Journal of Mathematics Education and Science

Existence And Uniqueness of Fixed Points on Non-Expansive Mapping In Quasi-Normed Spaces

Helmi Firdaus — 2025-10-06

This study examines the existence and uniqueness of fixed points of non-expansive mappings in quasi-normed spaces, to establish the existence of a solution to a non-expansive function in a quasi-normed space. The research method employed is a literature review, which provides some theorems with proofs and formal examples. The research began by outlining fundamental notions, such as convergence, Cauchy sequences, boundedness, and completeness, in the context of quasi-norms. Furthermore, the properties of compactness and their implications were elaborated as part of a theoretical framework. In the section on mappings, the characteristics of operators in quasi-normed spaces were first explained, including continuous and bounded mappings, along with their equivalence. Non-expansive and contraction mappings were then formally defined, serving as the basis for demonstrating the existence and uniqueness of fixed points. By applying a sequence approach and the completeness property, it was proven that every non-expansive mapping on a quasi-Banach space possesses a unique fixed point. Finally, it was shown that a quasi-normed space that is both compact and convex guarantees the existence of fixed points for non-expansive mappings defined on such spaces.

Exploring The Mathematical Problem-Solving Abilities of Grade Xi Students Based On Polya's Model

Agustinus Tamo Bapa — 2025-10-02

Problem-solving skills are essential in facing current challenges and developments. This study aims to describe students' ability to solve mathematical problems in the form of matrix story problems. This study employs a qualitative descriptive method and involves 93 eleventh-grade high school students. The instrument used is a written test consisting of two problem-solving questions. Subject selection was based on the results of a problem-solving ability test. Data collection utilized the problem-solving ability test questions and interviews. Qualitative data analysis was conducted through data reduction, data presentation, and conclusion drawing. The analysis was conducted according to Polya's model. The results showed that 7 students (8%) had very good mathematical problem-solving skills, as they were able to complete all four stages of Polya's model. Another 19 students (20%) were categorized as having good skills, although they only completed three stages of Polya's model without performing the final verification stage. Meanwhile, 30 students (32%) were only able to complete two stages of Polya's model without fully understanding the problem and without conducting a recheck, thus categorized as having adequate problem-solving skills. Additionally, 37 students (40%) were only able to complete one stage of Polya's model without fully understanding the problem, without formulating a plan, executing the plan, and without conducting a recheck. Thus, they were categorized as having poor problem-solving skills. This indicates that each student's ability to understand the problem, develop a problem-solving plan, implement the problem-solving plan, and check the answers is still in the low category. Therefore, it can be concluded that students' mathematical problem-solving abilities are still low. It is hoped that teachers can train students in learning, conduct effective learning, and thus improve students' problem-solving abilities.

Graph Coloring on the Primary Dryland Forest Cover Map of Kalimantan Using the Greedy Algorithm

Izzaty Farha — 2025-10-10

In graph theory, graph coloring is a popular approach, including in map creation, and this study aims to apply the Greedy algorithm to color forest land-cover maps while ensuring that adjacent areas do not share the same color. The data used consist of land-cover classification maps and the relationships between regions represented as planar graphs. The Greedy algorithm is implemented by arranging nodes based on their highest degrees and then coloring them sequentially. The coloring results show that the algorithm can provide an efficient solution with a minimum number of colors according to the upper bound of graph coloring, particularly for primary dry forest land-cover maps in East Kalimantan Province, achieving a chromatic number χ(G) = 4, ensuring no neighboring areas share the same color. Although it does not always yield an optimal solution, the algorithm proves effective, simple, and applicable to various other uses such as spatial analysis, regional clustering, or geographic information systems. The novelty of this study lies in its application to primary dry forests in Kalimantan, which have been rarely explored, and its contribution to spatial analysis and conservation efforts.

Finding The Shortest Route Between East Oku's Islamic Boarding Schools Using The Dijkstra Algorithm

Amanah Yulianti — 2025-08-09

This study aims to measure the distance between Islamic boarding schools in East Oku, using the Dijkstra Algorithm method to make it easier to determine the shortest route from the point of the Nurul Huda Sukaraja Islamic Boarding School to the Subulussalam Sriwangi Islamic Boarding School. In previous research, namely determining the shortest route when distributing from vegetable gardens to warehouses between toll and non-toll routes to minimize costs. In graph theory, the Dijkstra algorithm efficiently calculates the shortest path between any pair of nodes in a weighted graph, both positive and negative. This algorithm works with the principle of dynamic programming and can overcome graphs with a negative weight as long as there are no negative cycles. In its implementation, the Dijkstra algorithm iteratively updates the shortest distance between nodes by directly comparing paths with paths passing through other nodes. The advantage of this algorithm lies in its simplicity and ability to calculate the shortest distance between all pairs of nodes in a single process. The study results show that the Dijkstra Algorithm can show the fastest and most efficient alternative routes compared to conventional routes. Calculations using the Dijkstra Algorithm method produce the shortest trajectory starting from point 1-4-5 with a distance of 48 km, the most optimal route between the location and destination points.

Clustering Of Natural Disaster-Prone Areas In East Java Province Using Fuzzy C-Means Method

Deni Setiawan — 2025-10-10

Natural disasters are one of the most common problems in Indonesia. According to Data Informasi Bencana Indonesia (DIBI) from 2020 to 2024, East Java Province ranks third in terms of the frequency of natural disasters on the island of Java. Systematic mapping of disaster-prone areas is essential to support more effective mitigation and management efforts. This study aims to group 38 districts/cities in East Java Province based on their vulnerability to natural disasters. The methods used are Fuzzy C-Means for the grouping process and Silhouette Coefficient as a tool for evaluating cluster quality. The data used is secondary data with indicators of the number of incidents, number of victims, and amount of damage caused by floods, landslides, extreme weather, drought, earthquakes, volcanic eruptions, and forest and land fires. The clustering results produced three clusters, namely areas with high, medium, and low vulnerability levels. The clustering results were evaluated using the Silhouette Coefficient with a value of 0.2807, which indicates that the clustering results are in the fairly good category and indicate limitations in cluster separation due to the use of limited indicators and overlapping characteristics between regions. Nevertheless, the results of this study can contribute as a basis for consideration in the formulation of disaster mitigation policies, especially in determining intervention priorities and strengthening preparedness in areas with high disaster vulnerability.

Local Antimagic Edge Coloring Of Gear Graphs And Semi Parachute Graphs

Dian Sri Rahmadani — 2025-09-08

The graph G is a pair of sets consisting of a vertex set V(G) and an edge set E(G), denoted by G = (V (G),E(G)). Coloring a graph involves assigning colors to each vertex, edge, or region such that no adjacent vertices, edges, or regions share the same color. A bijective function f∶ V (G) → {1,2,3,...,|V (G)|} is called a local edge antimagic coloring if for any two adjacent edges e_1 and e_2, they have different weights, w(e_1) ≠ w(e_2), where e = uv ∈ E(G) and w(e) = f (u)+f (v). The chromatic number is the term used in the context of local antimagic coloring, referring to the minimum number of colors derived from local antimagic labeling. This research discusses the local antimagic edge coloring on the Gear Graph (G_n) and the Semi Parachute Graph (SP_(2n-1)). The aim of the research is to determine the chromatic number of local antimagic edge coloring χlea(G) for the researched graphs. The method used in this research is pattern detection to derive the general pattern. Based on the analysis, the chromatic number of local antimagic edge coloring is obtained for the Gear Graph (G_n) and the Semi Parachute Graph (SP_(2n-1)) are χlea (G_n)=n + 2 and χlea(SP_(2n-1) )=n+ 2.

Development of Ethnomathematics-Based Student Worksheets to Improve the Understanding of Concepts for Junior High School Grade IX Students

Ayu Pitaloka Saragi — 2025-10-12

Mathematics learning requires innovative and contextual teaching materials so that students can more easily understand concepts. However, the availability of teaching materials is still limited in schools. Often teachers only use package books as the only teaching materials used. This research aims to develop ethnomathematics-based Student Worksheets by integrating the Batak Gorga motif in the translation and reflection materials of grade IX of junior high school. The research model used is Research and Development (R&D) by adapting Borg and Gall's steps to the final product revision stage. The research instruments include expert validation, teacher and student response questionnaires, and concept understanding tests conducted through pre-tests and post-tests. The results of the study show that the average assessment from material and media experts is in the category of very valid. The responses of teachers and students gave an average assessment with a very practical category. In addition, the average results of the students' concept understanding test showed an increase from pre-test to post-test, so that the effectiveness of Student Worksheets was in the medium category. The integration of Gorga Batak motifs in the Student Worksheet is able to help students understand the concepts of translation and reflection more easily. This Student Worksheet can also be used by teachers as teaching materials based on local culture to increase the effectiveness of mathematics learning.