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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 21 Documents
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Search results for , issue "Vol 8, No 2 (2024): April" : 21 Documents clear
Dynamical of Prey Refuge in a Diased Predator-Prey Model with Intraspecific Competition for Predator Pratama, Rian Ade
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.v8i2.19893

Abstract

The predator-prey model described is a population growth model of an eco-epidemiological system with prey protection and predator intraspecific traits. Predation interactions in predator species use response functions. The aim of this research is to examine the local stable balance point and look at the characteristics of species resulting from mathematical modeling interventions. Review of balance point analysis, numerical simulation and analysis of given trajectories. The research results show the shape of the model which is arranged with a composition of 5 balance points. There is one rational balance point to be explained, using the Routh-Hurwitz criterion, . The characteristic equation and associated eigenvalues in the mathematical model are the local asymptotically stable balance points. In the trajectory analysis, local stability is also shown by the model formed. There are differences for each population to reach its point of stability. The role of prey protection behavior is very effective in suppressing the spread of disease. Meanwhile, intraspecific predator interactions are able to balance the decreasing growth of prey populations. If we increase the intraspecific interaction coefficient, we can be sure that the growth of the prey population will both increase significantly. When the number of prey populations increases significantly, of course disease transmission and prey protection become determining factors, the continuation of the model in exosite interactions. In prey populations and susceptible prey to infection, growth does not require a long time compared to the growth of predator populations. The time required to achieve stable growth is rapid for the prey species. Although prey species' growth is more fluctuating compared to predator populations. Predatory species are more likely to be stable from the start of their growth. The significance of predatory growth is only at the beginning of growth, while after that it increases slowly and reaches an ideal equilibrium point. Each species has its own characteristics, so extensive studies are needed on more complex forms of response functions in further research. 
Development of a Desmos-Assisted Planar Analytic Geometry Textbook to Support High Order Thinking Skills Ningsih, Yunika Lestaria; Octaria, Dina; Nopriyanti, Tika Dwi; Jumroh, Jumroh
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.v8i2.20775

Abstract

The study focuses on improving higher-order thinking skills (HOTS) in mathematics students using a Desmos-assisted planar analytic geometry course. Analytic geometry, which is essential for understanding geometric properties using analytic methods, requires students to develop problem-solving, analysis, assessment, and creativity abilities. However, current educational practices fall short of acquiring these abilities due to insufficient instructional techniques, textbooks, and a lack of integration with information and communication technologies. To address these shortcomings, the study proposes a Desmos-assisted textbook meant to increase students' HOTS through the use of interactive Desmos platform tools such as graphic depiction, experimentation, simulation, and collaborative learning. The textbook development followed the PLOMP model, which included preliminary research, prototyping, and assessment phases, ensuring the textbook's validity and practicality through reiterated evaluations. The findings show that the textbook is highly valid and practical for instructional purposes, improving students' knowledge of mathematical concepts and ability to engage in HOTS processes. Despite some difficulties with HOTS-related practice questions, generally student feedback was positive, emphasizing the textbook's function in supporting a deeper understanding of analytic geometry and encouraging problem-solving skills. The study indicates that integrating technology such as Desmos into mathematics education can greatly contribute to the development of students' HOTS, and recommends its use in teaching techniques as well as additional research on its implementation in educational contexts.
Nonparametric Smoothing Spline Approach in Examining Investor Interest Factors Pratama, Yossy Maynaldi; Fernandes, Adji Achmad Rinaldo; Wardhani, Ni Wayan Surya; Hamdan, Rosita
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.v8i2.20192

Abstract

The nonparametric approach is an appropriate approach for patterns of relationships between predictor variables and response variables that are not or have not been known in form. In other words, there is no complete information about the pattern of relationships between variables. Curve estimation is determined based on relationship patterns in existing data. The nonparametric approach has great flexibility for estimating regression curves. This study aims to form a model on investor interest factors in improving tourism investment decisions with a nonparametric approach. The nonparametric method used is the smoothing spline regression method. The smoothing spline method is used because the modeling results from the smoothing spline approach can follow the relationship model between variables contained in the data. Thus, this method really helps researchers to model relationships between variables that are not linear and whose linear form is unknown. The results of the analysis showed that the nonparametric smoothing spline regression analysis method could model data by 94.63%, indicates that data variance can be explained by 94.63% with models, while other variance outside the study explain the remaining 5.37%. That is, investment motivation is one of the most important factors to improve investment decisions. 
Identifying Factors Affecting Waste Generation in West Java in 2021 Using Spatial Regression Djuraidah, Anik; Rizki, Akbar; Alfan, Tony
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.v8i2.19664

Abstract

Responsible consumption and production is the 12th of the seventeen SDGs which is difficult for developing countries to achieve due to high waste production. Indonesia is the second largest producer of food waste in the world. Garbage is solid waste generated from community activities. Population density is an indicator to estimate the amount of waste generated in an area. The choice of West Java Province as the research area is based on the fact that this Province has the second highest population density in Indonesia. This study aimed to determine the predictors/factors that influence waste production in the districts/cities of West Java Province. The data used in this study are total waste as a response variable and GRDP (gross domestic product), total spending per capita, average length of schooling, literacy rate, number of MSMEs (micro, small, and medium enterprises), and several recreational and tourism places, the number of people's markets, and the number of restaurants as predictors. The methods used in this research are spatial autoregressive regression/SAR, spatial Lag-X/SLX, and spatial Durbin/SDM. The results of this study show that the SAR is the best model with the lowest BIC (74.442) and pseudo-R-squared (0.7934). Factors that significantly affect total waste production are literacy levels, the number of MSMEs, the number of traditional markets, and the number of recreational and tourist places. 
Structural Equation Modeling: The Influence of School Environment on Students' Interest in Selecting State University Simarmata, Justin Eduardo; Mone, Ferdinandus; Chrisinta, Debora
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.v8i2.19921

Abstract

Despite prior research on student interest in colleges, this study focuses specifically on how the school environment, including individual factors, friends, and teachers, influences students' interest in attending a state university. Understanding these influences can help improve educational systems to better guide students towards higher education. This study aims to determine the influence of the school environment on students' interest in selecting a state university. This research employs a quantitative approach, utilizing structural equation modeling to analyze the relationships between variables. This study examines how a school environment, captured by twelve indicators across individual, friend, and teacher influences, impacts students' interest in state universities. Therefore, data retrieval based on questionnaires is designed accordingly based on latent variables. The sample in this study were 474 high school and vocational school students on the Indonesia-Timor Leste border, which is precisely located in Timor Tengah Utara Regency. The results showed that the school environment that came from individuals, partners, and teachers had a major influence on students' interest in choosing State University. Based on the analysis of structural equations, it was found that individual environments had a direct influence of 98%, partner environments had an indirect influence of 90%, and teachers also indirectly affected 71%. This study contributes to the field by quantifying the distinct influences of individual, peer, and teacher aspects of the school environment on students' interest in attending state universities. This knowledge can inform the development of targeted interventions to improve educational guidance and support student decision-making.
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. 
Robust Optimization of Vaccine Distribution Problem with Demand Uncertainty Fikri, Faiqul; Silalahi, Bib Paruhum; Jaharuddin, Jaharuddin
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.v8i2.20035

Abstract

This study proposes a multi objective optimization model for vaccine distribution problems using the Maximum Covering Location Problem (MCLP) model. The objective function of the MCLP model in this study is to maximize the fulfillment of vaccine demand for each priority group at each demand point. In practice, the MCLP model requires data on the amount of demand at each demand point, which in reality can be influenced by many factors so that the value is uncertain. This problem makes the optimization model to be uncertain linear problem (ULP). The robust optimization approach converts ULP into a single deterministic problem called Robust Counterpart (RC) by assuming the demand quantity parameter in the constraint function is in the set of uncertainty boxes, so that a robust counterpart to the model is obtained. Numerical simulations are carried out using available data. It is found that the optimal value in the robust counterpart model is not better than the deterministic model but is more resistant to changes in parameter values. This causes the robust counterpart model to be more reliable in overcoming uncertain vaccine distribution problems in real life. This research is limited to solving the problem of vaccine distribution at a certain time and only assumes that the uncertainty of the number of requests is within a specified range so that it can be developed by assuming that the number of demand is dynamic.
The Application of Truncated Spline Semiparametric Path Analysis on Determining Factors Influencing Cashless Society Development Pramaningrum, Dea Saraswati; Fernandes, Adji Achmad Rinaldo; Iriany, Atiek; Solimun, Solimun
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.v8i2.19913

Abstract

Semiparametric path analysis is a combination of parametric and nonparametric path analysis. Semiparametric path analysis is used when there are partially nonlinear and unknown patterns of relationships. One approach to semiparametric pathways is truncated spline. Truncated spline approach tends to search for their own estimation of regression functions according to the data. This is because in the truncated spline there are knot points, which are intersection points that indicate changes in data behavior patterns. Truncated spline semiparametric path analysis will be applied to this study to determine the variables that have a significant effect on the development of the Cashless Society so that the result can be used as a reference for banks and the government in maximizing non-cash-based community development. The data used is the result of a questionnaire with 100 respondents of mobile banking users in Jakarta and will be analyzed using R Studio. Based on the results, it was found that the optimal knot point in the truncated spline function is 3 with many knots is 1, thus dividing the condition of digitizing electronic money into 2 regimes. It was concluded that the product and digitalization of electronic money had a significant effect on the development of cashless society where the modeling obtained could explain 83.87548% of the data. However, when electronic digitalization increases through the value of knot points, the development of cashless society tends to stagnate. This could be due to people who are not ready when the condition of digitizing electronic money is increasingly sophisticated because the available electronic money features are increasingly complex. Therefore, it is important for banks to pay attention to the sophistication of electronic money features provided to customers and adjust the target market so that customers are more accustomed and comfortable to use electronic money in the future.

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