Rangkiang Mathematics Journal

Bellman-Ford Algorithm for Shortest Path Selection

2025-02-01T09:55:21+00:00

Determining the shortest path from one point to another (destination) is a problem often encountered in life. With the development of science and technology, the problem of finding the shortest path can be solved using various algorithms. The algorithm that is often used to find the shortest route is the Bellman-Ford algorithm. The Bellman-Ford algorithm requires initial location parameters and a destination as input to determine the shortest path. The algorithm's results provide the shortest distance along with the route from the initial location to the destination. Applying the Bellman-Ford Algorithm provides the shortest distance as a solution to the problem. This research determines the shortest path from the origin to the destination point, modeled by a weighted graph. The Bellman-Ford algorithm starts the iteration by updating the distance at each vertex if a shorter distance is found.

Numerical Analysis of Hepatitis A Transmission Using the Susceptible-Infected-Treatment-Recovery (SITR) Model with Vaccination Using 14th-Order Runge-Kutta Method Runge Kutta Method

2025-03-16T02:37:52+00:00

Hepatitis A remains a serious health issue in Indonesia, particularly in areas with poor sanitation. Poor sanitation significantly contributes to the transmission of Hepatitis A, as the disease is commonly spread through contaminated water and food. Inadequate waste management, lack of clean water access, and poor hygiene practices increase the likelihood of outbreaks, especially in densely populated areas. This study aims to analyze the dynamics of Hepatitis A transmission using the SITR (Susceptible-Infected-Treatment-Recovered) model, incorporating vaccination and treatment interventions. The methodology involves mathematical model construction, stability analysis, and numerical simulation using MATLAB's 14th-order Runge-Kutta method. Simulation results indicate a decline in the susceptible population (S) from 80% to nearly 0% due to high transmission rates (beta = 0,4286-0,9) and vaccination effectiveness (sigma = 0,008-0,01). The infected population (I) decreases significantly through treatment interventions (eta = 0,1-0,3) and recovery rates (gamma = 0,0825-0,37), while the recovered population (R) dominates up to 95% by the end of the simulation. The combination of vaccination, expanded treatment access, and improved care quality effectively suppresses disease spread, even under high transmission conditions. This study recommends multidimensional interventions such as mass vaccination, sanitation education, and rapid medical response for controlling Hepatitis A outbreaks.

Comparison of Linear Regression and Polynomial Local Regression in Modeling Prevalence of Stunting

2025-04-14T08:18:53+00:00

Stunting is one of the main focuses of the government in Indonesia. This is because nutritional status is one of the benchmarks of community welfare. Stunting can be influenced by various societal aspects such as health, economy, social status, and education. One factor that is thought to be closely related to stunting is the level of education. Therefore, the prevalence of stunting and the level of education will be modeled; in this case, the mean years of schooling is used. Modeling uses two approaches: parametric through linear regression and nonparametric through local polynomial regression. This study compares both models to see which method better explains the stunting phenomenon. The comparison is made through the determination coefficient value or R², Root Mean Square Error or RMSE, and the fitted curve plot. The results of R² and RMSE for both models were obtained. The linear regression model has an R² of 32.94% and an RMSE of 4.84. Meanwhile, for the local polynomial model, it is R² 43.44% and RMSE 4.32. Based on these results, it can be concluded that local polynomial regression is better at modeling the relationship between the prevalence of stunting and mean years of schooling in Indonesia. This finding confirms that the polynomial local regression method can capture phenomena that occur for data that do not follow a particular pattern.

Artificial Neural Network Model for Forecasting Inflation Rate in Indonesia Using Backpropagation Algorithm in Indonesia

2025-03-21T02:28:27+00:00

Inflation is defined as a general and persistent rise in prices. Stable inflation is a prerequisite for sustainable Inflation, defined as a general and persistent rise in prices. Stable inflation is a prerequisite for sustainable economic growth. The importance of controlling inflation is based on the consideration that high and unstable inflation hurts the socio-economic conditions of the community. In this context, government and economic agents must know the future inflation rate. The backpropagation algorithm forecasting method can be a mathematical tool to forecast future inflation rates. The best forecasting model is obtained from applying the backpropagation algorithm, namely ANN BP (12,2,1), with a mean square error value of 0.15 and an absolute percentage error value of 11.09%. Based on these results, the back-propagation algorithm in artificial neural networks can accurately forecast the inflation rate. Thus, it is hoped that this research can be used in economic decision-making.

Evaluation of the Implementation of GeoGebra-assisted Advanced Calculus Courses Using the CIPP Model

2024-12-23T04:20:13+00:00

This study aims to evaluate the implementation of advanced calculus courses assisted by GeoGebra using the CIPP model. This evaluation assessed the relevance, effectiveness, and results of applying GeoGebra as an interactive learning medium. The research approach was descriptive quantitative, with data collection through questionnaires and observations. The research subjects were 36 students who attended advanced calculus courses at FMIPA Universitas Negeri Padang in the July–December 2024 semester. The evaluation results show that in the context aspect, the use of GeoGebra is aligned with the curriculum objectives that support the mastery of advanced mathematical concepts and visualization skills. Regarding input, lecturers have basic competence in using GeoGebra, but not all students are familiar with this software. In terms of process, GeoGebra-assisted learning is interactive, although it is constrained by students’ adaptation time to the software. In terms of product, the evaluation results showed increased students’ analytical skills and conceptual understanding, although the increase in exam results was not significant overall. The findings recommend the need for intensive training for lecturers and students related to the use of GeoGebra, the provision of technology-based learning guides, and adjustments to lecture strategies to maximize the effectiveness of GeoGebra in supporting advanced calculus lectures.

Analysis of the Implementation of Merdeka Curriculum in Mathematics Learning Based on Jean Piaget's Cognitive Development Theory in Junior High School

2025-02-01T09:56:34+00:00

This study aims to analyze the implementation of Merdeka Curriculum in mathematics learning in junior high schools based on Jean Piaget's cognitive development theory. The Merdeka Curriculum is designed to provide freedom for educators to arrange learning relevant to student needs, especially in mathematics subjects, which are often considered challenging. This research uses a qualitative approach with a case study type. The subject is a mathematics teacher. Data were obtained through document analysis and interviews, then analyzed descriptively through data reduction, data presentation, and conclusion drawing. To ensure data validity, source triangulation was carried out. The results showed that implementing the Merdeka Curriculum in mathematics learning supports students' formal operational cognitive development stage. The project-based approach and problem-solving at the core of the Merdeka Curriculum can develop logical, abstract, and analytical thinking skills essential in mathematics. However, several obstacles were found in the implementation, such as teachers‘ lack of understanding of learning strategies by students’ cognitive development stage, and limited interactive learning facilities. This research recommends comprehensive training for mathematics teachers to improve their ability to implement cognitive development-based learning strategies and the provision of adequate supporting facilities. With the right strategy, implementing the Merdeka Curriculum in mathematics learning in junior high schools can be more optimal in improving students' cognitive abilities.

The The Effect of the Discovery Learning Model with Student Worksheets on Students’ Mathematical Concept Comprehension Ability Comprehension Ability

2025-04-14T04:47:33+00:00

Mathematical concept comprehension is essential in learning mathematics. However, students’ comprehension of mathematical concepts is still low. This research aims to determine the effect of the discovery learning model with student worksheets on students’ mathematical concept comprehension ability. The method used in this research is quantitative. The type of research is a quasi-experimental design. Two classes were selected as the research sample using the simple random sampling technique. The instruments used in this research are a test of mathematical concept comprehension abilities and observation sheets of learning implementation. The data analysis techniques used in this research were descriptive analysis and inferential analysis (Independent Sample T-Test). Based on the data analysis results, the research shows that the discovery learning model with student worksheets positively affects students’ mathematical concept comprehension ability. This research implies that discovery learning with students' worksheets can be an effective alternative to improve students’ comprehension of mathematical concepts in classroom practice.