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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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Development of ACERA Learning Model Based on Proof Construction Analysis Deni Hamdani; Cholis Sa’dijah; Subanji Subanji; Sri Subarinah
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.12354

Abstract

Proof constructing is the process of justifying a claim using the methods and concepts of proof to produce mathematical proof. Proof constructing is also an aspect of proof, and is often the only way to assess student performance. However, proof construction is still a constant problem (difficulty) for every student. The cause of this difficulty is not only because of the content of proof in textbooks/sources, over-reliance on examples, understanding, underlying logic, and the ability to use proof writing strategies, but also due to the lack of proof discussion activities that train students to understand and answer proof practice questions, give proof reasoning against the proof that has been constructed, and validating own and other colleagues' answers. Thus, this study aims to develop a valid and practical ACERA (Activities, Classroom Discussion, Exercises, Reason, and Audience) learning model and has a potential effect on students' ability to proof construction. This study uses research design research development methods in three stages, namely the preliminary stage, the model development stage and the assessment stage. The research subjects were 23 students of the Mathematics Education study program at the University of Mataram. The development of the ACERA model offers an alternative solution to reduce the difficulty of proof construction, thus enabling this model to have characteristics that are valid, practical and have a potential effect in increasing the productivity of student proof construction.
Solution Formula of Korteweg Type by Using Partial Fourier Transform Methods in Half-Space without Surface Tension Yiyi Fikri Nurizki; Sri Maryani; Bambang Hendriya Guswanto
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14721

Abstract

Sharp-interface models and diffuse-interface models are the two basic types of models that describe liquid-vapour flow for compressible fluids. Their depictions of the line dividing liquid from vapour are different. The interface is modeled as a hypersurface in sharp-interface models. Sharp-interface models are free-boundary problems from a mathematical perspective since the position of the interface is a priori unknown and therefore a component of the solution to the free-boundary problem. A unique system of partial differential equations describes the motion of the fluid in the liquid and vapour phases, respectively. At the interface, boundary conditions between these systems are connected.. A mathematical model for liquid-vapour flows including phase transition known as the Navier-Stokes-Korteweg system which is the extension of the compressible Navier-Stokes equations. The purpose of Ihis article, we consider the soluton formula of Korteweg fluid model in half-space without surface tension. Since we consider in half-space case, Partial Fourier transform become appropriate method to find the formula of velocity and density for Korteweg type. The solution formula of the model problem for the velocity (u) and the (φ) are obtained by using the invers of partial Fourier transform. It consist multipliers. For the future research, we can investigate the estimation of the multiplier. Furthermore, by using Weis’s multiplier theorem we can find not only maximal Lp-Lq regularity class, but also we can consider the local well-posedness of the model problem. 
M/M/1 Non-preemptive Priority Queuing System with Multiple Vacations and Vacation Interruptions Rismawati, Dillah; Mangku, I Wayan; Sumarno, Hadi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14910

Abstract

Non-preemptive priority queue system is a type of priority queue where customers with higher priorities cannot interrupt low priority one while being served. High priority consumers will still be at the head of the queue. This article discusses the non-preemptive priority queue system with multiple working vacations, where the vacation can be interrupted. Customers are classified into two classes, namely class I (non-preemptive priority customers) and class II, with exponentially distributed service rates. Customers will still receive services at a slower rate than during normal busy periods when they enter the system while it is on vacation. Suppose other customers are waiting in the queue after completing service on vacation. In that case, the vacation will be interrupted, and the service rate will switch to the busy period service rate. The model's performance measurements are obtained using the complementary variable method and analyzing the state change equation following the birth and death processes to find probability generating function for both classes. The results of the numerical solution show that the expected value number of customers and waiting time of customers in the queue for both class customers will be reduced when the vacation times rate (θ) and the vacation service rate (μ_0 ) increase.
The Solution of Generalization of the First and Second Kind of Abel’s Integral Equation Muhammad Taufik Abdillah; Berlian Setiawaty; Sugi Guritman
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14193

Abstract

Integral equations are equations in which the unknown function is found to be inside the integral sign. N. H. Abel used the integral equation to analyze the relationship between kinetic energy and potential energy in a falling object, expressed by two integral equations. This integral equation is called Abel's integral equation. Furthermore, these equations are developed to produce generalizations and further generalizations for each equation. This study aims to explain generalizations of the first and second kind of Abel’s integral equations, and to find solution for each equation. The method used to determine the solution of the equation is an analytical method, which includes Laplace transform, fractional calculus, and manipulation of equation. When the analytical approach cannot solve the equation, the solution will be determined by a numerical method, namely successive approximations. The results showed that the generalization of the first kind of Abel’s integral equation solution can be determined using the Laplace transform method, fractional calculus, and manipulation of equation. On the other hand, the generalization of the second kind of Abel’s integral equation solution is obtained from the Laplace transform method. Further generalization of the first kind of Abel’s integral equation solution can be obtained using manipulation of equation method. Further generalization of the second kind of Abel’s integral equation solution cannot be determined by analytical method, so a numerical method (successive approximations) is used. 
Generalized Linear Models in Determining Factors Affecting the Number of Community Visits to Health Service with Bayesian Inference Approach Selfinia, Selfinia; Devianto, Dodi; Yanuar, Ferra
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.15186

Abstract

Public health plays an important role in achieving the Sustainable Development Goals (SDGs) set by the United Nations. The SDGs are a series of global targets and commitments aimed at addressing various challenges facing the world today, such as poverty, hunger, gender inequality, climate change, and others. Public health, as one of the important aspects of the SDGs, is closely linked to several sustainable development goals. Efforts made to achieve the SDGs in the health sector are to improve health services. The objective of this study was to identify factors that influence the number of community visits to health services. The data used is a small sample size as one hundred community respondents in Padang City, West Sumatra Province. In this study, the number of respondents' visits to health service was the measured variable, while the predictor variables consisted of five variables, namely the status of the implementation of clean and healthy living behavior, health history, distance to health services, type of insurance owned, and consumption patterns. The generalized linear models is used to identify predictor variables that have significance using the Bayesian inference approach. It was found that there are two predictor variables that are significant in influencing the number of community visits to health services, namely the consumption patterns of respondents and the health history of respondents. These two variables have a very dominant effect on the number of visits to health service facilities in Padang City. This result indicates the community has to pay attention to their consumption patterns and living behavior to prevent periodic disease outbreaks and take care of their health history factors.
Topological Indices of the Relative Coprime Graph of the Dihedral Group Syarifudin, Abdul Gazir; Santi, Laila Maya; Faradiyah, Andi Rafiqa; Wijaya, Verrel Rievaldo; Suwastika, Erma
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14913

Abstract

Assuming that G is a finite group and H is a subgroup of G, the graph known as the relative coprime graph of G with respect to H (denoted as Γ_(G,H)) has vertices corresponding to elements of G. Two distinct vertices x and y are adjacent by an edge if and only if (|x|,|y|)=1 and x or y belongs to H. This paper will focus on  finding the general formula for some topological indices of the relative coprime graph of a dihedral group. The study of topological indices in graph theory offers valuable insights into the structural properties of graphs. This study is conducted by reviewing many past literatures and then from there we infer a new result. The obtained outcomes will include measurements of distance, degree of vertex, and various topological indices such as the first Zagreb index, second Zagreb index, Wiener index, and Harary index that are associated with distance and degree of vertex.
Students’ Visual Reasoning Ability in Solving Quadratic Function in Terms of Learning Style Masduki, Masduki; Savitri, Dhea; Khotimah, Rita Pramujiyanti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.13547

Abstract

Visual reasoning plays an important role in problem-solving and the success of the student’s learning mathematics. This study aims to reveal the students’ visual reasoning ability in solving quadratic function problems in terms of activist, reflector, and pragmatic learning styles. This research used a qualitative approach with a case study were 30 9th-Grade students at one of the public junior high schools in Karanganyar District, Central Java, Indonesia. The Learning Style Questionnaire (LSQ) from Honey and Mumford was used to categorize the students’ learning style. In each category, the researcher selected two students purposively to be interviewed. The researchers used two quadratic equation problems to explore the students’ visual reasoning profile. Before being used, the questions were validated by two experts in mathematics education. The result showed that students with activist learning styles unable to demonstrate all indicators of visual reasoning. The students with pragmatics learning style can exhibit only one indicators of reasoning, namely interpretation. Then, students with reflector and theoretical learning style able to perform all indicators of visual reasoning. Thus, it can be concluded that the student’s learning style affect the visual reasoning ability in solving quadratic function.
Confidence Interval for Variance Function of a Compound Periodic Poisson Process with a Power Function Trend Irawan, Ade; Mangku, I Wayan; Budiarti, Retno
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14836

Abstract

This research is a follow-up research of Utama (2022) on asymptotic distribution of an estimator for variance function of a compound periodic Poisson with the power function trend. The objectives of this research are (i) to formulate a confidence interval for the variance function of a compound periodic Poisson process with a power function trend and (ii) to prove the convergence to 1-α probability of the parameter included in the confidence interval. This research process begins with a review of the existing formulation of the variance function estimator and its asymptotic distribution. Next, the confidence interval for the variance function of the compound periodic Poisson process with a power function trend is formulated and the convergence to 1-α is determined. After obtaining the confidence interval, the research continued by conducting computer simulations to confirmed the results obtained analytically. The results obtained show that the confidence interval for the variance function of a compound periodic Poisson process with a power function trend converges to 1-α both analytically and numerically for different finite time intervals.
RME Based Audiobook Development for Class IV Elementary School Students Sari, Arissona Dia Indah; Herman, Tatang; Sopandi, Wahyu; Jupri, Al
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.15074

Abstract

Learning mathematics at the Elementary School (SD) level is an important basis in building a good understanding of mathematical concepts in students. However, students often experience difficulties in understanding abstract and complex mathematical concepts. This can have an impact on reducing students' interest in learning mathematics. To overcome this problem, an audiobook based on RME (Realistic Mathematics Education) was developed which emphasizes the quality of sound recordings that are close to the experience of listening to voices directly, especially for mathematics materials at the elementary level. The research method used in this study is a research and development approach using the ADDIE model developed by Robert Maribe Branch. The ADDIE model is a development model consisting of five stages, namely analysis, design, development, implementation, and evaluation. The results of the study show that audiobooks based on RME are valid and can be implemented in learning. Based on these results, the RME-based audiobook is ready to be implemented on a large scale and used as an effective alternative learning media in increasing conceptual understanding and interest in learning mathematics for fourth grade elementary school students in multiplication material.
Biclustering Performance Evaluation of Cheng and Church Algorithm and Iterative Signature Algorithm Sumertajaya, I Made Sumertajaya; Ningsih, Wiwik Andriyani Lestari; Saefuddin, Asep; Rohaeti, Embay
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14778

Abstract

Biclustering has been widely applied in recent years. Various algorithms have been developed to perform biclustering applied to various cases. However, only a few studies have evaluated the performance of bicluster algorithms. Therefore, this study evaluates the performance of biclustering algorithms, namely the Cheng and Church algorithm (CC algorithm) and the Iterative Signature Algorithm (ISA). Evaluation of the performance of the biclustering algorithm is carried out in the form of a comparative study of biclustering results in terms of membership, characteristics, distribution of biclustering results, and performance evaluation. The performance evaluation uses two evaluation functions: the intra-bicluster and the inter-bicluster. The results show that, from an intra-bicluster evaluation perspective, the optimal bicluster group of the CC algorithm produces bicluster quality which tends to be better than the ISA. The biclustering results between the two algorithms in inter-bicluster evaluation produce a deficient level of similarity (20-31 percent). This is indicated by the differences in the results of regional membership and the characteristics of the identifying variables. The biclustering results of the CC algorithm tend to be homogeneous and have local characteristics. Meanwhile, the results of biclustering ISA tend to be heterogeneous and have global characteristics. In addition, the results of biclustering ISA are also robust.

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