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All Journal Jurnal Matematika UNAND Jurnal Saintika Unpam : Jurnal Sains dan Matematika Unpam InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS) Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Jurnal Eurekamatika Journal of Fundamental Mathematics and Applications (JFMA) Prosiding Seminar Nasional Pengabdian Kepada Masyarakat JMT (Jurnal Matematika dan Terapan)
Mahatma, Yudi
Universitas Negeri Jakarta
Humanities Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Environmental Science Industrial & Manufacturing Engineering Mathematics Physics Public Health Other

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Penentuan Derajat Optimum Interpolasi pada Metode Lagrange dan Metode Newton Gregory dalam Mengestimasi Kasus Pasien Sembuh dari Covid-19 di Indonesia Muhammad Julian; Lukita Ambarwati; Yudi Mahatma
JMT : Jurnal Matematika dan Terapan Vol 4 No 1 (2022): JMT (Jurnal Matematika dan Terapan)
Publisher : Program Studi Matematika Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/jmt.4.1.2

Abstract

Estimation is one method for approximation. The estimation method is the polynomial interpolation. Once of polynomial interpolation are Lagrange method and Newton Gregory method. In several references, the degrees of interpolation which is used on the Lagrange method or Newton Gregory method depends on the numbers of data. This paper was created to knowing the optimum degrees to interpolate 61 numbers of data. In this paper, points are determined to interpolate so that formed intervals of equal length. As for the degrees to be tested, namely degrees 2,4,5,10, and 20. Based on MAPE and MSE values for degree 2 are lower than degrees 4,5,10 and 20 in both methods so that the interpolation of the Lagrange and Newton Gregory degrees 2 is better than degrees 4,5,10, and 20.
Perbandingan Metode Perhitungan Jarak Euclidean dengan Perhitungan Jarak Manhattan pada K-Means Clustering Dalam Menentukan Penyebaran Covid di Kota Bekasi Faisal Nur Cahya; Yudi Mahatma; Siti Rohmah Rohimah
JMT : Jurnal Matematika dan Terapan Vol 5 No 1 (2023): JMT (Jurnal Matematika dan Terapan)
Publisher : Program Studi Matematika Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/jmt.5.1.5

Abstract

Clustering is a method of grouping in an information database based on certain conditions. The research applies the k-means clustering calculation problem with the euclidean distance calculation approach with the manhattan distance calculation. The method formed aims to compare in terms of the working process between the calculation of the Euclidean distance with the calculation of the Manhattan distance. The result is a comparison of the distance calculation between the distance calculation euclidean and the distance calculation manhattan in terms of the work process to be able to determine the center points of the spread of the covid disease from the comparison of the distance calculation Euclidean and the distance calculation Manhattan. The calculation results obtained are the K-Means calculation with the euclidean distance calculation approach, the number of iterations is 15 times, while by using the manhattan distance calculation, the number of iterations is 7 times. So it is concluded that in terms of processing manhattan is faster than euclidean. The calculation results obtained are the results of calculations from Covid-19 data in Bekasi City up to September 1, 2021.
Implementasi Metode ARIMA-GARCH Terhadap Peramalan Konversi Mata Uang Yen ke Rupiah Bintang Sirius; Widyanti Rahayu; Yudi Mahatma
JMT : Jurnal Matematika dan Terapan Vol 5 No 2 (2023): JMT (Jurnal Matematika dan Terapan)
Publisher : Program Studi Matematika Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/https://doi.org/10.21009/jmt.5.2.4

Abstract

Buying and selling transactions are always used by humans to meet their needs. One of the transaction tools used is money. Each country has its own currency including Japan, with Yen continues to experience a significant decline throughout April 2022 exceeding 5-10%. Therefore, it is necessary to anticipate the rate of increase/decrease in Yen. After testing and forecasting, it was concluded that the most appropriate model for analyzing the data in this study was the ARIMA(3,1,3) - GARCH (1,1) model. This is because the model can overcome the homogeneity of the data. The conversion of Yen to Rupiah currency from August 2022 to July 2023 can be predicted to have fluctuations, and produce a MAPE value of 19.29%, which indicates that the precision level of the ARIMA(3,1,3) - GARCH(1,1) is good enough to use for the conversion data.
ROUGH RINGS, ROUGH SUBRINGS, AND ROUGH IDEALS Agusfrianto, Fakhry Asad; Fitriani, Fitriani; Mahatma, Yudi
Journal of Fundamental Mathematics and Applications (JFMA) Vol 5, No 2 (2022)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v5i2.15194

Abstract

The basic concept in algebra that is set theory can be expanded into rough sets. Basic operations on the set such as intersections, unions, differences, and complements can still apply to rough sets. In addition, one of the applications of rough sets is the use of rough matrices in decision making. Furthermore, mathematical or informatics researchers who work on rough sets connect the concept of rough sets with algebraic structures (groups, rings, and modules) so that a concept called rough algebraic structures is obtained. Since the research related to rough sets is mostly carried out at the same time, different concepts have emerged related to rough sets and rough algebraic structures. In this paper, other definitions of rough ring and rough subring will be given along with related examples and theorems. Furthermore, it will also be defined the left ideal and the right ideal of the rough ring along with examples. Finally, we will discuss the theorem regarding rough ideals.
PELATIHAN CHARACTER BUILDING MENGGUNAKAN KONSEP PROBLEM SOLVING MATERI MATEMATIKA TINGKAT SD PADA GURU DAN SISWA DI PULAU TIDUNG KEPULAUAN SERIBU Hadi, Ibnu; Mahatma, Yudi; Wiraningsih, Eti Dwi; Zainati, Dini; Pratiwi, Rifa Khairunnisa
Prosiding Seminar Nasional Pengabdian Kepada Masyarakat Vol. 4 (2023): PROSIDING SEMINAR NASIONAL PENGABDIAN KEPADA MASYARAKAT - SNPPM2023
Publisher : Lembaga Penelitian dan Pengabdian kepada Masyarakat Universitas Negeri Jakarta

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Abstract

Abstract Character Building can be done using any media. Mathematics is a lesson that can be used as a media. In this paper, we will discuss how character building uses the concept of problem solving in elementary school mathematics material. The method used is in the form of training with teacher and student participants on Tidung Island, the Thousand Islands. In the early stages, students are given an explanation of the concept of character and its relation to mathematics. Then they were given elementary level mathematic problem solving questions. During the working, the students is guided structurally to solve the poblems, and they allow to work both independently or in a group. They are also introduced which characters that can be build through solving mathematical problems, such as discipline, honesty, hard work, creativity, curiosity, independence, communicative, disciplined habits in reasoning. The students were also given a pre-test and post-test to explore the comprehension of the relationship between character and mathematics. regarding the concept of character. From the results of the training provided, students can follow directions in solving problem solving problems. They also provide motivation on how to build character using mathematic materials. The students were enthusiastic in participating in the training provided. Many actions are needed from this training as a form of control over the results of the training that has been given. It is hoped that teachers can be actively involved in character building through problem solving in mathematics at the elementary level. Abstrak Pembentukan karakter dapat dilakukan menggunakan media apapun. Matematika merupakan pelajaran yang dapat digunakan sebagai sarananya. Pada tulisan ini akan dibahas bagaimana pembentukan karakter menggunakan konsep pemecahan masalah (problem solving) materi matematika tingkat sekolah dasar (SD). Metode yang digunakan adalah dalam bentuk pelatihan dengan peserta guru dan siswa di Pulau Tidung, Kepulauan Seribu. Pada tahap awal, siswa diberikan paparan mengenai konsep karakter dan kaitannya dengan matematika. Kemudian mereka diberikan masalah problem solving matematika tingkat SD. Dalam pengerjaannya, siswa dibimbing secara terstruktur untuk menyelesaikannya, dan mereka bekerja secara mandiri maupun berkelompok. Mereka juga dikenalkan karakter yang dapat dibangun melalui masalah problem solving matematika yaitu disiplin, jujur, kerja keras, kreatif, rasa ingin tahu, mandiri, komunikatif, kebiasaan disiplin dalam bernalar. Para siswa juga diberikan pre-test dan post-test untuk menggali pemahaman hubungan antara karakter dan matematika. mengenai konsep karakter Dari hasil pelatihan yang diberikan, siswa dapat mengikuti arahan dalam menyelesaikan masalah problem solving. Mereka juga diberikan motivasi bagaiana membangun karakter menggunakan materi matematika. Para siswa antusias dalam mengikuti pelatihan yang diberikan. Diperlukan tindak lanjut dari pelatihan ini sebagai bentuk kontrol terhadap hasil pelatihan yang sudah diberikan. Diharapkan guru dapat terlibat dengan aktif terhadap Pembangunan karakter melalui problem solving materi matematika di tingkat SD.
PENINGKATAN KOMPETENSI GURU SD KEPULAUAN SERIBU MELALUI PENDALAMAN MATERI KETERBAGIAN Mahatma, Yudi; Ibnu Hadi; Muhammad Eka Suryana; Tiara Nabila; Sandrina Widya Andani
Prosiding Seminar Nasional Pengabdian Kepada Masyarakat Vol. 4 (2023): PROSIDING SEMINAR NASIONAL PENGABDIAN KEPADA MASYARAKAT - SNPPM2023
Publisher : Lembaga Penelitian dan Pengabdian kepada Masyarakat Universitas Negeri Jakarta

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Abstract

Abstract The concept of thematic learning requires teachers to be able to master all lessons well. The concept of divisibility is a basic mathematical material so it is important to be mastered by elementary school teachers. For this reason, it is necessary to conduct a deepening training in mathematics related to divisibility material for elementary school teachers. As the target of this community service activity, the Mathematics Study Program of UNJ in collaboration with the Suku Dinas Pendidikan Kabupaten Administrasi Kepulauan Seribu held training for elementary school teachers. The training was held at SMKN 61 on Tidung Island. As feedback, questionnaires were distributed to participants before and after the training. From the results of the questionnaire, it can be seen that this activity can enrich the knowledge and insight of teachers in the field of mathematics. One of the outputs of this research is a video that has been uploaded to the official YouTube account of Matematika UNJ. Abstrak Konsep pembelajaran tematik menuntut para guru untuk dapat menguasai semua pelajaran dengan baik. Konsep keterbagian merupakan materi matematika yang mendasar sehingga penting untuk dikuasai oleh para guru SD. Untuk itu perlu dilakukan suatu pelatihan pendalaman materi matematika terkait materi keterbagian kepada para guru SD. Sebagai sasaran kegiatan pengabdian pada masyarakat ini, Program Studi Matematika UNJ bekerja sama dengan Suku Dinas Pendidikan Kabupaten Administrasi Kepulauan Seribu menyelenggarakan pelatihan untuk guru-guru SD. Pelatihan dilaksanakan di SMKN 61 di Pulau Tidung. Sebagai umpan balik, disebarkan kuesioner kepada para peserta sebelum dan sesudah pelatihan. Dari hasil kuesioner terlihat bahwa kegiatan ini dapat memperkaya pengetahuan dan wawasan para guru dalam bidang matematika. Salah satu luaran penelitian ini adalah video yang sudah diunggah di akun YouTube resmi Matematika UNJ.
Modifikasi algoritma Hill cipher dengan matriks kunci berupa matriks ketetanggaan Agusfrianto, Fakhry Asad; Ambarwati, Lukita; Mahatma, Yudi
Majalah Ilmiah Matematika dan Statistika Vol. 23 No. 2 (2023): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v23i2.36346

Abstract

Cryptography is one of the parts in mathematics, especially applied mathematics. Cryptography is the science that studies how to secure information that we don't want others to know about the information we have. Based on the development of the times, cryptography is divided into two consisting of classical cryptography and modern cryptography. In this paper, the focus of discussion is on classical cryptography. Furthermore, there are many kinds of classical cryptographic algorithms, such as the Caesar cipher algorithm, the Playfair cipher algorithm, the Vigenere cipher algorithm, and the Hill Cipher algorithm. The focus of discussion in this paper is on the Hill cipher algorithm. The modifications made to the Hill cipher algorithm lie in its key matrix. In this paper, it will be shown how to encrypt and decrypt the message we want to send using the Hill cipher algorithm with the matrix being a adjacency matrix. In which case, the adjacency matrix itself is obtained from the representation of the graph. It is hoped that this algorithm can avoid crypt attacks, especially on ciphertext only-attack.Keywords: Hill cipher algorithm, cryptography, adjacency matrix, plaintext, ciphertextMSC2020: 94A60
Graph Representation for the Solutions of Pythagorean Equation over the General Linear Group GL₂ (ℤ₂ ) Mahatma, Yudi; Hadi, Ibnu; Sudarwanto, Sudarwanto; Agustine, Debby
JMT (Jurnal Matematika dan Terapan) Vol. 7 No. 1 (2025): JMT (Jurnal Matematika dan Terapan)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/jmt.7.1.1

Abstract

In 2023, Hadi et al. found the solvability of the Fermat equation over the general linear group GL2(Zp) for p=2 and p=3. In particular, for Pythagorean equation over GL2(Z2) there are 12 solutions. In this research, we represent the set solutions as a graph and investigate the properties.
Stochastic Volatility Estimation of Stock Prices using the Ensemble Kalman Filter Mahatma, Yudi; Hadi, Ibnu
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 3 No. 2 (2021)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v3i2.20256

Abstract

AbstractVolatility plays important role in options trading.  In their seminal paper published in 1973, Black and Scholes assume that the stock price volatility, which is the underlying security volatility of a call option, is constant.  But thereafter, researchers found that the return volatility was not constant but conditional to the information set available at the computation time.  In this research, we improve a methodology to estimate volatility and interest rate using Ensemble Kalman Filter (EnKF).  The price of call and put option used in the observation and the forecasting step of the EnKF algorithm computed using the solution of Black-Scholes PDE.  The state-space used in this method is the augmented state space, which consists of static variables: volatility and interest rate, and dynamic variables: call and put option price. The numerical experiment shows that the EnKF algorithm is able to estimate accurately the estimated volatility and interest rates with an RMSE value of 0.0506.Keywords: stochastic volatility; call option; put option; Ensemble Kalman Filter. AbstrakVolatilitas adalah faktor penting dalam perdagangan suatu opsi.  Dalam makalahnya yang dipublikasikan tahun 1973, Black dan Scholes mengasumsikan bahwa volatilitas harga saham, yang merupakan volatilitas sekuritas yang mendasari opsi beli, adalah konstan. Akan tetapi, para peneliti menemukan bahwa volatilitas pengembalian tidaklah konstan melainkan tergantung pada kumpulan informasi yang dapat digunakan pada saat perhitungan.  Pada penelitian ini dikembangkan metodologi untuk mengestimasi volatilitas dan suku bunga menggunakan metode Ensembel Kalman Filter (EnKF).  Harga opsi beli dan opsi jual yang digunakan pada observasi dan pada tahap prakiraan pada algoritma EnKF dihitung menggunakan solusi persamaan Black-Scholes.  Ruang keadaan yang digunakan adalah ruang keadaan yang diperluas yang terdiri dari variabel statis yaitu volatilitas dan suku bunga, dan variabel dinamis yaitu harga opsi beli dan harga opsi jual. Eksperimen numerik menunjukkan bahwa algoritma ENKF dapat secara akurat mengestimasi volatiltas dan suku bunga dengan RMSE 0.0506.Kata kunci: volatilitas stokastik; opsi beli; opsi jual; Ensembel Kalman Filter.
Co-Authors Agusfrianto, Fakhry Asad Agustine, Debby Andita Sulistyaningrum Annisaa Prima Hayati Binastya Anggara Sekti Bintang Sirius Dea Febriliana Fajri Debby Agustine Debby Agustine Faisal Nur Cahya Fakhry Asad Agusfrianto Fitriani Fitriani Ibnu Hadi Ibnu Hadi Lorensya Lorensya Lukita Ambarwati Lukita Ambarwati Muhammad Eka Suryana Muhammad Julian Nadilla Okta Permitasari Pratiwi, Rifa Khairunnisa Sandrina Widya Andani Siti Rohmah Rohimah Sudarwanto, Sudarwanto Syarifah Ayu Angela Tiara Nabila Vera Maya Santi Widyanti Rahayu Wiraningsih, Eti Dwi Zainati, Dini