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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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Biplot Analysis Methods for Selecting the Consumer's Preferences of Primary Needs in Java Island Indonesia Jajang, Jajang; Supriyanto, Supriyanto; Maryani, Sri; Bawono, Icuk Rangga; Novandari, Weni; Gunawan, Diah Setyorini; Naufalin, Rifda
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.v8i3.22264

Abstract

The effect of COVID-19 pandemic in February 2020 had changingchanged human consumption pattern. Most people especially for lower and middle communitycommunities, they only be able to fulfils the primary needs. The COVID-19 pandemic had been made some companies done a work termination. Therefore, people is required to sort out and choose needs that are on a priority scale. This article used biplot methods to analyze behavior of the consumers consumer's primary needs during the COVID-19 pandemic. Respondents number of this research are 100 respondents from 4 districts in Java Island who filled out the questioner. In some references, biplot analysis methods focus on agriculture field such as determining the best genotypes and habitats of plants. Rarely of them cosider in economic point of view for example in consumers’ preferences. As we known that biplot analysis is a valuable technique for identifying environtmental condition. It is superior to other statistical methodologies because of its superior predictive accuracy. This method represent a grapics of multivariate data that plot information between the observation and variables in cartesian coordinates. Therefore, the goal of this study examines the consumers' preferences in the Java Island, Indonesia, using biplot analysis to assess preferences of primary needs such rice, cooking oil and margarine in four districts, Bekasi, Madiun, Tasikmalaya, Banyumas, in Java Island were conducted. Regarding to the result of principal component analysis, it shows that consumers have same priority to choose the brand of the cooking oil. It was shown from score of PC1 and PC2 values. The result provide helpful information about the consumer preferences of primary needs during COVID-19 from four districts in Java Island.  
Mathematical Model of COVID-19 Spread with Vaccination in Mataram City Hattamurrahman, Muhammad Putra Sani; Sianturi, Paian; Sumarno, Hadi
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.v8i4.23113

Abstract

The COVID-19 pandemic has had a significant impact on public health worldwide.. Mathematical modeling is considered an alternative tool for understanding real-life problems, including the dynamics of COVID-19 spread. This is an applied research that purpose adds vaccination to Zeb et al. (2020) SEIQR model of COVID-19 spread and examines the dynamic of COVID-19 spread in Mataram City. First, we construct the new model by making assumptions. The fixed point and basic reproduction number (R_0 ) are then used to analyze the model using the next-generation matrix method. The next-generation matrix method is utilized to estimate the R_0 in a compartmental disease model. Two fixed points are acquired, specifically the disease-free fixed point, which is locally asymptotically stable under the condition R_0<1 determined by the Routh Hurwitz criterion via linearization using the Jacobi matrix. And the disease-endemic fixed point, which is locally asymptotically stable under the condition R_0>1 indicated by Lyapunov function. The population dynamics when R_0<1 and R_0>1 can also be observed through numerical simulation. The results of a numerical simulation indicate that giving the proportion of number vaccinated 62 per cent is effective in suppressing the number of infections. 
Exploring Multivariate Copula Models and Fuzzy Interest Rates in Assessing Family Annuity Products Sari, Kurnia Novita; Febrisutisyanto, Ady; Deautama, Randi; Azirah, Nursiti; Mahani, Pida
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.17467

Abstract

This research explores the development of a reversionary annuity product transformed into a family annuity covering three individuals: husband, wife, and children. The innovative design of this product considers the sequencing of annuity payments post-participant's demise, aiming to mitigate the risk of parents' death impacting their children. Recognizing the inadequacy of assuming independence among individuals in premium calculations, the study employs a multivariate Archimedean Copula model to account for interdependence. The primary objective is to compute the survival single-life function for each individual taken from TMI IV 2009. Then the copula model is implemented with Clayton and Frank copulas at varying Kendall’s tau values (0.25, 0.5, and 0.75). Meanwhile, the interest rates are modeled using the BI-7-day (reverse) rate with a Triangular Fuzzy α-cut. The findings reveal that increasing Kendall’s tau values lead to higher pure premiums, and notably, the Frank Copula model yields higher premium values than the Clayton Copula model. This research contributes valuable insights into the actuarial assessment of family annuity products, shedding light on the significance of considering dependencies among individuals for more accurate premium calculations.
The Application of Delta Gamma Normal Value at Risk to Measure the Risk in the Call Option of Stock Astuti, Ayu; Sulistianingsih, Evy; Martha, Shantika; Andani, Wirda
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19669

Abstract

Call options of stock have a nonlinear dependence on market risk factors, thus encouraging the development of a method capable of measuring the risk of call option of stock, namely the Delta Gamma Normal Value at Risk (DGN VaR) method. The DGN VaR method can provide a more accurate VaR estimate than Delta Normal VaR (DN VaR) because of the Delta and Gamma sensitivity measures in the formula. The DGN VaR method uses the second-order Taylor Polynomial approach to approximate the return of stock price underlying the call option. This research applies the DGN VaR method to analyze the risk of call options of Atlassian Corporation (TEAM) and MicroStrategy Incorporated (MSTR). Both companies operate in the technology sector and are among the top 100 largest software companies based on market capitalization for the analysis period September 21, 2022 to September 21, 2023. The analyzed options in this research consist of in-the-money and out-of-the-money options with several strike prices (K). For in-the-money options, the strike prices are $105, $110, and $115 for TEAM, and $150, $160, and $170 for MSTR, while for out-of-the-money options, the strike prices are $190, $195, and $200 for TEAM, and $330, $340, and $350 for MSTR with varying confidence levels of 80%, 90%, 95%, and 99%. Based on the results of the analysis, the DGN VaR for the analyzed in-the-money option has a greater value than the DGN VaR for the analyzed out-of-the-money option.
CART Classification on Ordinal Scale Data with Unbalanced Proportions using Ensemble Bagging Approach Arini, Luthfia Hanun Yuli; Solimun, Solimun; Efendi, Achmad; Ullah, Mohammad Ohid
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20201

Abstract

CART is one of the algorithms in data exploration techniques with decision tree techniques. Unbalanced class proportions in the classification process can cause classification results of minor data to be incorrect. One way to overcome the problem of data imbalance is to use an ensemble bagging algorithm. The bagging algorithm utilizes the resampling method to carry out classification so that it can reduce bias in imbalanced data. The data used is secondary data from Fernandes and Solimun's 2023 research report. The number of sample are 100 respondents that has been valid and reliable. The sample for this research was mothers with toddlers in Wajak village, Malang Regency. The results showed that the ensemble bagging CART method is better at overcoming the problem of imbalance in the proportion of classes with a performance value of accuracy, sensitivity, specificity, and F1-Score values of 85%, 94.1%, 66.7%, and 78%. This research is limited to the Sumberputih Village area. So, the results of this research are only representative for the Wajak District area. 
Mental Comparison of Students Learning Abacus-Arithmetic and Not Learning Abacus-Arithmetic on Mathematics Material Judijanto, Loso; Lumbantoruan, Jitu Halomoan
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i1.17614

Abstract

Students' mental mastery in elementary school mathematics lessons in Indonesia is weak, slow, inaccurate, and declining. Mastery problems among elementary school students who have studied mental abacus arithmetic were found to be low. This is an urgent matter to research because there is a gap between theory, expectations, and reality. The purpose of this research was to compare the ability to solve mathematical problems between students who studied abacus mental arithmetic and students who did not study abacus mental arithmetic. This research involved 70 students. Data collection techniques using instruments, the instruments used were the first-semester mathematics exam and mental arithmetic exam. Data analysis techniques using SPSS Version 25.0 statistics, namely the t-test, were used to compare the ability to solve mathematical problems between students who studied mental abacus-arithmetic and students who did not study mental abacus-arithmetic. Pearson correlation was used to determine the relationship between students' mental arithmetic learning achievement and their ability to solve mathematical problems. The results of the research showed that there was a significant difference (p<0.05) in learning achievement on symbolic mathematics questions and mental arithmetic achievement between students who studied mental abacus calculation and students who did not study mental abacus calculation. The minimum score of the group that studied mental abacus calculation was higher compared to the group that did not study mental abacus calculation. However, there was no significant difference (p<0.05) in mathematics learning achievement between students who studied mental abacus-arithmetic and students who did not study mental abacus-arithmetic. 
Implementation of Gamma Regression and Gamma Geographically Weighted Regression on Case Poverty in Bengkulu Province Azagi, Ilham Alifa; Sumertajaya, I Made; Saefuddin, Asep
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.v8i3.22930

Abstract

Spatial analysis involves leveraging spatial references inherent in the data being analyzed. The method to be used in spatial analysis is the Geographically Weighted Regression (GWR) method. GWR is an extension of the linear regression model at each location by adding a weighting function to the model. Generally, the GWR model uses residuals with a normal distribution in its analysis. One distribution that can be used is the gamma distribution. With the development of methods in statistics, when a response variable follows a gamma distribution, analysis is performed using Gamma Regression (GR). GR analysis is conducted because the response variable meets the gamma distribution assumption. One method used for spatial effects with a gamma-distributed response variable is the Gamma Geographically Weighted Regression (GGWR) method. In 2022, Bengkulu Province was among the ten poorest provinces in Indonesia. Therefore, the main objective is to compare the GR and GGWR models and analyze the factors affecting poverty in Bengkulu Province using these models. The results of this study show that the GR model has an R² accuracy of 87.93%, while the GGWR model has an R² accuracy of 95.87%. This indicates that the best model for the analysis is the GGWR. An example of the GGWR model equation for poverty in Bengkulu Province is Y=exp⁡(-6.039+3.15×〖10〗^(-6) X_1-0.055X_2+0.156X_4-0.00021X_5+0.004X_7-0.021X_8-0.006X_9+4.794×〖10〗^(-5) X_10). The factors influencing the GGWR model in Bengkulu Province are Population, Life Expectancy, Average Years of Schooling, Adjusted Per Capita Expenditure, School Participation Rate, Per Capita Expenditure on Food, Households Receiving Rice for the Poor, and Gross Regional Domestic Product. The benefit of this research is to serve as a reference for the provincial government of Bengkulu regarding the variables that influence poverty. It is expected that this will help the government reduce the poverty rate in Bengkulu Province. 
Exploring Students Learning Difficulties in Linear Function: A Diagnosis of Grade 9 Inayah, Sarah; Jupri, Al; Darhim, Darhim; Prabawanto, Sufyani
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i1.17259

Abstract

The aim of this research is to determine students' learning difficulties in completing diagnostic tests on linear function material. In managing data, quantitative procedures are used with the aim of reducing data. After that the data is analyzed using inductive data analysis and the processed data will be presented in narrative form. So this type of research is qualitative research. The subjects in this research were class IX students at a junior high school in Cianjur. The instruments used in this research were documentation, tests and interviews. The conclusions of the research results obtained include the types of student difficulties in straight line equation material are (1) difficulties in algorithmic abilities including a lack of planning abilities (strategy knowledge) and in solving abilities (algorithmic knowledge) which are shown from incomplete answers or lack of steps , the lack of accuracy of students in working; (2) difficulties in using the principle of linear functions, lack of mastery of the basics of algebra and lack of understanding (schematic knowledge) as indicated by difficulties in recognizing linear functions in contextual problems, errors in algebraic computations, difficulty in determining the point through which the line passes, and difficulty in apply the principle of parallel or perpendicular gradients; and (3) difficulties in using the concept including the inability to remember the concept, the inability to deduce useful information from a concept and the lack of understanding skills (schematic knowledge) which is shown by incompleteness in writing formulas. This research will be useful as a preliminary study in making learning designs to overcome student learning difficulties in linear function material based on empirical findings.
Integrating Ethnomathematics Through Traditional Maluku Snacks to Enhance Geometric Understanding of Junior High Students Purba, Pratiwi Bernadetta; Nurwijaya, Sugian
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.v8i3.20526

Abstract

This study explores the potensial of utilizing traditional Maluku snacks (pom poms, bagea, embal kacang, sagu lempeng, serut kenari) as pedagogical tools to enhance students’ understanding of geometric conceps. The aim of this research is to describe how to integrate Ethnomathematics through traditional Maluku snacks to improve junior high school students' understanding of geometry concepts. This research was carried out in November 2023 at Yos Sudarso Junior High School Dobo. The subjects in this research were 30 grade 8 students. In this research, students used traditional Maluku snacks to understand geometric concepts through demonstrations and discussions. This research uses a qualitative approach where the type of research is descriptive qualitative. The data collection technique in this research is through observation using students’ worksheets, interviews, and documentation using a recording device. Furthermore, data analysis in this research is qualitative analysis with stages of data reduction, data presentation, and drawing conclusions. The results of the research are that students understand the concept of 2D shapes in traditional Maluku snacks: pom-poms (triangles and rectangles), bagea (circles), serut kenari (circles and rectangles), sagu lempeng (trapezoids and rectangles), and embal kacang (rectangle). The concept of 3D shapes in traditional Maluku snacks: pom-poms (triangular prisms), bagea (balls), serut kenari (tubes), sagu lempeng (trapezoidal prisms), and embal kacang (cube-shaped). The integration of ethnomathematics in learning can include learning experiences to the formation of mathematical concepts, especially geometry, mathematical problems, the use of terms in geometry. It is hoped that the integration of ethnomathematics in geometry learning at school can develop meaningful learning.
Forecasting Beef Production with Comparison of Linear Regression and DMA Methods Based on n-th Ordo 3 Tundo, Tundo; Yel, Mesra Betty; Nugroho, Agung Yuliyanto
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.v8i4.24706

Abstract

Beef is considered a high-value commodity because it is an important food source of protein. Interest in beef is increasing along with increasing people's incomes and awareness of the importance of fulfilling nutrition. Demand for beef is expected to continue to increase. According to the Central Statistics Agency (CSA), beef production in Jakarta shows an increasing trend every year. In the last 10 years, beef production has increased significantly, but in 2020 there was a decrease in production of 7,240.68 tons due to the lockdown due to the corona virus outbreak. After that, in 2021, production reached 16,381.81 tons and will continue to increase in 2022 and 2023. Based on the above phenomenon, the aim of this research is to support the success and sustainability of the beef industry by ensuring that supply matches demand, resources are used optimally, and risks can be managed well. To predict beef production, an accurate method, model or approach is needed. One way to predict beef production in Jakarta is to use the Linear Regression and Double Moving Average (DMA) methodsThe way the Linear Regression and DMA methods work is to forecast based on concepts and properties. The concepts and properties of Linear Regression are models, functions, estimates and forecasting results, while DMA performs time series analysis based on moving averages. After analysis using MAPE, it was found that the algorithm that had the smallest error value was the linear regression algorithm with a percentage for the monthly period of 15% while for the year period it was 17% compared to DMA. So in this case it would be very appropriate to use the Linear Regression method from the error values obtained.

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