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Jurnal Fourier
Published by Universitas Islam Negeri Sunan Kalijaga Yogyakarta
ISSN : -     EISSN : -     DOI : -
Core Subject : Economy, Science, Education,
Computer Science & IT Economics, Econometrics & Finance Education Mathematics
FOURIER adalah Jurnal Ilmiah bidang yang memadukan dan mengembangkan ilmu Matematika dan pembelajarannya yang diintegrasikan dan interkoneksikan dengan nilai-nilai keislaman terbit sejak tahun 2012 dengan frekuensi terbit 2 kali dalam setahun yang dengan bahasa utama (Bahasa Indonesia dan Bahasa Inggris) yang proses reviewernya sesuai dengan disiplin ilmunya (Analisis, Aljabar, Matematika Terapan, Statistika, dan Pendidikan Matematika).
Arjuna Subject : -
Articles 188 Documents
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Peningkatan Kemampuan Kolaborasi dan Komunikasi Matematis Peserta Didik Kelas X SMA Melalui Penerapan Model Cooperative Learning Tipe TGT Terintegrasi CASEL Lathifah Siti Nur Azizah; Anisa Amalia; Puguh Wahyu Prasetyo
Jurnal Fourier Vol. 14 No. 1 (2025)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2025.141.21-28

Abstract

Abstrak Penelitian ini dilatarbelakangi oleh rendahnya kemampuan kolaborasi dan komunikasi matematis peserta didik kelas X-A SMA Muhammadiyah 1 Yogyakarta, yang tercermin dari hasil asesmen diagnostik dan pernyataan peserta didik tentang kesulitan dalam pengerjaan soal matematika. Penelitian ini bertujuan untuk meningkatkan kemampuan kolaborasi dan komunikasi matematis melalui penerapan model pembelajaran kooperatif tipe Teams Games Tournament (TGT) yang terintegrasi dengan pendekatan CASEL. Metode yang digunakan dalam penelitian ini adalah Penelitian Tindakan Kelas (PTK) dengan instrumen lembar observasi untuk mengukur kemampuan kolaborasi dan tes untuk menilai komunikasi matematis. Indikator kolaborasi meliputi produktivitas, partisipasi aktif, penghargaan terhadap pendapat kelompok, fleksibilitas, dan tanggung jawab, sementara indikator komunikasi matematis meliputi pengungkapan situasi dalam bahasa matematika, penyajian penyelesaian secara terstruktur, dan evaluasi ide matematis. Hasil penelitian menunjukkan peningkatan signifikan pada kemampuan kolaborasi dan komunikasi matematis peserta didik setelah penerapan model TGT. Rata-rata nilai tes komunikasi matematis meningkat dari 64% pada siklus I menjadi 90% pada siklus II, sedangkan kemampuan kolaborasi meningkat dari 62% menjadi 73%. Peserta didik menunjukkan keterlibatan yang lebih aktif dalam diskusi dan saling mendukung selama pembelajaran, yang berkontribusi pada peningkatan kemampuan penyelesaian soal matematika. Hasil ini menunjukkan bahwa penerapan model TGT efektif dalam meningkatkan kemampuan kolaborasi dan komunikasi matematis peserta didik. Kata Kunci: CASEL, Kolaborasi, Komunikasi, Matematis, TGT Abstract This research is motivated by the low ability of mathematical collaboration and communication of class X-A students of SMA Muhammadiyah 1 Yogyakarta, which is reflected in the results of diagnostic assessments and student statements about difficulties in working on mathematics problems. This study aims to improve mathematical collaboration and communication skills through the application of the Teams Games Tournament (TGT) type cooperative learning model integrated with the CASEL approach. The method used in this study is Classroom Action Research (CAR) with observation sheet instruments to measure collaboration skills and tests to assess mathematical communication. Collaboration indicators include productivity, active participation, respect for group opinions, flexibility, and responsibility, while mathematical communication indicators include expressing situations in mathematical language, presenting solutions in a structured manner, and evaluating mathematical ideas. The results showed a significant increase in students' mathematical collaboration and communication skills after the application of the TGT model. The average mathematical communication test score increased from 64% in cycle I to 90% in cycle II, while collaboration skills increased from 62% to 73%. Students showed more active involvement in discussions and supported each other during learning, which contributed to improving their mathematical problem-solving abilities. These results indicate that the implementation of the TGT model is effective in improving students' mathematical collaboration and communication abilities. Keywords: CASEL, Collaboration, Communication, Mathematical, TGT
Pemodelan SITR Pada Penyebaran Penyakit Tuberculosis Dengan Penggunaan Masker Medis Dan Treatment Thessa Rahma Donita; Irma Suryani
Jurnal Fourier Vol. 13 No. 2 (2024)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2024.132.76-86

Abstract

Penelitian ini mengembangkan model SITR pada penyakit tuberculosis dengan menambahkan penggunaan masker medis dan treatment. Populasi dibagi menjadi Susceptible without mask (S) yaitu individu rentan tidak menggunakan masker medis, Susceptible With Mask ( yaitu individu rentan dengan menggunakan masker medis, Infected without mask (I) yaitu individu terinfeksi yang tidak menggunakan masker medis, Infected with mask yaitu individu terinfeksi yang menggunakan masker medis, Treatment (T) yaitu jumlah individu yang melakukan pengobatan, Recovered (R) yaitu jumlah individu sembuh. Penelitian ini bertujuan untuk menentukan titik ekuilibrium bebas penyakit dan endemik penyakit, bilangan reproduksi dasar (R0), analisis kestabilan dan simulasi numerik. Berdasarkan hasil penelitian hasil uji kestabilan titik ekuilibrium menggunakan nilai eigen diperoleh bahwa jika R0 < 1 maka titik ekuilibrium bebas penyakit stabil asimtotik lokal, artinya populasi akan bebas dari penyakit tuberculosis. Jika R0 > 1 maka titik ekuilibrium endemik penyakit stabil asimtotik lokal, artinya pada keadaan ini dalam populasi akan selalu terdapat penyakit tuberculosis.
Ethnomathematics: Mathematical Concepts In The Gaple Card Game Afandi, Muhammad Irfan; Almaghfiroh, Violina; Marhayati
Jurnal Fourier Vol. 13 No. 2 (2024)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2024.132.87-93

Abstract

The purpose of this research is to describe the mathematical elements contained in the gaple card game. This study uses ethnographic research with a qualitative approach. The focus of this research is the tools, rules and processes of the gaple card game. Data collection techniques used are observation, interviews, field notes, and documentation. This study uses triangulation data analysis which consists of data reduction, presentation and conclusion. The results of this study found mathematical concepts in the gaple card game, namely set, addition, opportunity and inequality.
Generalized Gaussian Fibonacci Numbers and its Determinantal Identities Panwar, Yashwant Kumar; Vinod Kumar Gupta; Minal Gwala
Jurnal Fourier Vol. 13 No. 2 (2024)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2024.132.111-117

Abstract

In this paper, we present the determinantal identities of generalized Gaussian Fibonacci numbers. The generalized Gaussian Fibonacci sequence is defined by the recurrence relation. This was introduced by S. Pethe and A. F. Horadam. Also, we present its determinantal identities with classical numbers like gaussian Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, jacobsthal-Lucas, Bronze, Nickel and Mersenne numbers.
Performa Naïve Bayes, SVM, dan IndoBERT pada Analisis Sentimen Twitter IndiHome dengan Strategi Penanganan Data Tidak Seimbang Anas Qolbu, Adinda; Fitriyati, Nina; Inayah, Nur
Jurnal Fourier Vol. 14 No. 1 (2025)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2025.141.29-44

Abstract

Penelitian ini bertujuan untuk membandingkan performa tiga pendekatan analisis sentimen, yaitu Naïve Bayes, Support Vector Machine (SVM), dan Indonesian Bidirectional Encoder Representations from Transformers (IndoBERT), pada layanan IndiHome menggunakan data Twitter. Keterbatasan model tradisional melatarbelakangi penelitian ini dalam mengenali opini positif dan tantangan ketidakseimbangan data yang sering muncul dalam analisis berbasis media sosial. Data penelitian berupa 7393 tweet (Januari 2019–Agustus 2024) yang dilabeli secara manual menjadi sentimen positif dan negatif. Model dievaluasi menggunakan stratified 10-fold cross validation dan data uji, dengan penerapan teknik penanganan ketidakseimbangan berupa Synthetic Minority Oversampling Technique (SMOTE) dan pembobotan kelas (class weighting). Hasil menunjukkan IndoBERT unggul dengan akurasi 0,96 dan F1-score makro 0,95 tanpa penanganan khusus, sedangkan SVM mencapai akurasi 0,95 dengan pembobotan kelas, dan Naïve Bayes meningkat dari akurasi 0,89 menjadi 0,92 setelah SMOTE. Analisis tren sentimen menunjukkan opini negatif mendominasi, terutama terkait kecepatan dan kestabilan layanan. Temuan ini menegaskan bahwa IndoBERT lebih efektif dalam memahami konteks bahasa Indonesia, sementara teknik penanganan data tetap relevan untuk meningkatkan performa model tradisional. Hasil penelitian ini penting karena memberikan dasar empiris dalam pemilihan model analisis sentimen yang lebih akurat, adaptif terhadap bahasa Indonesia, dan bermanfaat dalam meningkatkan kualitas layanan.   This study aims to compare the performance of three sentiment analysis approaches, namely Naïve Bayes, Support Vector Machine (SVM), and Indonesian Bidirectional Encoder Representations from Transformers (IndoBERT), on IndiHome services using Twitter data. The limitations of traditional models underlie this study in recognizing positive opinions and the challenge of data imbalance that often arises in social media based analysis. The research data consist of 7,393 tweets (January 2019–August 2024) manually labeled into positive and negative sentiments. Models were evaluated using stratified 10-fold cross validation and test data, with the application of imbalance handling techniques such as Synthetic Minority Oversampling Technique (SMOTE) and class weighting. Results show IndoBERT excels with 0.96 accuracy and 0.95 macro F1-score without special handling, while SVM reaches 0.95 accuracy with class weighting, and Naïve Bayes improves from 0.89 to 0.92 accuracy after SMOTE. Sentiment trend analysis indicates negative opinions dominate, mainly regarding speed and service stability. These findings confirm IndoBERT is more effective in understanding Indonesian context, while data handling remains relevant for improving traditional models. This study’s results are important because they offer an empirical foundation for choosing sentiment analysis models that are more accurate, adaptive to Indonesian language, and useful for improving service quality.  
ANALISIS HIERARCHICAL CLUSTERING (SINGLE LINKAGE) DAN K-MEDOIDS PADA DATA PENGHASILAN DAN DEMOGRAFI AREA KOMUNITAS CHICAGO salsa, Salsadilla Azizi Firda; Haikal Agung Widiyanto; Regina Adelisa; Etis Sunandi
Jurnal Fourier Vol. 14 No. 2 (2025)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2025.142.68-79

Abstract

Penelitian ini menganalisis metode Hierarchical Clustering Single Linkage dan K-Medoids dalam mengelompokkan data pendapatan dan demografi di Chicago. Dengan menggunakan data sekunder dari situs Kaggle, penelitian ini mengelompokkan 77 komunitas area berdasarkan kesamaan karakteristik sosial dan ekonomi. Hasil analisis dengan metode Hierarchical Clustering Single Linkage menunjukkan bahwa terdapat satu komunitas area yang terpisah dalam klaster kedua, sementara sisanya tergabung dalam satu klaster utama. Sebaliknya, metode K-Medoids menghasilkan dua klaster yang lebih seimbang dalam distribusi datanya. Berdasarkan visualisasi clustering, metode K-Medoids dianggap lebih baik karena mampu membagi data secara lebih seimbang. Namun, jika ditinjau dari nilai Silhouette Score dan Dunn Index, metode Hierarchical Clustering Single Linkage lebih unggul karena memiliki nilai yang lebih tinggi, menunjukkan fragmentasi klaster yang lebih jelas. Dengan demikian, pemilihan metode terbaik bergantung pada tujuan analisis, di mana K-Medoids lebih sesuai untuk interpretasi distribusi data yang lebih merata, sedangkan Hierarchical Clustering Single Linkage lebih optimal dalam kriteria klaster yang jelas.   This study analyzes the Hierarchical Clustering Single Linkage and K-Medoids methods in clustering income and demographic data of communities in Chicago. Using secondary data from the Kaggle website, this study clusters 77 community areas based on similarities in social and economic characteristics. The analysis using the Hierarchical Clustering Single Linkage method reveals that one community area is isolated in the second cluster, while the rest are grouped into a single main cluster. In contrast, the K-Medoids method produces two clusters with a more balanced distribution. Based on clustering visualization, the K-Medoids method is considered superior as it provides a more evenly distributed classification. However, when evaluated using the Silhouette Score and Dunn Index, the Hierarchical Clustering Single Linkage method outperforms K-Medoids due to its higher values, indicating clearer cluster separation. Thus, the choice of the best method depends on the analytical objective, where K-Medoids is more suitable for interpreting a more balanced data distribution, while Hierarchical Clustering Single Linkage is optimal for achieving distinct cluster separation.
Analysis of Inflation Rates During and After the COVID-19 Pandemic Using the K-Means Clustering Method and Kruskal-Wallis Test Fadhila, Riska Nuril; Ulinnuha, Nurissaidah; Hafiyusholeh, Moh
Jurnal Fourier Vol. 14 No. 2 (2025)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2025.142.56-67

Abstract

Inflation occurs when excessive demand results in an overall increase in the prices of goods and services. During the COVID-19 pandemic, the inflation rate in Indonesia leveled off due to the weakening economy. However, in 2022, there was a spike in post-COVID-19 inflation due to increased public demand as pandemic conditions improved. Stable inflation is a requirement for sustainable economic growth and improving people's welfare. In handling inflation problems in various regions, variables and unique circumstances in each region are very important. This research aims to determine whether significant differences exist in the clustering of inflation rates in Indonesia during and after the COVID-19 pandemic. The research results using the Kruskal-Wallis test and the K-Means method obtained that the clustering of inflation rates with k=2 provides good results, as indicated by the Silhouette Coefficient value of 0.66. In addition, there is a significant difference between the current (2020-2021) and post (2022-2023) years of COVID-19 as evidenced by the Kruskal-Wallis test with a p-value < 0.05.
Model Matematika Penjadwalan Obat Kemoterapi Kanker secara Optimal Menggunakan Non-dominated Sorting Genetic Algorithm-II (NSGA-II) Ashilah Azmii, Yusyifa; Yulianti, Kartika; Sispiyati, Ririn
Jurnal Fourier Vol. 14 No. 1 (2025)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/fourier.2025.141.45-55

Abstract

In this study, a mathematical model for cancer chemotherapy drug scheduling was developed, which is the problem of scheduling drugs given to patients. The mathematical model developed has an objective function of reducing cancer cells while reducing toxicity in the patient's body, with constraints in the form of limits for the number of healthy cells, cancer cells, drug concentration, and patient toxicity. The influential and interrelated variables are arranged in a system of differential equations consisting of the number of healthy cells, number of cancer cells, drug dose, drug concentration, patient toxicity and drug effect, which describes the chemotherapy of non-specific cancer cell cycles. Optimal solution was obtain numerically using Runge-Kutta Method and Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The results showed that this algorithm was able to produce a solution with an optimal dosing schedule every 8 days for 106 days with 14 drug doses. Doses ranged from 20.00 to 29.55 mg/m² with an average of 24.28 mg/m² and a standard deviation of 3.64 mg/m² so as to minimize the number of cancer cells and damage to healthy cells.

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