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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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Forecasting Maximum Water Level Data for Post Sangkuliman using An Artificial Neural Network Backpropagation Algorithm Mislan, Mislan; Dani, Andrea Tri Rian
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.v8i2.20112

Abstract

Neural Network (NN) is an information processing system that has characteristics similar to biological neural networks. One of the algorithms in NN is Backpropagation Neural Network (BPNN). BPNN is an excellent method for dealing with complex pattern recognition problems. In this research, maximum water level forecasting was carried out at Sangkuliman Post using a Backpropagation Neural Network. This research aims to obtain modeling for forecasting maximum water level, as well as forecasting results using the best model. The research results show that the best model is five neurons in hidden layer 1 and 3 neurons in hidden layer 2 with the backpropagation algorithm, the activation function used is binary sigmoid, the learning rate is 0.001, and the maximum iteration is 10,000,000 with the smallest RMSE result being 1.816. The forecast results for the following 12 periods are 1.672, 1.779, 1.523, 1.271, 1.752, 1.692, 1.335, 1.479, 1.750, 1.779, 1.340, 1.269, and 1.754. Forecasting results can be used by various parties in decision-making and planning in multiple fields, as an example to see the patterns of biological and vegetable life around Sangkuliman Post. Based of forecasting results, certain months show an increase in maximum water levels. 
Platelet Modeling in DHF Patients Using Local Polynomial Semiparametric Regression on Longitudinal Data Utami, Tiani Wahyu; Chamidah, Nur; Saifudin, Toha
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.v8i1.17427

Abstract

Regression analysis is one of the statistical methods used to model the relationship between response variables and predictor variables. Semiparametric regression is a combination of parametric and nonparametric regression. The estimator used in estimating the semiparametric regression model in this research is the Local Polynomial. Longitudinal data can be found in the health sector, including dengue hemorrhagic fever (DHF) data. The laboratory criteria for indication of DHF is thrombocytopenia. This research aims to obtain platelets model for DHF patients that can be used for forecasting so that it is hoped that it can provide information to the medical team in treating DHF patients. The estimated model used is Local Polynomial semiparametric regression on longitudinal data. The response variables in this research were platelets of DHF patients, which were influenced by hemoglobin as parametric predictor variable and examination time while hospitalized as nonparametric predictor variable. In the local polynomial regression model, it is necessary to select the optimal bandwidth and polynomial order method, GCV. The optimum bandwidth selection based on the GCV method obtained is 1.5 and polynomial order of 2, then applied to DHF patient platelet data, producing an estimated local polynomial semiparametric regression model that follows the actual data pattern. Modeling the platelets of DHF patients obtained using a local polynomial estimator resulted in an R2 value of 84.25% and MAPE of 4.5%, indicating highly accurate forecasting, so it can be concluded that the resulting model is better at predicting.
Kanoma: Learning Media to Improve Students’ Understanding Mathematical Concepts Sigarini, Khofifah Aluh; Fitriana, Laila; Setiawan, Rubono
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.v8i3.23076

Abstract

This research was conducted to determine the validity, practicality, and effectiveness of Kanoma’s learning media in improving the understanding of mathematical concepts in high school students in class X. This research applied development research design with the PLOMP approach developed by Tjeerd Plomp. The stages of development using the PLOMP approach include preliminary investigation, product design, construction, testing, and implementation. The population in this research were all ten-grade students at a vocational high school. The research sample consisted of 16 students in the experimental class and 14 students in the control class. These students were selected randomly using the cluster random sampling technique. The instruments utilized in the study included assessments by media experts, questionnaires for students and teachers, and pretest and posttest evaluations of mathematical understanding. The instruments given to media experts is used to validate the Kanoma media and its content. The questionnaires for students and teachers were used to test the practicality of the developed Kanoma media. These quistionnaires gathered feedback on how easy and useful the media was in a classroom setting. The pretest and posttest were designed to measure students’ understanding of mathematical concepts related to finding the roots of quadratic equations. The average value given by material experts from the two validators of Kanoma’s media is 0.82. The average value given by media experts from the two validators is 0.90. The results show that the Kanoma media was categorized as “very valid” by both material and media experts. This indicates that media was suitable for use by class X students in senior high school. Kanoma media is also classified as practical based on the average percentage of student and teacher responses. The responses from students scored 73%, categorized as “practice”. The responses from teachers scored 81%, categorized as “very practice.” Kanoma media is effective based on the Mann-Whitney Asyptotic Sig. (0.002) <α (0.05). The results showed a significant improvement in mathematical understanding. Students who used the Kanoma media had a better grasp of the mathematical concepts than those who did not.
Exploring Local Culture through Geometry Transformation: a Study of Banyumasan Batik Novikasari, Ifada; Febriana, Maghfira
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.v8i1.17298

Abstract

Banyumasan batik is one of Indonesia's cultural heritages from Banyumas Regency, which has unique and interesting patterns and motifs. This research paper describes the mathematical modelling of geometric transformations in Banyumasan batik. Geometric transformation is a mathematical technique for changing the shape or position of an object on a plane. This is qualitative research with an ethnographic approach. Data is collected through observation, interviews, and documentations. The data obtained were analysed using content analysis to identify various Banyumasan batik motifs that can be transformed into geometric forms. This study describes the basic geometric transformations, namely translations in Sekar Tirta batik motif, reflections in Bawor Kembar batik motif, dilations in Kawung Jenggot batik motif, and rotations in Manggar Bawor batik motif which applied to Banyumasan batik motifs. The results of this study include geometric transformations of Banyumasan batik motifs which are expected to positively contribute to the development of Indonesian art and culture, especially in the field of batik, enrich insight and knowledge about the application of mathematics in everyday life, and can be used for mathematical modelling and mathematics education based on local culture.
Analysis of Critical Criteria for Assessment of Logistics Service Provider Company (Case Study: PT. Pos Logistik Indonesia) Suzana, Yenny; Irwansyah, Budi; Suparni, Suparni; Darmawan, Wanda
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.v8i3.21670

Abstract

The quality of services provided by logistics providers has a direct impact on an organization's business. Organizations need to critically evaluate the performance of their LSPs and choose service providers rationally. LSPs understand the importance of service quality to their survival and growth and strive to provide high-quality services. PT Pos Logistik Indonesia (PLI) is a company that operates in the field of Logistics Delivery Services which can include documents, electronic products, logistics, and others.  PT Pos Logistik Indonesia (PLI) in Langsa City should have criteria as a logistics service provider to ensure customer satisfaction. This research aims to analyze these criteria through a survey collected from 120 Small and Medium Enterprises (SMEs) organizations in Langsa City that use the services of PT Pos Logistik Indonesia (PLI). Small and Medium Enterprises (SMEs) are individual business entities or legal entities that have small initial capital, or a small value of wealth (assets) and a small (limited) number of employees. Questionnaire strategies were used to identify criteria selection-based sustainable logistics service quality (SLSQ) theoretical framework, that is sustainable transport elements, training, collaboration, sustainable packaging, and sustainable information. The explanatory factor analysis method was employed. The top three ranked criteria for evaluating logistics service provider criteria selection based on sustainable logistics service quality are the trained PLI employees, the sustainable packaging, and the commitment to environmental goals. Through this research, it confirms that sustainable logistics practices can bring value to PLI as LSPs and better improve their performance and customer satisfaction.
Panel Data Spatial Regression Modeling with a Rook Contiguity Weighting Function on the Human Development Index in West Sumatera Province Arum, Prizka Rismawati; Anggraini, Lisa; Nur, Indah Manfaati; Purnomo, Eko Andy
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.v8i1.16675

Abstract

The achievement of the level of welfare of a region or country can be seen from the level of human development as measured by the Human Development Index (HDI). West Sumatra is one of the provinces with HDI achievements above the national average. However, there are still regencies/cities in West Sumatra Province that have HDI achievements below the national average and HDI achievements in West Sumatra Province Regencies/Cities have changed in 2017-2021. Therefore, in this study, spatial analysis of panel data was used. The aim of this research is to find out the general description of the HDI of West Sumatra Province, obtain a panel data spatial regression model and obtain variables that significantly influence on HDI in West Sumatra Province 2017─2021because differences in HDI achievement were suspected to have influences from areas that were side by side and the area was observed more than once. The model formed from this analysis using the rook contigutiy weighting function is Random Effect Spatial Autoregressive because the spatial interactions formed in human development index data in West Sumatra Province are real at lag. This model is a suitable model based on panel spatial model selection and has an R2 value of 92.94%. Analysis of human development index data in regencies/cities in West Sumatra Province using spatial regression panel data obtained results that expectations of school length (X1), average length of schooling (X2), and population density (X3) significantly directly influenced the human development index in regencies/cities in West Sumatra Province.  
Modeling the Dynamics of Forest Fires: A Vector Autoregressive Approach Across Three Fire Classifications Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri
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.v8i4.24792

Abstract

The problem of forest fires is one that, with each passing year, gets more difficult to mitigate. A significant number of people will be affected by this case, particularly in terms of their health. The need for targeted initiatives must be balanced. Look at the forecasts for the number of forest fires expected to occur in the following period. Cases of forest fires reported to the Ministry of Environment and Forestry are categorized into three distinct categories: high, medium, and low. In addition to future estimates, it is reasonable to anticipate that classifications will also affect one another. The vector autoregressive (VAR) model is a statistical tool that may produce future projections based on three categories of forest fires in a specific period. This information can be utilized to make predictions. The aim of the study was to model 3 classifications of forest fire cases using the Vector Autoregressive (VAR) model. The data utilized is a summary of the number of forest fire cases in Pulang Pisau Regency, Central Kalimantan, categorized as low, medium, and high, from January 2013 to March 2024. During this study, the VAR modelling process was broken down into three primary stages: order identification (the findings that were achieved were VAR(4)), parameter estimation, and diagnostic testing (VAR(4) was declared to fulfil the requirements for the diagnostic test). It is possible to generate a predicted value for the subsequent three times based on these stages, which may be considered when calculating the proper amount of effort to put forward. The accuracy of forest fire case modeling utilizing the VAR(4) model is 70.23%. Moreover, the predictive outcomes for each categorization indicate a rise in medium and low-level forest fires compared to previous data, although the contrary is observed for high-level forest fire incidents.
Dynamical Analysis of a Predator-Prey Model Involving Intraspecific Competition in Predator and Prey Protection Resmawan, Resmawan; Nuha, Agusyarif Rezka; Nasib, Salmun K.; Nashar, La Ode
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.v8i3.22154

Abstract

This article explains the interaction of the prey-predator model in the presence of wild harvesting and competition intra-specific predator populations and prey protection zones.  Model construction is based on literature studies related to the basic theory of the model and the biological properties between predator and prey populations. This study aims to look at the dynamic conditions of the predator-prey model in the form of the existence of prey and predator populations and the impact that occurs in the long term for both populations due to changes in parameter values. The model analysis begins with the formulation of the solution conditions and boundaries model, and next with the determination of the equilibrium point. Every equilibrium point is analyzed by the characteristic of its stability is neither local or global. The model owns three equilibrium points, namely the equilibrium point of population extinction (E_0), the equilibrium point of predator extinction (E_1), and the equilibrium point of persistence of the two populations (E_2). These equilibrium points are stable locally or globally if certain conditions are met. Next, it is shown that bifurcation proceeds Which describes the changing of characteristic stability point equilibrium Which depends on the threshold parameter values h_1, Ω^*, and ρ^*. In the end, numerical simulations are presented in the form of phase, time-series, and bifurcation diagrams to support the analytical results of the model, as well as to visually show the dynamic behaviour of the interaction between the two populations based on changes in predation levels, illegal harvesting, prey refuge zones, and intra-specific competition.
The Impact of Differences in Attitudes of Male and Female Prospective Teachers in Understanding Statistics Judijanto, Loso; Lumbantoruan, Jitu Halomoan
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.v8i2.20396

Abstract

Universities have understood the gender gap of prospective teachers towards attitudes in facing statistics lessons is increasingly growing. However, the understanding of universities about gender in influencing prospective teachers' attitudes toward statistics lessons is still minimal. This is urgent to be studied because there is a gap between expectations in universities and facts in the field, so this study aims to analyze differences in attitudes towards statistics based on gender and identify factors that influence attitudes towards statistics. The research method used is a quantitative survey type. The research sample was 395 prospective mathematics teachers from 18 universities that prepare prospective mathematics teachers in Jakarta and the sample was selected randomly. The data collection technique was a survey using an instrument. The instrument was developed and validated. The instrument was distributed with a rating scale from point 1 to point 5. Data were collected with the help of Google. The data analysis technique used was descriptive statistics with the help of SPSS Version 25.0, assessing the mean, variance, standard deviation, and the t-test. The results found that prospective teachers have a positive attitude towards statistics and the female gender has a significant and more positive influence on attitudes towards statistics lessons. The conclusion is that gender is important in shaping prospective teachers' attitudes towards statistics lessons. The research implies that higher education needs to pay attention to gender factors in implementing the curriculum and provide training to prospective teachers to increase interest in learning statistics.
Determination of Optimal Portfolio by Calculating Transaction Costs using Genetic Algorithms on the Jakarta Islamic Index Fadhila, Sinta Oktavia Nur; Abadi, Agus Maman; Setiawan, Ezra Putranda
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.v8i1.17469

Abstract

The optimal portfolio is a portfolio that can provide maximum returns at the same level of risk. In investing, the term "high return, high risk" is known, meaning that the higher the return, the higher the risk. Therefore, investors need to develop an optimal portfolio to obtain the maximum return on investment at the same level of risk. This study aims to determine the optimal formation of a stock portfolio by calculating transaction costs using the genetic algorithm method on stocks that are members of the Jakarta Islamic Index. This research uses data of daily return on stocks included in Jakarta Islamic Index from 1 August 2020-1 August 2022. The dataset consists of two variables: the date of observation and daily stock returns. The method used in this study is the minimum variance method and the genetic algorithm. Data analysis was divided into two stages: model formulation and model testing through case studies. The analysis of optimal portfolio formation using genetic algorithms shows that in terms of performance, the minimum variance portfolio is superior to the genetic algorithm portfolio, as indicated by the Sharpe ratio value. Meanwhile, the genetic algorithm portfolio is superior to the minimum variance portfolio regarding transaction costs. The genetic algorithm portfolio can provide a fairly high total return, small transaction costs, and good performance compared to the minimum portfolio. Hence, the genetic algorithm portfolio is worthy of recommendation to investors.

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