JTAM (Jurnal Teori dan Aplikasi Matematika)
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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540 Documents
<![CDATA[Characteristic Polynomial and Eigenproblem of Triangular Matrix over Interval Min-Plus Algebra ]]>
<![CDATA[Rahmawati, Anita Dwi]]>;
<![CDATA[Siswanto, Siswanto]]>;
<![CDATA[Wibowo, Supriyadi]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i3.22305
<![CDATA[A min-plus algebra is a linear algebra over the semiring R_ε', equipped with the operations “"⊕'=min" ” and “⊗=+”. In min-plus algebra, there is the concept of characteristic polynomial obtained from permanent of matrix. Min-plus algebra can be extended to an interval min-plus algebra, which is a set 〖 I(R)〗_ε' equipped with the operations ¯("⊕'" ) and ¯("⊗" ). Matrix over interval min-plus algebra has some special forms, one of which is a triangular matrix. The concept of characteristic polynomial and eigenproblem can be applied to a triangular matrix. There is a more concise formula for solving the eigenproblem of triangular matrix because this matrix is a special form of matrix. This research will discuss the characteristic polynomial and solving eigenproblem of triangular matrix over interval min-plus algebra using its characteristic polynomials. The research method used is a literature study. From the research results, the permanent formula and characteristic polynomial formula of the triangular matrix are obtained. It is also obtained that the smallest corner of the characteristic polynomial is the principal eigenvalue and the vector eigen corresponding to the principal eigenvalue can be obtained through the matrix A_λ. For readers who are interested in this topic, can research about characteristic polynomial and eigenproblem of matrices with other special forms over min-plus interval algebra.]]>
<![CDATA[Robust Optimization of Vaccine Distribution Problem with Demand Uncertainty ]]>
<![CDATA[Fikri, Faiqul]]>;
<![CDATA[Silalahi, Bib Paruhum]]>;
<![CDATA[Jaharuddin, Jaharuddin]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i2.20035
<![CDATA[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.]]>
<![CDATA[Digital Media Innovation Based on Multimedia Cognitive and Constructivist Theory in a Cultural Context: Encouraging Students' Higher Order Thinking Skills ]]>
<![CDATA[Siregar, Budi Halomoan]]>;
<![CDATA[Panjaitan, Asmin]]>;
<![CDATA[Hasratuddin, Hasratuddin]]>;
<![CDATA[Kairuddin, Kairuddin]]>;
<![CDATA[Mulyono, Mulyono]]>;
<![CDATA[Rahman, Arief Aulia]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i1.16800
<![CDATA[The high-order thinking skills of students in Indonesia are classified as low, this is in line with the results of diagnostic tests conducted in class IX junior high school. Thus, it is necessary to develop digital media based on multimedia and constructivist cognitive theory with cultural context as one of the alternative solution. This study aims to (1) develop digital learning media based on constructivist and cognitive multimedia theories with a cultural context that fulfills the categories of validity, practicality and effectiveness; and (2) improve students' high-order thinking skills after using these media in the learning process. The research subjects were 30 students in class IX junior high school and the research objects were digital learning media based on constructivist theory and cognitive multimedia with a cultural context to improve students' high-level thinking skills on the topic of dilation. This is a research design with the Plomp model, which consists of (1) Preliminary research; (2) Prototyping phase; and (3) Assessment phase. The research instruments used were interviews, questionnaires and tests. The results showed that the product developed was included in the very valid, very practical, and effective category, where: (a) classical learning completeness reached 97%; (b) positive response by product users reached 97%; and (c) the N-Gain value was 0.791 in the very high category. Thus, it can be stated that the product meets the quality standard criteria, where the product can be used to improve students' high-level thinking abilities. ]]>
<![CDATA[Development of Mathematical Maturity through the Amalgamation of Computational Thinking and Technology-Enhanced Learning ]]>
<![CDATA[Prabawa, Harsa Wara]]>;
<![CDATA[Rosjanuardi, Rizky]]>;
<![CDATA[Nurlaelah, Elah]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i3.23766
<![CDATA[Advancements in technology and global information infrastructure have transformed education, leveraging a constructivist approach that enhances knowledge construction through student interaction with computer applications. The research aimed to explore the facilitation of enhancing mathematical maturity through the integration of technology in mathematics education using computational thinking. This research employed a qualitative method with a case study approach. The participants in this study were 15 Grade XI students from various classes of the Vocational High School, selected from a total of 159 students. The data collection techniques used in this research included observation and open-ended test instruments. The data analysis techniques involved data reduction, data presentation, and conclusion drawing. The research results show: (1) technology enhances mathematics education; (2) computers deepen mathematical understanding; (3) technology creates contextual learning environments for problem-solving; (4) combining computational thinking and technology aids in mastering mathematical concepts. The conclusion is that integrating computational thinking with technology-enhanced learning significantly fosters mathematical maturity among students.]]>
<![CDATA[Implementation of Inquiry Learning Model in Collaboration with PBL to Improve Student Understanding in Number Theory Course ]]>
<![CDATA[Tristanti, Lia Budi]]>;
<![CDATA[Nusantara, Toto]]>;
<![CDATA[Maf’ulah, Syarifatul]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i1.17421
<![CDATA[The purpose of this study was to describe the presence or absence of the influence of the infusion learning model collaboration with Problem-Based Learning (PBL) to develop students' understanding of proof and mathematical argumentation in number theory courses. This research is an experimental study with a randomized control group pretest-posttest design, two groups namely the experimental group and the control group. The experimental group is the group that uses the infusion learning model in collaboration with PBL, while the control group is the group that uses conventional learning. The subjects of this study consisted of 40 students at a university in Jombang, Indonesia. Data collection techniques through observation sheets, proof understanding tests and observation sheets of students' mathematical argumentation abilities. The results of the research show that the significant difference between the average proof of understanding of students in the experimental group and the control group. The difference between the average proof of understanding in the experimental group and the average proof of understanding of students in the control group was 21.75. Furthermore, the significant difference between the average argumentation ability of students in the experimental group and the control group. The difference between the average argumentation ability of students in the experimental group and the average argumentation ability of students in the control group is 5.25. Therefore, the implementasion of infusion learning in collaboration with PBL is more effective than conventional learning models for developing students' ability to understand mathematical proof and argumentation. This learning model promotes the development of critical thinking skills, problem-solving, conceptual and different understanding needed to construct a formal proof, and strong and valid arguments.]]>
<![CDATA[Equating by Using Circle Equation Approach: Applied Mathematics Formula for Prevent Discrimination ]]>
<![CDATA[Iriyadi, Deni]]>;
<![CDATA[Rustam, Ahmad]]>;
<![CDATA[Hartati, Hevriana]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i3.22195
<![CDATA[This study aims to determine the accuracy of the equating method that uses a circle equation approach in terms of its circular arc (Simplified Circle Arc). This research uses 2015 National Examination data from two questions packages. Using the number of preliminary samples as many as 2135 on the X and 2271 test devices on the Y test. After doing a Rasch analysis using a Mean Square Outfit (MNSQ), the data was acquired and analyzed. Following this, replication was performed up to a maximum of 50 times for each kind of data distribution. For each replication, up to a maximum of 50 respondents were selected from the original data set to be used as data for score equalization. The Root Mean Square Error (RMSE) statistic is then used to analyze the outcomes of the equating score. The results showed that the average RMSE group that has the same distribution will provide a lower RMSE value compared to groups that have different data distributions. The low average RMSE value indicates the accuracy of the equal of the scores performed. Thus, the use of the SCA method is highly recommended to equalize scores, especially in small samples in classes at school to prevent discrimination in grading.]]>
<![CDATA[The Application of Truncated Spline Semiparametric Path Analysis on Determining Factors Influencing Cashless Society Development ]]>
<![CDATA[Pramaningrum, Dea Saraswati]]>;
<![CDATA[Fernandes, Adji Achmad Rinaldo]]>;
<![CDATA[Iriany, Atiek]]>;
<![CDATA[Solimun, Solimun]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i2.19913
<![CDATA[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.]]>
<![CDATA[Fuzzy Logic Speed Regulator for D.C. Motor Tuning ]]>
<![CDATA[Raza, Wasim]]>;
<![CDATA[Adzikya, Dieky]]>;
<![CDATA[Mehmood, Saba]]>;
<![CDATA[Wasti, Syeda Rabbia]]>;
<![CDATA[Hussain, Muhammad Jafar]]>;
<![CDATA[Ahmad, Aftab]]>;
<![CDATA[Usman, Muhammad Talha]]>;
<![CDATA[Raza, Sajid]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i1.16919
<![CDATA[A D.C. motor's rotational speed is regulated in this study using a PID controller and a fuzzy logic controller. In contrast to the fuzzy logic controller, which uses rules based on knowledge and experience, the proportional-integral-derivative (PID) controller requires a mathematical system model. This study investigates the regulation of a DC motor's velocity using PID and fuzzy logic controllers. The PID controller utilizes a mathematical model and parameter tuning by trial and error. Still, the fuzzy logic controller (FLC) operates on rule-based knowledge, enabling it to handle the nonlinear features of the DC motor effectively. The FLC design entails intricate determinations, including the establishment of a rule base and the process of fuzzification. A total of 49 fuzzy rules have been devised to achieve precise control. Based on MATLAB/SIMULINK simulations, the study concludes that the Fuzzy Logic Controller (FLC) beats the Proportional-Integral-Derivative (PID) controller. The FLC exhibits superior transient and steady-state responses, shorter response times, reduced steady-state errors, and higher precision. This study emphasizes the efficacy of the FLC (Fuzzy Logic Controller) in dealing with the difficulties associated with DC motor control. It presents a strong argument for the suitability and efficiency of FLCs in industrial environments compared to conventional PID (Proportional-Integral-Derivative) controllers. There are a wide variety of ways to construct a fuzzy logic controller. The speed error and the rate of change in the speed error are two inputs to the FLC. Defuzzification is done by focusing on the core of the problem. The results show that FLC is superior to PID controllers in efficiency and effectiveness due to its reduced transient and steady-state factors.]]>
<![CDATA[Dual Optimization of Weighted Fuzzy Time-Series Forecasting: Particle Swarm Optimization and Lagrange Quadratic Programming ]]>
<![CDATA[Zamelina, Armando Jacquis Federal]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Fitriani, Rahma]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i3.22554
<![CDATA[Time series Forecasting is one of crucial techniques that helps with strategic decision-making and mitigating potential risks –One of which is Weighted fuzzy time series (WFTS). Moreover, the interval length of the WFTS plays a crucial role in its modelization and accuracy in predicting future values. Therefore, this research implements a dual optimization on WFTS, which are (1) Particle Swarm Optimization to find the optimum interval length of the WFTS and (2) a Lagrange quadratic to optimize the weight of the fuzzy interval. In this research, a univariate Average Air Temperature located in Malang is used to perform forecasting model. The dataset is taken from BMKG-Indonesia. This research aims to acquire an optimized interval length on fuzzy time series forecasting, i.e., improving its accuracy by finding the optimal interval length. Based on the result, the proposed dual optimization model outperforms the classical WFTS on forecasting. The proposed model excels based on the evaluation matrix values. It has been noticed also that implementing PSO to find the optimum interval length has improved the accuracy of the classical WFTS. The classical WFTS has MAPE and RMSE of 2.4 and 0.73, respectively, while the proposed dual optimized model has 1.01 and 0.3. This approach identifies the best interval values and provides optimum weights related to each data point, providing solid insights for air temperature forecasting. ]]>
<![CDATA[Structural Equation Modeling Semiparametric in Modeling the Accuracy of Payment Time for Customers of Credit Bank in Indonesia ]]>
<![CDATA[Junainto, Fachira Haneinanda]]>;
<![CDATA[Fernandes, Adji Achmad Rinaldo]]>;
<![CDATA[Solimun, Solimun]]>;
<![CDATA[Hamdan, Rosita Binti]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i4.23668
<![CDATA[Credit risk assessment is crucial for financial institutions to ensure loan repayment. To enhance the prediction accuracy of creditworthiness and timely repayment, this research employs semiparametric structural equation modeling (SEM) to analyze the factors influencing credit repayment timeliness. The research was conducted to apply semiparametric SEM modeling to the timeliness of paying credit. Semiparametric SEM is structural modeling in which two combined approaches of parametric and nonparametric approaches are used. The analysis method in this research is semiparametric SEM with a nonparametric approach using a truncated spline. Truncated splines are chosen for their flexibility, ability to model complex relationships, continuity, interpretability, and strong performance in nonparametric regression tasks. The data in the study were obtained through questionnaires distributed to Bank X mortgage debtors and are confidential. The quetionnairs in the Likert scale, with five options. The study used 3 variables consisting of one exogenous variable, one intervening endogenous variable, and one endogenous variable. The results showed that: (1) the effect of capacity and willingness to pay variables on timeliness of payment is significant; (2) modeling the capacity variable on willingness to pay also produces a significant estimate; (3) the effect of the capacity variable on the timeliness of payment variable is not influenced by the willingness to pay variable as an intervening variable; and (4) the R^2 value of 0.763 or 76.33% indicates that the model has good predictive relevance. To continue to develop punctuality of paying credit, banks need to pay attention to the financial stability of consumers. Besides the financial stability, banks should pay attention to the sense of responsibility that customers have.]]>
