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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Riset Mahasiswa Matematika
Az-Zahra, Aisyah Dhifa
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Mathematics

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Forecasting the Number of Dropout Student in Indonesia using ARIMA Model Az-Zahra, Aisyah Dhifa; Fajriati, Luthfia Azzahra; Sari, Sherlyana Devita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.31625

Abstract

The high rate of dropout students in Indonesia remains a matter of considerable concern, as it erodes the quality of education and hinders the long-term development of human capital. The government of Indonesia has endeavored to address the issue of high dropout rates among students by implementing a range of initiatives. To demonstrate the effectiveness of this program, forecasting is necessary to measure and predict its outcomes. The purpose of this study is to utilize a time series approach, specifically the Autoregressive Integrated Moving Average (ARIMA) model, to predict the number of dropout students in the forthcoming years. This study employs a quantitative analysis using secondary data obtained from Statistics Indonesia (BPS) for the period 1970-2023. The ARIMA method is a statistical technique used to determine the most suitable forecasting model from historical data. This method has gained widespread popularity in the field of time series analysis due to its ability to manage non-stationary data effectively. The result shows that ARIMA (0,2,1) has the smallest AIC and meets the significant criteria model, also having the lowest MAPE value of 1.9%, indicating excellent forecasting accuracy. The plot of the result indicates a downward trend in the number of dropout students over the coming years. This downward trend aligns with the timeline of government interventions, suggesting a potential causal relationship between the implementation of educational support programs and the declining dropout rates. Thus, the prediction supports the effectiveness of these initiatives in mitigating dropout student in Indonesia.
Bilangan Kromatik Titik Graf Pembagi Nol Atas Modul Az-Zahra, Aisyah Dhifa; Jauhari, Mohammad Nafie; Juhari, Juhari
Jurnal Riset Mahasiswa Matematika Vol 5, No 3 (2026): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v5i3.39233

Abstract

Modul merupakan himpunan tak kosong yang dilengkapi dengan perkalian skalar oleh elemen-elemen dari suatu ring. Pembagi nol pada suatu modul adalah seluruh elemen pada modul yang merupakan hasil perkalian annihilator dengan modul tersebut. Himpunan pembagi nol dapat direpresentasikan dalam bentuk graf yang dapat disebut sebagai graf pembagi nol atas modul, yaitu graf yang titik-titiknya merupakan pembagi nol dan dua titik saling terhubung langsung apabila keduanya dikalikan hasilnya adalah nol. Bilangan kromatik titik adalah jumlah minimum warna yang digunakan untuk mewarnai seluruh titik pada graf. Tujuan penelitian ini adalah untuk menentukan rumus umum graf pembagi nol atas modul. Pada penelitian ini, modul yang digunakan adalah modul  dan  atas ring  dengan  dan adalah bilangan prima. Dari hasil penelitian ini, dapat disimpulkan bahwa bilangan kromatik titik graf pembagi nol atas modul  dan  adalah 2, sedangkan bilangan kromatik titik graf pembagi nol atas modul  adalah .
Co-Authors Fajriati, Luthfia Azzahra Juhari Juhari, Juhari Mohammad Nafie Jauhari Sari, Sherlyana Devita