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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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Probabilistic Inventory Model Using All Unit Discount Factor and Inflation Mohammad Soleh; Arinal Haque; Yuslenita Muda
Jurnal Fourier Vol. 10 No. 2 (2021)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Abstract

Inflation causes the price per unit of goods to rise in the future. To offset inflation, companies can take advantage of discounts provided by suppliers. But ordering goods must be adjusted according to demand to avoid storage costs. This study describes a probabilistic supply model with demand at a time with a Gamma distribution and waiting for the discount and inflation factors. Backorder conditions in this model is assumed. The research produces a probabilistic inventory model and an algorithm to obtain the optimal number of orders and optimal ordering times for items that are all discounted and inflated with Gamma distribution demand.
A Mathematical Model of Microplastic Spreading into Fish Digestive Based On Abiotic Factor Zani Anjani Rafsanjani HSM; Nurul Suwartiningsih; Ichsan I Luqmana
Jurnal Fourier Vol. 10 No. 2 (2021)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Abstract

In this research, we observe the fish from seven different river location on Yogyakarta by evaluating its digestive weight. We investigate the microplastics spreading on fish digestive based on the abiotic factor such as river temperature, acidity, and river flow microplastics granules to be carried into the digestive tract of the fish. The rate of microplastics in the fish body can be describe mathematically using differential equation. We build a model based on the diagram flow of the relationship between each variables. Thus we have a differential system as the model. In the next step we analyze the model analytically. To show the accurancy of the model, we make a simulation using data simulation to the system and we compare it with the computing results using observation data. At the end of our research, we give a justification for the most influential abiotic factor for microplastic sreading.
Aplikasi Spherical Trigonometry dalam Menentukan Arah Kiblat Umat Islam Churun Lu'lu'il Maknun
Jurnal Fourier Vol. 10 No. 2 (2021)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Abstract

Matematika banyak diterapkan di berbagai bidang keilmuan, seperti sains, teknologi, ekonomi termasuk dalam bidang agama. Salah satu penerapan penting matematika dalam agama khususnya agama Islam adalah dalam menentukan arah kiblat. Hal ini penting karena kondisi permukaan bumi yang terus berubah akibat pergeseran lempeng sehingga arah kiblat secara kontinu akan terus dilakukan. Hasil dan pembahasan dalam artikel ini diperoleh melalui kajian literatur dengan cara mengkonstruksi  definisi dan teorema yang berkaitan dengan bentuk permukaan bumi, dan perhitungan geometris pada elipsoid. Dengan menggunakan prinsip geometri bola, segitiga bola dan trigonometri bola yang mencerminkan bentuk bumi yang berupa ellipsoid dapat dirumuskan cara menghitung arah kiblat untuk setiap daerah di permukaan bumi, yaitu dengan menggunakan aturan kosinus sebagai berikut: cos B= (cos b - cos a cos c)/sin a sin c. Selain itu disajikan pula bagaimana penggunaan rumus tersebut dengan menerapkan teknologi Google Earth dalam contoh konkrit penentuan arah kiblat dari suatu kota di Indonesia ke Kabah. Ketepatan penentuan koordinat lokasi menjadi penentu presisi dari sudut arah kiblat. [There are numerous applications of mathematics in other fields such as science, technology, economics and religion. One of the most important application of mathematics in religion is its use in deciding the direction of Kaaba for Moslem. This problem is important since the earth surface periodically changes due to the tectonic shift. The result of this study retrieved from literature study by constructing both the definitions and theorems of earth surface and geometrics calculation on ellipsoid. Using the spherical geometry, spherical trigonometry, and spherical triangle the formula to calculate the angle of Kaaba direction from particular point was constructed as follows: cos B= (cos b - cos a cos c)/sin a sin c. Further, the explanation of how to use and calculate the formula was also presented in this paper using the asssistance of Google earth technology. To sum up, the precision of coordinate of location becames main factor to obtain exact angle.]
Mathematical Model, Stability Analysis and Numerical Simulations for The Spread of Malaria Disease in Yogyakarta City, Indonesia Prihantini Prihantini
Jurnal Fourier Vol. 10 No. 2 (2021)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Abstract

Indonesia is a country with frequent malaria cases. Therefore, a mathematical model is needed to model the distribution of malaria. The purpose of this study is to create a model with susceptible, infected, dormant and recovered compartments and to see the results of the simulation performed using maple 18 software. From the simulation results, it can be concluded that there is a decrease in the infected population and an increase in the recovered population over time.
Analysis of the Stability of Bessel, Legendre and Euler Differential Equations Muchammad Abrori
Jurnal Fourier Vol. 10 No. 1 (2021)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Abstract

The Bessel, Legendre and Euler differential equations discussed in this paper are second-level differential equations. These three equations become a system with two equations. The equilibrium point of all three of these equations is at the point (0,0). These three equations are locally asymptotically stable at the equilibrium point (0,0).
Pemodelan Return Saham Syariah di Indonesia menggunakan Model AGARCH dengan Distribusi Skewed Student-t Muhammad Safi’ Mulhan; Mohammad Farhan Qudratullah
Jurnal Fourier Vol. 10 No. 1 (2021)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Abstract

Terdapat 2 hal yang selalu menyertai investasi, yaitu return dan risiko, hal ini berlaku juga pada investasi saham syariah. Harga saham setiap harinya mengalami perubahan, datanya memiliki volatilitas yang tidak konstan (heterokedastisitas) dan bersifat tidak simetri (asimetri). Sehingga untuk memodelkannya dapat menunakan model Asymmetric Generalized Autoregressive Conditional Heteroscedasticity (AGARCH) dengan distribusi Skewed Student-t. Penelitian ini membahas pemodelan return saham syariah mengunakan data penutupan harian Jakarta Islamic Index (JII) periode Maret 2013-April 2017 dengan model AGARCH-Skewed Student-t. Hasil dari penelitian ini diperoleh bahwa model ARIMA(0,0,3)-AGARCH(2,0) adalah model terbaik untuk meramalkan return saham syariah. [Two things always accompany investment, namely, return and risk, this also applies to Islamic stock investments. Stock prices change every day, the data has the volatility that is not constant (heteroscedasticity) and is asymmetry. So to model it, we can use the Asymmetric Generalized Autoregressive Conditional Heteroscedasticity (AGARCH) model with the Skewed Student-t distribution. This study discusses the modeling of Islamic stock returns using the daily closing data of the Jakarta Islamic Index (JII) for the period March 2013-April 2017 with the AGARCH-Skewed Student-t model. The results of this study show that the ARIMA(0,0,3)-AGARCH (2,0) model is the best model for predicting Islamic stock returns.]
Efektivitas Contextual Teaching and Learning pada Materi Kubus dan Balok terhadap Kemampuan Berpikir Kritis Peserta Didik Madrasah Ibtidaiyah Urip Meilina Kurniawati; Iwan Kuswidi
Jurnal Fourier Vol. 10 No. 1 (2021)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Abstract

Penelitian ini dilakukan berdasar persoalan tentang masih rendahnya kemampuan berpikir kritis peserta didik Madrasah Ibtidaiyah pada bidang matematika, terutama materi geometri kubus dan balok. Berdasar hasil kajian, model pembelajaran contextual teaching and learning diperkirakan dapat menyelesaikan permasalahan tersebut. Penelitian ini bertujuan untuk mengetahui bagaimana efektivitas contextual teaching and learning terhadap kemampuan berpikir kritis peserta didik Madrasah Ibtidaiyah. Metode yang digunakan dalam penelitian ini adalah quasi eksperiment dengan desain non equivalent control group design. Kontrol pada penelitian ini adalah kelas dengan pembelajaran konvensional. Teknik pengumpulan data dalam penelitian ini meliputi wawancara, tes uraian pretest dan posttest, serta lembar observasi proses pembelajaran. Instrumen pembelajaran dengan Rencana Pelaksanaan Pembelajaran (RPP), dan Lembar Kerja Peserta Didik (LKPD). Adapun teknik analisis pada penelitian ini yaitu analisis deskriptif dan inferensial menggunakan uji Mann Whitney. Hasil pengujian menunjukkan bahwa pembelajaran pada kelas eksperimen lebih efektif daripada kelas kontrol. Pada kelas eksperimen, rata-rata n-gain sebesar 56,01% menunjukkan bahwa efektifitas contextual teaching and learning berada pada kategori cukup efektif, sedangkan pada kelas kontrol diperoleh nilai rata-rata n-gain sebesar 32,77% yang menunjukkan efektifitas pembelajaran konvensional pada kategori tidak efektif. Berdasarkan analisis tersebut, dapat disimpulkan bahwa pembelajaran yang menggunakan contextual teaching and learning lebih efektif dibandingkan pembelajaran dengan model konvensional terhadap kemampuan berpikir kritis peserta didik. [This research is based on the problem that occurs, namely the low critical thinking ability of Madrasah Ibtidaiyah students in mathematics subjects, especially geometry cube and cuboid. Based on the results of the study, the contextual teaching and learning model is estimated to be able to solve these problems. This study aims to determine the effectiveness of contextual teaching and learning on the critical thinking skills of Madrasah Ibtidaiyah students. The method used in this study is a quasi-experimental design with a non-equivalent control group design. The control in this study was a class with conventional learning. Data collection techniques in this study include interviews, pretest and posttest, and observation of the learning process. Learning instruments with learning plans (RPP), and student worksheets (LKPD). The analysis technique in this study is a descriptive and inferential analysis using the Mann-Whitney test. The test results show that learning in the experimental class is more effective than in the control class. In the experimental class, an average n-gain of 56.01% indicates that the effectiveness of contextual teaching and learning is in the quite effective category, while in the control class an average value of n-gain is 32.77% which indicates the effectiveness of conventional learning in the ineffective category. Based on this analysis, it can be concluded that learning using contextual teaching and learning is more effective than learning with conventional models on students' critical thinking skills.]
Profil Kesiapan Guru Matematika Madrasah Tsanawiyah dalam Melaksanakan PTK Suparni Suparni; Sayidatul Maghfiroh Az Zahra
Jurnal Fourier Vol. 10 No. 1 (2021)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

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Abstract

Tujuan penelitian ini adalah mendeskripsikan profil kesiapan guru matematika madrasah tsanawiyah di wilayah DI Yogyakarta dalam melaksanakan Penelitian Tindakan Kelas (PTK), apa saja kendala yang dihadapi, dan upaya apa saja yang dilakukan guru matematika dalam melaksanakan PTK. Jenis penelitian ini deskriptif kualitatif. Guru matematika madrasah tsanawiyah se wilayah DI Yogyakarta yang tergabung dalam MGMP Matematika DIY menjadi subyek dari penelitian ini. Hasil penelitian ini adalah kesiapan guru matematika madrasah tsanawiyah DIY ditinjau dari faktor dalam (keahlian, kompetensi, dan motivasi) dan luar guru (kesempatan dan kondisi madrasah). Kendala yang dihadapi guru matematika madrasah tsanawiyah berkaitan dengan kemampuan melaksanakan PTK, kemampuan menuliskan hasil PTK dalam karya tulis ilmiah, dan kemampuan kolaborasi dengan teman sejawat dan pihak terkait. Upaya yang dapat dilakukan adalah mengikuti pelatihan PTK, pelatihan penulisan karya ilmiah untuk publikasi, dan meningkatkan kolaborasi dengan teman sejawat. [The purpose of this study was to describe the profile of the readiness of the mathematics teachers at the Madrasah Tsanawiyah in the DI Yogyakarta region in carrying out Classroom Action Research (CAR), what obstacles were encountered, and what efforts were made by mathematics teachers in implementing CAR. This type of research is descriptive qualitative. The mathematics teachers of Madrasah Tsanawiyah in the DI Yogyakarta region who are members of the DIY Mathematics MGMP are the subjects of this research. The result of this research is the readiness of mathematics teachers at the Madrasah Tsanawiyah DIY in terms of internal factors (expertise, competence, and motivation) and external factors (opportunities and conditions of the madrasa). Obstacles faced by mathematics teachers at Madrasah Tsanawiyah are related to the ability to carry out CAR, the ability to write CAR results in scientific papers, and the ability to collaborate with colleagues and related parties. Efforts that can be made are participating in CAR training, training in writing scientific papers for publication, and increasing collaboration with colleagues.]
Ideal Fuzzy Semiring Atas Level Subset Saman Abdurrahman
Jurnal Fourier Vol. 11 No. 1 (2022)
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.2022.111.1-6

Abstract

Semiring merupakan salah satu perluasan dari ring, dengan cara menghilangan salah satu aksioma pada operasi pertama yaitu aksioma invers. Pada semiring terdapat konsep subsemiring dan ideal dengan kondisi bahwa setiap ideal semiring adalah selalu subsemiring. Tetapi kondisi kebalikannya belum tentu berlaku. Selain konsep subsemiring dan ideal semiring, pada struktur semiring diperkenalkan konsep homomorfisma semiring. Kondisi ini, analog dengan homomorfisma di ring, sehingga sifat-sifat yang ada pada semiring dapat dinduksi dari sifat - sifat di ring, seperti konsep image dan preimage di bawah homomorfisma semiring analog dengan konsep image dan preimage di bawah homomorfisma ring. Konsep ideal pada semiring jika dipadukan dengan konsep fuzzy, akan menghasilkan konsep baru, yaitu konsep ideal fuzzy semiring. Pada makalah ini, akan diperkenalkan konsep ideal fuzzy semiring, image dan preimage ideal fuzzy dari suatu homomorfisma semiring. Lebih lanjut, akan diselidiki sifat-sifat ideal fuzzy semiring, image dan preimage ideal fuzzy dibawah homomorfisma semiring melalui suatu level subset. [Semiring is one of the extensions of the ring by disappearing one of the axioms in the first operation, namely the inverse axiom. In semiring, there is the concept of subsemiring and ideal with the condition that every ideal semiring is always subsemiring. However, the opposite condition does not necessarily apply. In addition to the concept of subsemiring and the ideal of a semiring, in the semiring structure was introduced the concept of semiring homomorphism. This condition is analogous to the homomorphism in the ring so that the properties present in the semiring can be induced from the properties in the ring, such as the concept of image and preimage under the homomorphism of semiring analogous to the concept of image and preimage under the homomorphism of the ring. If combined with the fuzzy concept, the ideal concept in semiring will produce a new concept, namely the ideal concept of fuzzy semiring. This paper will introduce the concept of an ideal fuzzy semiring, image, and preimage ideal fuzzy from a semiring homomorphism. Furthermore, the properties of the fuzzy ideal semiring, image, and preimage of the fuzzy ideal will be investigated under the semiring homomorphism through a subset level.]
Analisis Kemampuan Koneksi Matematis Siswa dalam Menyelesaikan Soal Persamaan Trigonometri Halimatus Sadiyah; Dian Permatasari
Jurnal Fourier Vol. 11 No. 2 (2022)
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.2022.112.59-68

Abstract

Matematika merupakan salah satu mata pelajaran wajib yang ada di sekolah. Kebanyakan siswa menganggap pelajaran matematika merupakan pelajaran yang sulit. Hal ini karena matematika merupakan pelajaran yang abstrak. Namun dibalik kesulitanya, mempelajari matematika mempunyai banyak manfaat. Salah satunya adalah membangun koneksi matematis. Penelitian ini bertujuan untuk mengetahui kemampuan koneksi matematis siswa dalam menyelesaikan soal persamaan trigonometri, kesahalan-kesalahan yang sering siswa lakukan, faktor penyebab dan juga cara meningkatkan kemampuan matematis siswa. Metode yang dilakukan merupakan metode deskriptif kualitatif dengan subjek penelitian kelas XI Mipa 2 di salah satu SMA yang ada di Yogyakarta. Adapun teknik pengambilan data dalam penelitian ini berupa teknik tes dan teknik non tes yang berupa wawancara. Instrumen yang digunakan adalah butir soal tes uraian koneksi matematis persamaan trigonometri dan pedoman wawancara. Teknik analisis data dilakukan dengan reduksi data, penyajian data, dan menarik kesimpulan. Adapun hasil dari rata-rata kemampuan koneksi matematis siswa berada di tingkat sedang yaitu dengan presentase sebanyak 55,56% dengan jumlah 20 siswa. Sedangkan siswa dengan kemampuan koneksi matematis tinggi sebanyak 16,67% dan siswa dengan kemampuan matematis rendah sebanyak 27,77%. Hal ini menunjukkan sebagian besar siswa mampu mengaitkan koneksi matematis siswa antar konsep/prinsip matematika maupun antar topik matematika. [Mathematics is one of the compulsory subjects in school. Most students consider mathematics a difficult lesson. This is because mathematics is an abstract subject. But behind the difficulties, studying mathematics has many benefits. One way is to build mathematical connections. This study aims to determine students' mathematical connection abilities in solving trigonometry equations, mistakes that students often make, causal factors and also ways to improve students' mathematical abilities. The method used is a qualitative descriptive method with research subjects in class XI Mipa 2 at one of the high schools in Yogyakarta. The data collection techniques in this study were in the form of test techniques and non-test techniques in the form of interviews. The instruments used were test items describing the mathematical connection of trigonometry equations and interview guidelines. Data analysis techniques were carried out by data reduction, data presentation, and drawing conclusions. The results of the average student mathematical connection ability are at a moderate level, namely with a percentage of 55.56% with a total of 20 students. While students with high mathematical connection abilities were 16.67% and students with low mathematical abilities were 27.77%. This shows that most students are able to relate students' mathematical connections between mathematical concepts/principles and between mathematical topics.]

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