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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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Ratio Interval-Frequency Density with Modifications to the Weighted Fuzzy Time Series Vianita, Etna
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.v8i1.16910

Abstract

The improvement of plantation forecasting accuracy, particularly with regard to coffee production, was an essential aspect of earth observations for the purpose of informing plantation management alternatives. These decisions included strategic and tactical decisions on supply chain operations and financial decisions. Many research initiatives have used a variety of methodologies to the forecasting of plantation areas and related industries, such as coffee production. One of these methods was known as the fuzzy time series (FTS) technique. This  study combined ratio-interval and frequency density to get universe of discourse and partition followed by adopted weighted and modified that weighted. The first step was defined universe of discourse using ratio-interval algorithm. The second step was partition the universe of discourse using ratio-interval algorithm followed by frequency density partitioning. The third step was fuzzyfication. The fourth step built fuzzy logic relationship (FLR) and fuzzy logic relationship group (FLRG). The fifth step was adopted the modification weighted. The last step was defuzzyfication. The  models evaluated  by  average  forecasting  error  rate  (AFER)  and  compared  with  existing methods.  AFER  value  1.24%  for  proposed method.
A Comparison of Welch Powell Algorithm and Greedy Algorithm in Odd Semester Lecture Room Scheduling Optimization Faculty of Computer Science Fadilah, Alif Nur; Subarkah, Pungkas; Pramudya, Reyvaldo Shiva; Syabani, Amin
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.v8i4.23142

Abstract

Scheduling is a systematic method to optimize work time, and avoid failure when problems occur. Scheduling is widely applied in the world of education, one of which is in preparing course schedules. Scheduling itself needs to be optimized to ensure a smooth lecture process without any problems between courses. As happened at the Faculty of Computer Science, Amikom Purwokerto University, where in the preparation of the schedule there is no information about lecture rooms. Therefore, the author compiled a lecture hall scheduling optimization journal by comparing the performance between the Welch Powell Algorithm and the Greedy Algorithm as optimization and graph coloring on the lecture hall schedule.The data used in this study are 88 courses spread across 3 study programs, namely Informatics Study Program, Information Systems Study Program, and Informatics Engineering Study Program. This research uses a comparative method on graph vertex coloring, where execution time as duration, lines as algorithm complexity, and manual algorithm calculation as parameters. Based on the research that has been done, the results of 14 full spectrum colors are obtained which are then applied to 23 lecture rooms that can be used without clashes at the Faculty of Computer Science. This can minimize the possibility of overlapping room usage between courses. In addition to comparing the performance of the Welch-Powell Algorithm and the Greedy Algorithm to produce optimal scheduling of lecture rooms, this research can also optimize the schedule of lecturers when entering class to optimize students to be more organized in entering lecture classes at the Faculty of Computer Science, Amikom Purwokerto University.
The Application of the Classical Assumption Test in Multiple Linear Regression Analysis (a Case Study of the Preparation of the Allometric Equations of Young Makila) Mardiatmoko, Gun
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.v8i3.22179

Abstract

The preparation of allometric equations generally uses multiple linear regression equations. The use of this regression equation is usually not carried out through various tests but goes directly to the t test and F test stages. Therefore, this paper aims to provide an example of determining the regression equation through the classical assumption test stages. Makila (Litsea angulata BI) was chosen as an example because it provides environmental services, especially in dealing with climate change and has not been widely studied. The research method used is a quantitative method. Destructive sampling was taken and the material used consisted of 40 young Makila plants planted in polybags next to the greenhouse at the Faculty of Agriculture, Pattimura University, Ambon. The diameter of each sample was measured from the ground surface to a height of 5 cm and numbered 1 to 40. After being coded, the plant samples were cut down and all young trees were divided into stem segments, branches, twigs, leaves and roots. The root segments were collected carefully to facilitate their separation from the soil in polybags. The parts of the roots that still contain soil are cleaned with a machete and brush until they are free of soil and other dirt. Next, each segment was weighed for its wet weight (in g) and dry weight, thus enabling the determination of the biomass content (in g) for each segment. Data analysis was carried out using the Multiple Linear Regression Equation method. The regression model was examined for normality and suitability in predicting independent variables, ensuring there were no issues with multicollinearity, heteroscedasticity, and autocorrelation. The results of the normality test showed that the significance value for the remaining data was 0.813 > 0.05, indicating normal distribution. TThe results of the multicollinearity test show that there is no multicollinearity problem, this is indicated by the VIF value of the two independent variables (tree diameter and tree height each 1.049) < 10 and the Tolerance value (tree diameter and tree height 0.953 each) > 0.100. The results of the heteroscedasticity test show that the two independent variables have a significance value of more than 0.05. The results of the autocorrelation test show the Durbin Watson (DW) value = 1.956 with a range of 1.65 – 2.35 which means there is no correlation problem. The results yielded a multiple linear regression: Y = -1131.146 + 684.799X1 + 4.276X2, where Y is biomass, X1 is the diameter, and X2 is the tree height. Based on the results of the t-test: variable X1 partially affected Y while variable X2 partially had no effect on Y. The F-test indicated that variables X1 and X2 jointly affected Y with R Square: 0.919 or 91.9% and the rest was influenced by other unexplored factors. To simplify biomass prediction and field measurement, a regression equation that used only 1 independent variable, namely tree diameter, was used for the experiment. Allometric equation only used 1 variable, Y = - 1,084,626 + 675,090 X1, where X1 = tree diameter, Y = Total biomass with R = 0.957, and R square = 0.915. The regression equation for young Makila plant provides assurance that the regression equation obtained is accurate in estimation, unbiased and consistent. This is because in data processing classical assumptions have been tested. This equation can save time, costs and energy, as well as make measurements easier in the field so that future researchers can develop allometric equations in other plants for efficiency. 
Price Model with Generalized Wiener Process for Life Insurance Company Portfolio Optimization using Mean Absolute Deviation Putra, Hilman Yusupi Dwi; Silalahi, Bib Paruhum; Budiarti, Retno
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.v8i4.23093

Abstract

The Financial Services Authority (OJK) has issued Regulation of the Financial Services Authority of the Republic of Indonesia Number 5 Year 2023. Article 11 paragraph 1d explains the limitations of assets allowed in the form of investment, investment in the form of shares listed on the stock exchange for each issuer is a maximum of 10% of the total investment and a maximum of 40% of the total investment. The investment manager of a life insurance company needs to adjust its investment portfolio. In 1991, Konno and Yamazaki proposed an approach to the portfolio selection problem with Mean Absolute Deviation (MAD) model. This model can be solved using linear programming, effectively solving high-dimensional portfolio optimization problems. Another problem in stock portfolio formation is that the ever-changing financial markets demand the development of models to understand and forecast stock price behavior. One method that has been widely used to model stock price movements is the generalized Wiener Process. The generalized Wiener process provides a framework that can accommodate the stochastic nature of stock price changes, thus allowing portfolio managers to be more sensitive to unanticipated market fluctuations. The stock price change model using the Generalized Wiener Process is very good at predicting stock price changes. The results of this stock price prediction can then be used to find the optimal portfolio using the MAD model. The portfolio optimization problem with the MAD model can be solved using linear programming to obtain the optimal stock portfolio for life insurance companies. 
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.
Control Chart for Correcting the ARIMA Time Series Model of GDP Growth Cases Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul; Utami, Dewi Setyo; Umairah, Tarisa; Arini, Nani Fitria
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.v8i1.19612

Abstract

The essential prerequisite for attending the G20 conference is a country's GDP because G20 members can significantly boost the economy and preserve the nation's financial stability. Time series data can be thought of as a country's Gross Domestic Product (GDP) at a particular point in time. In this research, the GDP numbers from five Southeast Asian nations that are attending the G20 fulfilling are used. The total was 47 observations made yearly, which extended from 1975 to 2001. A time series analysis was performed on the data gathered. The correctness of time series models is also evaluated using control charts based on this research. The control chart is constructed using the time series model's residuals as observations. After applying the IMR control chart for verification, the results revealed that the residuals, specifically the models for GDP in Malaysia, Singapore, and Thailand, are out of control. The white noise assumption is fulfilled by the time series model obtained for Brunei and Indonesia's GDP, but the residuals are out of control. Whether controlled residuals are used depends on the accuracy with which the time series model predicts the future. If the amount of residuals is under control, then the time series model produced is accurate and good enough for prediction. After using the IMR control chart to verify the residuals, the results indicate that the residuals, namely the models for GDP in Malaysia, Singapore, and Thailand, are not under control. The assumption of white noise is proved correct by the time series model obtained for the GDP of Brunei Darussalam and Indonesia. With that being said, the residuals are entirely out of control. The model must improve its ability to forecast various future periods. It is a consequence of the unmanageable residuals that the model contains. Even if the best available model has been obtained based on the criteria that have been defined, it is anticipated that the research findings will improve the theories that have previously been developed and raise knowledge regarding the usefulness of testing the time series model. In addition to all of that, it is intended that the research will produce a summary of cases of an increase in GDP from five Southeast Asian countries participating in the G20 conference. 
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. 
Nonlinear Principal Component Analysis with Mixed Data Formative Indicator Models in Path Analysis Hardianti, Rindu; Solimun, Solimun; Nurjannah, Nurjannah; Hamdan, Rosita
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.v8i1.17559

Abstract

This research aims to obtain the main component score of the latent variable ability to pay, determine the strongest indicators forming the ability to pay on a mixed scale based on predetermined indicators, and model the ability to pay on time as mediated by fear of paying using path analysis. The data used is secondary data obtained through distributing questionnaires with a mixed data scale. The sampling technique used in the research was purposive sampling. The number of samples used in the research was 100 customers. The method used is nonlinear principal component analysis with path analysis modeling. The results of this research show that of the five indicators formed by the Principal Component, 74.8% of diversity or information is able to be stored, while 25.20% of diversity or other information is not stored (wasted). Credit term is the strongest indicator that forms the ability to pay variable. The variable ability to pay mortgage has a significant effect on payments by mediating the fear of being late in paying with a coefficient of determination of 73.63%. 
Application of the Fractal Geometry in Development Surya Majapahit Batik Motif Juhari, Juhari; Pratiwi, Alfrista Anggraini
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.v8i3.22811

Abstract

The Mandelbrot and Julia sets are generated through iterative mathematical functions applied to points in the complex plane. These operations enable the detailed and intricate patterns characteristic of these fractals, allowing for modifications and zooming to explore different regions of the sets. TThe Mojokerto Surya Majapahit batik motif is a motif that has eight corners. One way to develop a Mojokerto batik motif that is similar to Surya Majapahit is by applying the science of fractal geometry. Fractal geometry studies a fractal pattern that can change shape according to input parameters and the number of iterations carried out. This research was conducted to determine the application of Mandelbrot and Julia’s fractal geometry using geometric transformations to obtain batik motif variants that is similar to Surya Majapahit. There are three steps in forming this motif variant. First, generating Mandelbrot fractals and Julia fractals. Second, the patterns generated by Mandelbrot and Julia are applied using geometric transformations. The geometric transformations that will be used are rotation, dilation, and translation. Finally, these patterns will be modified by combining patterns implementing logic operations using Python computer applications. The results of this research obtained four variants of batik motif that is similar to Surya Majapahit. The difference in each variant lies in the order of transformation. Variant 1 and variant 3 can be carried out by changing the sequence of geometric transformations, namely rotation, translation and dilationVariant 1 is obtained by applying rotation, dilation, and translation to the Mandelbrot and Julia pattern. Variant 2 is obtained with the Mandelbrot pattern applying rotation, dilation with two different scales, and translation, while the Julia pattern only applied rotation and translation. Variant 3 is obtained by applying rotation, dilation and translation to the Mandelbrot and Julia pattern. Variant 4 is obtained with the Mandelbrot pattern applied by rotation, dilation with three different scales, and translation, while the Julia pattern was applied only by rotation and translation. Meanwhile variants 2 and 4 apply different rotations, dilation scales, namely 0.451 and 0.318, and translation to the Mandelbrot pattern.
The Application of Frieze Groups and Crystallographic Groups in Generating Batak Toba Ornament Motifs Using a Matlab Graphical User Interface Sinaga, Marlina; Kartika, Dinda
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.v8i1.17130

Abstract

Gorga is a carving or sculpture typically found on the exterior of a Toba Batak traditional house. The Batak people use fractal (geometric) dimensions in Batak gorga carvings. In mathematics, repetitive and symmetrical patterns in planes that result from transformations are included in the plane symmetry groups. Ethnomathematics is a cultural approach to the concept of mathematics. A frieze group can be defined as a symmetrical group which arises from a unidirectional translation and subsequently generates a linear pattern that recurs exclusively in a single direction. There are seven different pattern types in the frieze groups. Meanwhile, crystallographic patterns are flat two-dimensional patterns that form a lattice. There are 17 crystallographic types of patterns with five different types of unit lattices. The purpose of this study is to generate motifs for Batak ornaments based on frieze groups and crystallographic groups using a Matlab Graphical User Interface (GUI). A total of 119 new motifs were generated based on seven types of patterns in the frieze groups, namely, F1,F2,F3,F4,F5,F6, and F7. Meanwhile, in the crystallographic groups, 153 new motifs were generated based on nine types of patterns, namely, p1,p2,pm,pg,cm,pmg,pmm,cmm, and pgg. To keep with trends, the new motifs generated can be used in everyday life as decorations or business symbols that are characteristic of the Toba Batak region.

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