohammed Mohsen Mones
Jurnal Pendidikan Matematika Vol. 3 No. 1 (2025): November
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v3i1.2078

Abstract

Conventional Mahalanobis metric learning (MML) algorithms exhibit significant sensitivity to outliers and noise in training data, leading to biased distance metrics with poor generalization performance on unseen data, to address this limitation, we propose a systematic framework integrating tunable regularization with K-fold cross-validation for robust metric learning. Specifically, we augment standard MML objectives with a Frobenius norm regularization term λ‖M‖²_F to penalize solution complexity and control overfitting. Crucially, we employ K-fold cross-validation as a data-driven mechanism to automatically determine the optimal regularization hyperparameter λ* that maximizes generalization potential, the resulting learned metric M* demonstrates enhanced resistance to noise and superior generalization capability. Empirical evaluation across 12 benchmark datasets (including real-world noisy data like Food-101N and CheXpert) confirms that our approach significantly outperforms non-regularized baselines and manually tuned alternatives: It reduces overfitting to noisy training constraints by 13.8–22.4% and improves test accuracy on distance-based tasks (k-NN classification, clustering) by 10.3–17.2% under severe noise conditions (40% label flips, 30% feature corruption), these results establish that the synergistic combination of mathematical regularization and cross-validated hyperparameter selection provides a principled, effective solution for learning reliable Mahalanobis metrics in noisy real-world environments
A Hierarchical Bayesian Approach to Adaptive Multi-Task Modeling Shaheen Ahmed Jihad Sultan
Jurnal Pendidikan Matematika Vol. 3 No. 1 (2025): November
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v3i1.2079

Abstract

Multi-task learning (MTL) aims to improve generalization by leveraging shared information across related tasks. However, conventional methods often rely on restrictive, pre-defined assumptions about task relationships, limiting their effectiveness in complex, heterogeneous environments, this paper introduces a Hierarchical Bayesian Model for Adaptive Multi-Task Learning (HB-MTL), a fully integrated probabilistic framework that learns the inter-task relationship structure directly from the data. By placing hyper-priors on the parameters of a shared task distribution, our model can flexibly capture a rich mosaic of relationships, including positive, negative, and null correlations, we employ Variational Inference for tractable posterior approximation, we validate our approach on a challenging synthetic benchmark, "MetroSim," designed to emulate the structural complexities of real-world systems, the results demonstrate that our model significantly outperforms a suite of strong baselines, particularly in its unique ability to leverage negative correlations and avoid negative transfer with unrelated tasks, the framework not only yields superior predictive accuracy but also provides an interpretable map of the learned task structure and robust uncertainty quantification, making it a powerful tool for practical applications
Mathematical Techniques for Parameter Estimation in Bayesian Inference Mohammed Shakir Zghair
Jurnal Pendidikan Matematika Vol. 3 No. 1 (2025): November
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v3i1.2080

Abstract

Combining observed data with previous knowledge, Bayesian inference is a strong statistical technique for parameter estimation. Parameters are seen as random variables; previous opinions are updated using Bayes' theorem to generate the posterior distribution. By means of this approach, model parameters can be uncertain and change with additional data. Still, calculating the posterior analytically is sometimes impossible, mostly in complex models with high dimensional data. Markov Chain Monte Carlo (MCMC) methods, such as Metropolis Hastings and Gibbs sampling, use repeated processes produce samples from the posterior distribution thereby addressing this issue. Varitional inference offers a faster, deterministic option by approximating the posterior with a simpler distribution. The Laplace approximation uses local curvature for a Gaussian approximation. Common uses of these methods are statistics and machine learning for parameter estimation, model selection, and uncertainty analysis. The study evaluates each approach's effectiveness, showing that MCMC offers the best accuracy but variational inference and Laplace approximations offer quicker but less precise substitutes. The results emphasize the importance of choosing the appropriate method depending on the complexity of the data and the computational efficiency
Estimating The Hazard Function for A Mixed Distribution Using the Genetic Algorithm with A Practical Application Taha Faeq Farhan
Jurnal Pendidikan Matematika Vol. 3 No. 1 (2025): November
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v3i1.2081

Abstract

In this research, we presented the EKIW (Exponentiated Kumaraswamy Inverse Weibull) Distribution, which is a flexible distribution used in survival and reliability analysis. This distribution includes parameters (α, β, λ, η, θ). Statistical properties such as the hazard function, the quantile function, and the entropy measure were derived for this distribution. The research aims to estimate the hazard function based on one of the artificial intelligence algorithms, which is the genetic algorithm. It was compared with the maximum likelihood method. To prove the applicability of this distribution and which of the two methods is better, sample sizes (n=5, 15, 30, 80, 150) were generated using the comparison criterion, which is the integral mean square error (IMSE). The research also included a practical application for lung cancer patients obtained from the Medical City Hospital in 2025. The results showed that the hazard function's capabilities increased with increasing time of infection for the group of lung cancer patients under study. This is consistent with the theoretical properties of this function, as it is an increasing monotonic function
An In-Depth Study of Cauchy-Euler Differential Equations and Their Numerical Solutions Using MATLAB Bassam Fayyad Kanaan
Jurnal Pendidikan Matematika Vol. 3 No. 1 (2025): November
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v3i1.2083

Abstract

The Cauchy–Euler differential equation, distinguished by its dependence on the independent variable through variable coefficients, represents an essential category of linear differential equations with broad applications across mathematics, physics, and engineering. The present work provides a comprehensive exploration of both homogeneous and non-homogeneous forms of these equations, focusing on their analytical treatments as well as numerical approaches for cases in which explicit closed-form solutions are not easily attainable. Through the use of a logarithmic substitution, reckonings with mutable constants can be distorted into constant-coefficient reckonings, allowing the application of classical strategies such as the characteristic polynomial method and the approach of undetermined coefficients. Illustrative examples are included to show the derivation of both general and particular solutions, covering situations with repeated or complex roots. In addition, the study incorporates numerical techniques—particularly MATLAB’s ode45 solver—to approximate solutions of Cauchy–Euler equations, especially for non-homogeneous problems and systems subject to initial conditions. These implementations highlight the adaptability and efficiency of numerical solvers in scenarios where analytical methods are difficult or infeasible. By combining analytical and computational methodologies, this work provides an integrated framework for addressing a wide range of differential equations encountered in scientific and engineering applications. It also emphasizes the enduring significance of Cauchy–Euler equations and the crucial role of computational platforms such as MATLAB in modern differential equation analysis
An Overview of Multivariate Statistical Methods and Their Practical Applications Abdulqader Mutlag Hamad
Jurnal Pendidikan Matematika Vol. 3 No. 1 (2025): November
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v3i1.2084

Abstract

Multivariate data analysis is a powerful statistical approach used to analyze data involving multiple variables simultaneously. Researchers can use this method to find complicated ties, reduce the number of factors, and group data more effectively. When you need to understand data with more than one variable, you can use tools such as factor analysis, cluster analysis, discriminant analysis, principal component analysis, and multivariate regression. More and more fields, like business, engineering, health, and the social sciences, need multivariate analysis. This is because computers and other strong tools are getting better all the time. You will learn about some important multivariate methods and how they are used in the real world in this study. It also talks about the ideas that make them work. It talks about how these ways can help people make better decisions based on facts

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