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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.
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Articles 23 Documents
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Search results for , issue "Vol 9, No 1 (2025): January" : 23 Documents clear
Optimizing Long-Term Meteorological Data Completeness in North Aceh, Indonesia: A Comparative Analysis of Interpolation Methods Sasmita, Novi Reandy; Saragih, Novita Sari; Rahayu, Latifah; Malfirah, Malfirah
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.v9i1.27929

Abstract

More data in meteorological records is needed to ensure the accuracy of meteorological modeling, particularly in long-term datasets. This study aims to identify the most effective interpolation method for addressing missing data in North Aceh's meteorological dataset from 2010 to 2023, with a focus on the accuracy of methods applied across various meteorological variables. The study analyzed data from North Aceh Regency, Indonesia, comprising 25,565 daily observations of temperature, humidity, rainfall, sunshine duration, and wind speed. Missing values were interpolated using three methods: spline, stineman, and moving average interpolation. Performance was evaluated using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Squared Logarithmic Error (MSLE) across 10%, 20%, and 30% levels of simulated missing data. All analysis in this study were carried out using R-4.4.2 software. While spline interpolation performed reasonably well, it showed increased variability, especially for high-variance variables like rainfall. Moving average interpolation was less reliable, with error rates increasing alongside higher levels of missing data. In contrast, stineman interpolation consistently achieved the lowest error metrics across all levels of missing data, with MAE ranging from 0.219 to 0.6691, MSLE from 0.035 to 0.109, and RMSE from 1.247 to 2.245, demonstrating superior robustness. Stineman interpolation offers a highly effective approach for managing missing meteorological data in North Aceh’s long-term dataset, enhancing data reliability for meteorological modeling and decision-making in meteorological-sensitive sectors. This study provides practical recommendations for selecting optimal interpolation techniques, especially in regions with variable meteorological data quality.
Comparison of Nonparametric Path Analysis and Biresponse Regression using Truncated Spline Approach Azizah, Laila Nur; Rohma, Usriatur; Fernandes, Adji Achmad Rinaldo; Wardhani, Ni Wayan Surya; Astutik, Suci
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.v9i1.26739

Abstract

Nonparametric path analysis and biresponse nonparametric regression are two flexible statistical approaches to analyze the relationship between variables without assuming a certain form of relationship. This study compares the performance of the two methods with the truncated spline approach, which has the advantage of determining the shape of the regression curve through optimal selection of knot points. This study aims to evaluate the best model based on linear and quadratic polynomial degree with 1, 2, and 3 knot points. The model is applied to data with 100 samples and simulated data of various sample levels. The results show that the best model in nonparametric path analysis is a quadratic model with three knots, while the best model in biresponse nonparametric regression is a quadratic model with two knots. Biresponse nonparametric regression has a coefficient of determination of 88.8% which is higher than the nonparametric path analysis of 70.9%. The best biresponse nonparametric regression model is the model with quadratic order and two knots.
The Model of Students’ Emotional Intelligence of Professional Education Program in Indonesia Yanuarto, Wanda Nugroho; Setyaningsih, Eka; Suanto, Elfis; Isnawan, Mohamad Galang
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.v9i1.27483

Abstract

Recently, there has been a noticeable increase in the significance of students' emotional intelligence (EI) and personality traits regarding self-awareness, self-management, and social awareness. This is to guarantee that their workforce is trained successfully and continuously produces good results. The aims of the study are as follows. (1) to assess how well the proposed model fits the students' data, and (2) to identify the connection between EI domains. The authors opted for a cross-sectional study design by questionnaire survei for EI domains. A total of 1,284 students were involved in this research. The purposive design procedure that resulted in the sample selection involved five departments within the Professional Educational Programs at Universitas Muhammadiyah Purwokerto in Indonesia. The structural model includes all of the interdependencies between the variables. Statistics for Windows 24.0 and Analysing Moment Structures (AMOS) 24 Version were utilized for data analysis. According to the findings, students' levels of self-awareness significantly affect their ability to self-manage in professional education programs, and vice versa. Thus, our study strengthened the idea that EI with an emotion-response process mask is a quality requirement for effective students in any kind of learning environment. 
XportID: Website for Clustering Indonesian Export Commodities by Destination Continent using Gaussian Mixture Model Lisanthoni, Angela; Trimono, Trimono; Prasetya, Dwi Arman
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.v9i1.27500

Abstract

Exports play a crucial role in driving economic growth and increasing foreign exchange reserves. However, Indonesia's export performance has not yet reached its optimal potential, as evidenced by an 11% decline in export value in 2023. The decrease is partly attributed to the limited range of export destination markets. Therefore, this study aims to analyze export trade patterns to identify the most ideal and potential market locations. The research will employ a quantitative approach, using secondary data from the Central Bureau of Statistics and the 2022 BACI dataset, focusing on the top 5 HS2 commodity types by highest export quantity. Clustering analysis is applied to group markets based on similar characteristics, identifying countries with high, medium, and low export potential for Indonesia’s export strategy. The research develops a website-based clustering system called XportID, utilizing a Gaussian Mixture Model (GMM) with the Expectation-Maximization (EM) algorithm to determine optimal cluster parameters. GMM is preferred for its flexibility and probabilistic system, providing more accurate results compared to distance-based methods. There will be 3, 4, and 5 clusters formed and then the best cluster will be selected by comparing the silhouette score obtained. Results show that the Asian continent has 5 clusters with the best value of 0.7035, the American continent has 3 clusters with the best value of 0.8165, the African continent has 3 clusters with the best value of 0.8534, the Australian continent has 3 clusters with the best value of 0.8540, and the European continent has 4 clusters with the best value of 0.8654. Overall results, the clustering system is categorized as strong structure with average value of 0.8185. Countries with high export potential include Malaysia, Philippines, South Korea, Brazil, Mexico, New Zealand, and Spain. Specifically in Africa, commodities related to HS2-15 show potential for growth.
Development of Ramsey RESET to Identify the Polynomials Order of Smoothing Spline with Simulation Study Nurdin, Muhammad Rafi Hasan; Fernandes, Adji Achmad Rinaldo; Sumarminingsih, Eni; Ullah, Muhammad Ohid
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.v9i1.26785

Abstract

Path  analysis is used to determine the effect of exogenous variables on endogenous variables. One of the assumptions in path analysis is the linearity assumption. The linearity assumption can be tested using Ramsey RESET. If the Ramsey RESET results show that all variables are non-linear then one of the alternative models that can be used is nonparametric smoothing spline. The smoothing spline method requires a smoothing spline polynomial order in estimating the nonparametric path analysis function. This polynomial order results in the smoothing spline method having good flexibility in data adjustment. The selection of the smoothing spline polynomial order becomes an obstacle because there is no test to determine the best order. Therefore, the purpose of this study is to find out how the value of V for order 3 and 4, develop Ramsey RESET to identify the best spline polynomial order, and evaluate the Ramsey RESET algorithm through simulation studies on various errors. The results of V values of order 3 and 4 can be obtained through the integral process and it is found that the higher the order, the value of V has a higher rank. Ramsey RESET development is done by modifying the second regression using nonparametric regression functions of order 2, 3, and 4. The simulation study results show that the classical Ramsey RESET can be used to detect linear shapes well because it is not affected by the value of the error variance. However, the classical Ramsey RESET has limitations in detecting non-linear forms other than quadratic and cubic forms so that other forms such as smoothing spline are needed. In testing non-linear models, the lowest p value is obtained in the form that matches the actual conditions, this can be interpreted that the modified Ramsey RESET can detect non-linear forms with spline polynomial orders well. The contribution of this research is to provide a test to identify the best smoothing spline polynomial order using Ramsey RESET modification
Mathematical Modeling of Stunting with the Influence of Nutritional Intervention Himmah, Elok Faiqotul; Kaestria, Rommi; Riana, Riana
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.v9i1.26817

Abstract

The high number of stunting in Central Kalimantan with a prevalence that is still quite far from the WHO threshold, which is 26.9%, requires serious handling from the Central Kalimantan Provincial Government. Through the stunting reduction acceleration program, the government is targeting the prevalence of stunting in Central Kalimantan to decrease to 15.38% by 2024. The purpose of this study was to build a mathematical model to determine the dynamics of stunting events in Central Kalimantan with the influence of nutritional interventions. This model will be used to predict changes in stunting prevalence over time, and evaluate the impact of nutritional interventions on reducing stunting. This is a mixed method research that combines quantitative and qualitative approaches. with a mathematical modelling approach. The research method used in this study is a literature study with data collection techniques through semi-structured interviews with sources from the Health Office, Bappedalitbang and BKKBN which are included in the TPPS of Central Kalimantan, and also the BPS of Central Kalimantan. The data collected includes the prevalence of stunting, types and coverage of nutritional interventions, factors that influence stunting in Central Kalimantan, the nutritional status of toddlers, and indicators of nutritional interventions successstunting prevalence. Model simulation with Python programming shows the effectiveness of the intervention in preventing stunting and helping toddlers at risk of stunting to achieve normal nutritional status. Nutritional interventions have successfully reduced the prevalence of stunting in Central Kalimantan by 3.16% and increased the number of toddlers at risk of stunting who managed to achieve normal nutritional status after receiving nutritional interventions by 7%. It can be concluded that early intervention in toddlers at risk of stunting is very important to prevent stunting, and targeted intervention in stunted toddlers is also needed to accelerate recovery and reduce the overall prevalence of stunting.
Implementation of Capital Asset Pricing Model in Optimal Portfolio Formation on IDX High Dividend 20 Auditiyah, Cellyn; Farida, Yuniar; Utami, Wika Dianita
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.v9i1.27799

Abstract

The IDX High Dividend 20 (IDX HIDIV20) is an Indonesian stock index known for its high dividend payouts, appealing to passive income investors. However, annual changes and fluctuating stock prices present challenges, necessitating diversification strategies. This study aims to create an optimal portfolio to balance returns and risks amidst market volatility on the IDX High Dividend 20 stock index. This research uses the Capital Asset Pricing Model (CAPM) method. The CAPM determines the relationship between risk and an asset's expected rate of return, especially shares. This model helps in evaluating whether an asset or investment provides sufficient returns commensurate with its risk. In this study. We used weekly stock price data and composite stock prices from Yahoo Finance and BI interest rates taken from Bank Indonesia from January 2020 to December 2023. The research findings found that there were 6 out of 12 samples forming the optimal portfolio, namely ITMG (28.0%), ADRO (16.6%), BMRI (29.2%), BBNI (13.7%), BBCA (11.8%), and BBRI (0.6%) with a portfolio return of 0.41% and a portfolio risk level of 0.16%. The study emphasizes the importance of diversification for investors, particularly in volatile markets, to manage risks and enhance returns. It also highlights the strategic value of investing in high-dividend stocks for consistent income and portfolio stability, offering practical insights for optimizing investment strategies.
Study of Economic Growth in IKN based on Autoregressive and Distributed Lag Approach Amelia, Dita; Suliyanto, Suliyanto; Zah, Alfian Iqbal; Mutyaravica, Astrid
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.v9i1.27513

Abstract

Indonesia's economy plays an important role in supporting national development and government policies in various sectors such as education, health, and infrastructure. In the first quarter of 2024, Indonesia's economy experienced an increase from the same period in 2022. East Kalimantan experienced significant growth supported by the mining sector, metal industry, and the National Capital City project. However, East Kalimantan is dependent on raw material exports and faces challenges in economic transformation. The government aims to increase exports of processed products to reduce poverty and unemployment. This study analyzes whether economic growth in IKN affects the economy of East Kalimantan, by considering inflation, CPI, export value, and GRDP. This study uses quantitative research methods using Autoregressive Distributed Lag (ARDL) with the advantage that it can be used in models with different levels of stationary and does not matter the number of samples with the data used is secondary data from BPS. The best model obtained is ARDL (3, 3, 4, 3, 4) based on the smallest AIC value which shows the long-term and short-term relationship. Economic growth, export value, and GRDP from the previous quarter affect growth negatively, while GRDP from the same period and the previous quarter affect growth positively. In the long run, export value and GDP significantly affect growth. These results provide insights for the government in managing East Kalimantan's growth, supporting sustainable development and SDG achievement. The results of this study are expected to be a reference for the central government to make policies related to factors that affect Economic Growth in the hope of increasing economic growth in East Kalimantan. 
Structural Equation Modeling on Data on Students' Knowledge and Interest in Entrepreneurship in Lampung Sholiha, Sangidatus; Vahia, Ira; Dewi, Wardhani Utami
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.v9i1.26557

Abstract

Entrepreneurship plays a crucial role in economic growth and reducing unemployment, particularly in regions like Lampung, Indonesia, which face challenges such as limited entrepreneurial resources and low interest in entrepreneurship. This research aims to explore the relationship between entrepreneurial knowledge and entrepreneurial interest among students in Lampung, using Structural Equation Modeling (SEM) for analysis. A quantitative approach with a cross-sectional design was applied, involving 300 students randomly selected using simple random sampling from Lampung. The study focuses on entrepreneurial knowledge as the independent variable and entrepreneurial interest as the dependent variable. Data were collected using a questionnaire and analyzed with R Studio 4.2.1 using the lavaan package for SEM. The results show that entrepreneurial knowledge significantly influences entrepreneurial interest, explaining 86.10% of its variation. These findings suggest that strengthening entrepreneurial knowledge through curriculum development and innovative learning approaches can boost students’ entrepreneurial interest. Higher education institutions in Lampung can improve entrepreneurial education by integrating practical knowledge, case studies, and mentorship programs to foster entrepreneurial attitudes. This research contributes to the growing field of entrepreneurship education and offers actionable insights for policymakers and educators to develop sustainable entrepreneurs in Lampung.
Determinants of Tridiagonal and Circulant Matrices Special Form by Chebyshev Polynomials Nurliantika, Nurliantika; Fran, Fransiskus; Yundari, Yundari
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.v9i1.27871

Abstract

Along with the development of science, many researchers have found new methods to determine the determinant of a matrix of more than three orders. Chebyshev polynomial can be used to find and develop a more efficient formula in calculating the determinant of matrices. This research explores the Chebyshev polynomials of the first kind T_n (x) and second kind U_n (x). Both types of Chebyshev polynomials, T_n (x) and U_n (x), can be represented using recurrence relations. This research aims to determine the determinant of tridiagonal and circulant matrices of special form using Chebyshev polynomials T_n (x) and U_n (x). Determining the determinant of a matrix is a fundamental problem in linear algebra that plays an important role in both theoretical and applied mathematics. Its theoretical contributions include a deeper understanding of matrix properties, the development of efficient computational methods, and the explanation of the relationship between matrices and orthogonal polynomials. By utilizing Chebyshev polynomials, this study strengthens determinant theory, particularly for matrices with special shapes. The steps to determine the determinant of tridiagonal and circulant matrices involve the application of elementary row operations. The first step is to perform row operations on the tridiagonal and circulant matrices to obtain a matrix form that conforms to the determinant theorem of the tridiagonal and circulant matrices. After the elementary row operation is applied, if the form of the tridiagonal and circulant matrices each satisfies the form in the determinant theorem of the tridiagonal and circulant matrices, then the determinant of the matrices can be calculated using each of the theorems that satisfy. Then the determinants of the tridiagonal and the circulant matrices are obtained. The results of this study show that the determinant of tridiagonal and circulant matrices of special form can be determined using Chebyshev polynomials T_n (x) and U_n (x).

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