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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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Prediction of Maternity Recovery Rate of Group Long-Term Disability Insurance Using XGBoost Kusnadi, Felivia; Wijaya, Andry; Lesmono, Julius Dharma
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16825

Abstract

To help insurers determine insurance rates incorporating maternity factors, it is crucial to understand the maternity recovery rate, which was a metric used by insurance companies to understand how much of the expenses associated with maternity care and related medical services are covered by their policies. This paper employed Extreme Gradient Boosting (XGBoost), a powerful method for handling complex data relationships and preventing overfitting, on North American Group Long-Term Disability dataset obtained from the Society of Actuaries, which listed maternity as one of its categories, to predict the maternity recovery rate. In comparison, other machine learning methods such as Gradient Boosting Machine (GBM) and Bayesian Additive Regression Tree (BART) were used, with Root Mean Squared Error (RMSE) values calculated the difference between predicted and observed maternity recovery rates. Four datasets, 3 imbalanced and 1 fairly-balanced, were created out of the original dataset to test each method’s predictive prowess. The study revealed that XGBoost performed exceptionally well on the imbalanced datasets, while BART showed slight superiority in fairly-balanced data. Furthermore, the model identified the duration, exposures, and age of participants in both predicting maternity recovery rates and the underwriting process. 
Characteristic Min-Polynomial and Eigen Problem of a Matrix over Min-Plus Algebra Maghribi, Sahmura Maula Al; Siswanto, Siswanto; Sutrima, Sutrima
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16498

Abstract

Let R_ε=R∪{-∞}, with R being a set of all real numbers. The algebraic structure (R_ε,⊕,⊗) is called max-plus algebra. The task of finding the eigenvalue and eigenvector is called the eigenproblem. There are several methods developed to solve the eigenproblem of A∈R_ε^(n×n), one of them is by using the characteristic max-polynomial. There is another algebraic structure that is isomorphic with max-plus algebra, namely min-plus algebra. Min-plus algebra is a set of R_(ε^' )=R∪{+∞} that uses minimum (⊕^' ) and addition (⊗) operations. The eigenproblem in min-plus algebra is to determine λ∈R_(ε^' ) and v∈R_(ε^')^n such that A⊗v=λ⊗v. In this paper, we provide a method for determining the characteristic min-polynomial and solving the eigenproblem by using the characteristic min-polynomial. We show that the characteristic min-polynomial of A∈R_(ε^')^(n×n) is the permanent of I⊗x⊕^' A, the smallest corner of χ_A (x) is the principal eigenvalue (λ(A)), and the columns of A_λ^+ with zero diagonal elements are eigenvectors corresponding to the principal eigenvalue.
Numerical Solution of the Advection-Diffusion Equation Using the Radial Basis Function Sabran, La Ode; Syafi'i, Mohamad
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16239

Abstract

The advection-diffusion equation is a form of partial differential equation. This equation is also known as the transport equation. The purpose of this research is to approximatio the solution of advection-diffusion equation  by numerical approach using radial basis functions network. The approximation is performed by using the multiquadrics basis function. The simulation of the numerical solution is run with the help of the Matlab program. The one-dimensional advection-diffusion equation used is  ∂u/∂t+C ∂u/∂x=D (∂^2 u)/(∂x^2 )  with given initial conditions, boundary conditions, and exact solution u(x,t). The numerical solution approximation using the radial basis function network with dt=0.004 and dx=0.02 produces the value at each discretization point is close to the exact solution. In this study, the smallest error between numerical solution and the exact solution is obtained 2.18339 ×〖10〗^(-10).
MICE Implementation to Handle Missing Values in Rain Potential Prediction Using Support Vector Machine Algorithm Putri, Aina Latifa Riyana; Surarso, Bayu; SRRM, Titi Udjiani
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16699

Abstract

Support Vector Machine (SVM) is a machine learning algorithm used for classification. SVM has several advantages such as the ability to handle high-dimensional data, effective in handling nonlinear data through kernel functions, and resistance to overfitting through soft margins. However, SVM has weaknesses, especially when handling missing values in data. The use of SVM must consider the missing values strategy chosen. Missing values in data mining is a serious problem for researchers because it causes many problems such as loss of efficiency, complications in data handling and analysis, and the occurrence of bias due to differences between missing data and complete data. To overcome the above problems, this research focuses on understanding the characteristics of missing values and handling them using the Multiple Imputation by Chained Equations (MICE) technique. In this study, we utilized secondary data experiments that contain missing values from the Meteorological, Climatological, and Geophysical Agency (called BMKG) related to predictions of potential rain, especially in DKI Jakarta. Identification of types or patterns of missing values, exploration of the relationship between missing values and other variables, incorporation of the MICE method to handle missing values, and the Support Vector Machine Algorithm for classification will be carried out to produce a more reliable and accurate prediction model for rain potential. It shows that the imputation method with the MICE gives better results than other techniques (such as Complete Case Analysis, Imputation Method Mean, Median, Mode, and K-Nearest neighbor), namely an accuracy of 89% testing data when applying the Support Vector Machine algorithm for classification.
Enhancing the Ability of 'Spatial Nets' through Outdoor Learning-Based on Traditional Game 'Baju Simi' Yumiati, Yumiati; Haji, Saleh; Antasari, Melisa
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16411

Abstract

Traditional games are rooted in a regional culture with educational values that are important for future generations. These educational values, among others, contain various mathematical concepts (geometry). This study aims to improve students' Spatial Nets ability through the outdoor learning-based traditional game 'Baju Simi.' The type of research used is classroom action research. The research subjects were 20 students of class VI Sekolah Dasar Negeri 98 Kaur, Bengkulu. The study was conducted in the Even Semester 2022/2023. The instrument used is a test on 'Spatial Nets' with as many as ten essay questions. In addition, it also uses questionnaire instruments, observation guidelines, and interview guidelines. Data were analyzed qualitatively. The results obtained are as follows: (1) In Cycle 1, there was an increase in the ability of 'spatial nets' by 0.21 with low pre-test and post-test scores of 45 and 56.5, respectively; and (2) In Cycle 2, there was an increase in the ability of 'spatial nets' by 0.36 with an average pre-test and post-test score of 53 and 70.25 respectively. As many as 92% of students can understand the meaning of space-building nets correctly. 87% and 82% of students can precisely define the webs of cubes and blocks. This study implies that traditional games can be used as a medium and source of learning mathematics (geometry) in elementary schools so that students are highly motivated (4.2 on a scale of 5) in learning mathematics (geometry). 
In-House Refurbishing and Outsourcing Refurbishing Models with Degree of Interchangeability in Product Design Kurdhi, Nughthoh Arfawi; Vania, Kezia Abigail; Widyaningsih, Purnami; Sudibyo, Nugroho Arif
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.15787

Abstract

Refurbishing is the process of processing used products into products with the quality of new products. Refurbishing can be done by the manufacturer itself (in-house) or the manufacturer can delegate the refurbishing process to other manufacturers (outsourcing). This research aims to construct an in-house refurbishing model and an outsourced refurbishing model, determine the optimum solution, analysis, and application so that optimum benefits are obtained, and compare the in-house refurbishing model and the outsourced refurbishing model. Multivariable function optimization is used to get optimum profit. Judging from the optimum production results, manufacturers who carry out in-house refurbishing choose a higher degree of interchangeability and produce more new products. Products with an interchangeability design are products that can be used to replace similar products with the same function. Based on economic benefits, manufacturers who carry out in-house refurbishing get greater profits than outsourcing refurbishing. Viewed from environmental sustainability, outsourcing refurbishing is more environmentally friendly than in-house refurbishing.
Improving the Spatial Ability of Distance Learning Students on the Material of Three-Dimensional Shapes through Mobile Learning Applications Based on Augmented Reality Anam, Khaerul; Wiradharma, Gunawan; Prasetyo, Mario Aditya; Suko, Imelda Paulina
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16902

Abstract

This research develops a mobile learning application that produces a feasible and attractive product to be used as a learning resource. Then, the product was tested quantitatively on users to determine the product's readiness and its relationship to increasing the user's spatial abilities. This research is a continuing research that has been carried out previously regarding the development of ABRAR (Application of three-dimensional shapes with Augmented Reality) application (Anam et al., 2022). The product has been validated by content and media experts and has received positive feedback from student users. Data was collected in Nusa Tenggara: Regional Offices of UT Mataram and UT Kupang, involving 3.098 Elementary Education Study Program students. The sample size consisted of 310 respondents, determined using the Lemeshow formula. The product produced from this research is an augmented reality-based mobile learning application that serves as a learning resource. The results of the mobile learning media trial developed were interpreted as very positive. It shows that using mobile learning in geometry subjects provides a positive response and increases motivation in the learning process. In addition, the implementation of mobile learning in spatial ability has shown a 30% improvement in imagining the position of three-dimensional shapes. It indicates that mobile learning has influenced the respondents' spatial ability. Respondents can visualize three-dimensional shapes from a certain point of view by utilizing augmented reality (AR) technology. Furthermore, based on the feasibility test results, the resulting mobile learning meets the criteria of being excellent and feasible to use as a geometry learning medium. The result of the research is mobile learning application so that it can be applied for distance education with requirements has an Android application system and easy to connect the internet. Thus, the ABRAR application can support learning anytime and anywhere, improve understanding of the material, and improve students' spatial abilities.
Employee Benefits Program Valuation with Multiple Decrement Model Based on PSAK 24 Post-COVID-19 Pandemic Ekasasmita, Wahyuni; Rahmi, Nur; Iskandar, M. Fauzan
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.v8i1.17417

Abstract

In this article, we evaluate the post-labor compensation program based on PSAK-24 in the new normal era of the COVID-19 pandemic. In order to create a table multiple decrements based on a single table decrement namely, death, withdrawal, total permanent disability, and retirement. In the new normal era of the COVID-19 pandemic, the benefits of death, death caused by COVID-19, withdrawal, total permanent disability, and retirement were then aggregated. The method used in this study is a quantitative method with a case study approach of COVID-19. The data used is secondary data on the number of COVID-19 positive cases in Indonesia from January 2021 to December 2022. In this study, an actuarial model, the Multiple Decrement Model, was applied to calculate the valuation of the post-labor compensation program based on PSAK-24 using five decrements as the cause of claims consisting of death, death cause of COVID-19, withdrawal, total permanent disability and retirement. The calculation results that can be seen that large annual net premiums multiple decrement cases that provide benefits according to the cause of failure getting bigger as that person gets older. 
Discovering Ethnomathematics in Sundanese Gamelan: Explore Mathematics Aspect in Gamelan Supriyadi, Edi; Turmudi, Turmudi; Dahlan, Jarnawi Afgani; Juandi, Dadang; Sugiarni, Rani
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.v8i3.21768

Abstract

Ethnomathematics is important in recent decades, specifically in the production of gamelan instruments. Therefore, this research aimed to examine the intricate relationship between mathematics and cultural craftsmanship in Sundanese gamelan instruments made at Gong Factory in Bogor, West Java. Ethnographic methods were used to observe and describe the practices of gamelan craftsmen and the data collection process comprised carefully selected artists. These individuals actively acquire data by reviewing relevant material, observing, analyzing, and interviewing. Miles and Huberman's framework for data analysis included data reduction, presentation, inference, and verification. The procedures understood the delicate relationship between mathematics and culture in the investigated setting. The results showed that Gong Factory in Bogor preserved and promoted a unique musical heritage. Furthermore, the instruments were known for exceptional sound quality, serving as cultural relics and didactic tools, as well as teaching visitors about the manufacturing process. The factory preserved culture through the manufacture of gamelan instruments including gong, bonang, and saron. In this context, the craftsmanship used mathematical principles, specifically precise proportions and ratios. The instruments' visual and auditory qualities depended on geometry. The results significantly impacted mathematics education by enhancing cross-cultural connections, improving proportional reasoning and mathematical comprehension, and recognizing the wider relevance of principles. Culture, mathematics, and education were connected, showing that conserving Indonesian musical tradition benefited local and global populations.
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. 

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