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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.
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Articles 25 Documents
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Search results for , issue "Vol 7, No 3 (2023): July" : 25 Documents clear
Analysis Dynamics Two Prey of a Predator-Prey Model with Crowley–Martin Response Function Rian Ade Pratama; Syamsuddin Toaha
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.v7i3.14506

Abstract

The predator-prey model has been extensively developed in recent research. This research is an applied literature study with a proposed dynamics model using the Crowley–Martin response function, namely the development of the Beddington-DeAngelis response function. The aim of this research is to construct a mathematical model of the predator-prey model, equilibrium analysis and population trajectories analysis. The results showed that the predator-prey model produced seven non-negative equilibrium points, but only one equilibrium point was tested for stability. Stability analysis produces negative eigenvalues indicating fulfillment of the Routh-Hurwitz criteria so that the equilibrium point is locally asymtotically stable. Analysis of the stability of the equilibrium point indicates stable population growth over a long period of time. Numerical simulation is also given to see the trajectories of the population growth movement. The population growth of first prey and second prey is not much different, significant growth occurs at the beginning of the growth period, while after reaching the peak the trajectory growth slopes towards a stable point. Different growth is shown by the predator population, which grows linearly with time. The growth of predators is very significant because predators have the freedom to eat resources. Various types of trajectory patterns in ecological parameters show good results for population growth with the given assumptions.
The Ideal Over Semiring of the Non-Negative Integer Aisyah Nur Adillah; Fitriana Hasnani; Meryta Febrilian Fatimah; Nikken Prima Puspita
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.v7i3.14997

Abstract

Assumed that (S,+,.) is a semiring. Semiring is a algebra structure as a generalization of a ring. A set I⊆S is called an ideal over semiring S if for any α,β∈I, we have α-β∈I and sα=αs∈I for every s in semiring S.  Based on this definition, there is a special condition namely prime ideal P, when for any αβ∈P, then we could prove that α or β are elements of ideal P. Furthermore, an ideal I of S is irreducible if Ia is an intersection ideal from any ideal A and B on S, then I=A or I=B. We also know the strongly notion of the irreducible concept. The ideal I of S is a strongly irreducible ideal when I is a subset of the intersection of A and B (ideal of S), then I is a subset of A, or I is a subset of B. In this paper, we discussed the characteristics of the semiring of the non-negative integer set. We showed that pZ^+ is an ideal of semiring of the non-negative integer Z^+ over addition and multiplication. We find a characteristic that 〖pZ〗^+  is a prime ideal and also a strongly irreducible ideal of the semiring Z^+ with p is a prime number.
Differences in Students' Algebraic Thinking in Online and Offline Learning Abdillah Abdillah; Ajeng Gelora Mastuti; Kasliyanto Kasliyanto; Rasna Buamona
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.v7i3.13916

Abstract

Mathematics teachers still have to create their creativity in online and offline learning. Therefore, mathematics teachers must pay attention to the assignments given to their students. One of the higher-order thinking skills that teachers must consider is algebraic thinking. This study aims to describe students' algebraic thinking as impact of online and offline learning. Researchers want to see the difference in algebraic thinking between students who are given online mathematics learning and students who are given offline mathematics learning. This study uses a qualitative research approach. Participants in this study consisted of 30 students taken from 2 junior high schools taken in the city of Ambon. The research procedure carried out in this research process is the stage of giving questions and thinking hard, as well as the interview stage. The interview guide was made based on indicators of algebraic thinking (Herbert & Brown, 1997). The results showed that the algebraic thinking skills of students who were subjects of online learning were said to be incomplete because they experienced construction holes at the stage of looking for patterns and generalizations. In contrast, students who were subjects of offline learning had complete algebraic thinking according to the algebraic thinking process.
Modelling Dependencies of Stock Indices During Covid-19 Pandemic by Extreme-Value Copula Retno Budiarti; Kumala Intansari; I Gusti Putu Purnaba; Fendy Septyanto
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.v7i3.15109

Abstract

Quantifying dependence among variables is the core of all modelling efforts in financial models. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. The COVID-19 pandemic is an extreme event that has caused the collapse of various economic activities which resulted in the decline of stock prices. The modelling of extreme events is therefore important to mitigate huge financial losses. Extreme-value copula can be suitable to quantify dependencies among assets under an extreme event. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data. This model was applied in the portfolio of the IDX Composite Index (IHSG), Straits Times Index (STI) and Kuala Lumpur Stock Exchange (KLSE). Each individual asset return is modelled by the ARMA-GARCH and the joint distribution is modelled using extreme value copulas. This empirical study showed that Gumbel copula is the most appropriate extreme value copulas for the three indices. The results of this study are expected to be used as a basis for investors in the formation of a portfolio consisting of 2 financial assets and a portfolio consisting of 3 financial assets. 
Mathematical Reasoning Ability of Male and Female Students in Problem Base Learning Habibi Ratu Perwira Negara
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.v7i3.15023

Abstract

Considering the objectives and standards of the mathematics learning process, mathematical reasoning is an ability that students are expected to have. Nonetheless, the mathematical reasoning abilities of Indonesian students are still inadequate, and learning resources are still inadequate. The researcher then tries to solve it by combining the problem-based learning (PBL) paradigm with the use of GeoGebra in the classroom. The aim of this research is to identify and analyze the effect of GeoGebra and Gender-assisted problem-based learning (PBL) models on students' mathematical reasoning abilities. The study involved 35 students of XI State Senior High School at one of the schools in Mataram City. The research instrument used a mathematical reasoning ability test consisting of five essay questions. The study applied a one-group pretest-posttest design to observe the increase in students' mathematical reasoning abilities. Mathematical reasoning ability tests were given before and after the implementation of the GeoGebra-assisted PBL model. Data analysis used descriptive statistics, paired t-tests, and independent t-tests. The results of the analysis show that improving students' mathematical reasoning abilities can be done by applying the GeoGebra-assisted PBL model in the classroom. Observation of the psychological aspects of Gender showed significant results in students' mathematical reasoning abilities.
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 Dillah Rismawati; I Wayan Mangku; Hadi Sumarno
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; Dodi Devianto; Ferra Yanuar
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.

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