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All Journal Jurnal Matematika & Sains Jurnal Fourier BAREKENG: Jurnal Ilmu Matematika dan Terapan International Journal on Emerging Mathematics Education Community Empowerment Journal of Fundamental Mathematics and Applications (JFMA) Journal of Mathematics UNP Jurnal Matematika Integratif
Uha Isnaini
Universitas Gadjah Mada, Yogyakarta, Indonesia
Arts Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation

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Pembentukan Ring Bersih Menggunakan Lokalisasi Ore Isnaini, Uha; Wijayanti, Indah Emilia
Jurnal Matematika dan Sains Vol 19 No 1 (2014)
Publisher : Institut Teknologi Bandung

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Abstract

Misalkan diberikan sebarang ring R (tidak harus komutatif) dan himpunan multiplikatif S Í R yang tidak memuat elemen nol. Lokalisasi Ore merupakan salah satu teknik pembentukan ring sehingga setiap elemen S memiliki invers di ring yang baru. Ring hasil lokalisasi tidak selalu mempertahankan sifat ring awal. Suatu ring sebarang dapat disisipkan ke  ring bersih, ring bersih-n dan ring peralihan. Pada paper ini akan dikaji sifat-sifat yang diperlukan untuk menyisipkan sebarang ring ke ring tersebut menggunakan lokalisasi. Kata kunci : Lokalisasi Ore, Elemen Satuan, Ring Bersih, Ring Peralihan, Ring Bersih-n.   Construction of Clean Ring using Ore Localization Abstract Let R be any ring (can be non commutative) and S Í R is a multiplicative set that does not contain any zero element. Ore localization is a powerful technique to construct a universal S-inverting ring. However the localization results do not always inherit properties of the first ring. An arbitrary ring can be inserted into the clean ring, n-clean ring, and exchange ring. Here, we show properties needed to insert any ring to the ring using localization. Keywords: Ore Localization, Unity, Clean Ring, Exchange Ring, n-Clean Ring.
Pembentukan Ring Bersih Menggunakan Lokalisasi Isnaini, Uha
Jurnal Matematika dan Sains Vol 21 No 1 (2016)
Publisher : Institut Teknologi Bandung

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Abstract

Diberikan sebarang ring R (tidak harus komutatif) dan himpunan multiplikatif S R  yang tidak memuat elemennol. Lokalisasi Ore merupakan salah satu teknik pembentukan ring sehingga setiap elemen S memiliki invers di ringyang baru. Ring hasil lokalisasi tidak selalu mempertahankan sifat ring awal. Suatu ring sebarang dapat disisipkanke ring bersih, ring bersih-n dan ring peralihan. Sehingga sangat menarik untuk dikaji sifat-sifat yang diperlukanuntuk menyisipkan sebarang ring ke ring tersebut menggunakan lokalisasi.
Beberapa Sifat Ideal Bersih-N Uha Isnaini
Jurnal Fourier Vol. 5 No. 2 (2016)
Publisher : Program Studi Matematika Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1073.489 KB) | DOI: 10.14421/fourier.2016.52.65-70

Abstract

Diketahui R ring dengan elemen satuan dan I ideal di R. Dalam tulisan ini akan dikaji ideal bersih-n yang merupakan perumuman ideal bersih dan belum pernah dikaji oleh peneliti sebelumnya. Ideal I disebut ideal bersih-n jika untuk setiap elemen ideal I dapat dinyatakan dalam jumlahan suatu idempoten di R dengan n buah unit di R. Dalam tulisan dibicarakan beberapa sifat dari ideal bersih-n yang meliputi : definisi dan contoh ideal bersih-n, hubungan antara ideal bersih-n dengan ideal peralihan, sifat ideal bersih-n jika dikaitkan dengan isomorfisma, Kartesian produk dari ideal bersih-n, serta pembentukan matriks atas ideal bersih-n.
Developing Number Theory Textbook for Pre-Service Mathematics Teacher of International Program Rully Charitas Indra Prahmana; Puguh Wahyu Prasetyo; Afit Istiandaru; Uha Isnaini; Burhanudin Arif Nurnugroho
International Journal on Emerging Mathematics Education IJEME, Vol. 5 No. 2, September 2021
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/ijeme.v5i2.19779

Abstract

The long-term objective of this research is to produce valid, practical, and effective textbooks for courses in international program of mathematics education of Universitas Ahmad Dahlan. For the short-term, this research aims to produce valid and practical textbook for number theory course. The validity was based on the relevancy towards the students’ expected competence, while the practicality was measured from the implementation of learning using the textbook. This research used design research with the type of development studies. It followed four steps, i.e. (1) preliminary research, (2) prototyping stage, (3) summative evaluation, and (4) systemic reflection and documentation. In the preliminary research, we analyzed the need of the textbook in the international program and found that the textbook of number theory course is very needed. In the prototyping stage, we wrote the textbook based on the need analysis. The prototype was then discussed with expert and revised in the stage of summative evaluation and applied to the lecture meetings. The result was the final product of the textbook used for the stage of systemic reflection and documentation when we wrote all the results according to the preset research framework. Finally, the developed number theory textbook is valid and practical.
Interpretasi Kombinatorial Kongruensi Fungsi Partisi Biner Modulo 2 Agung Aldhi Prastya; Uha Isnaini
Journal of Mathematics UNP Vol 8, No 1 (2023): Journal Of Mathematics UNP
Publisher : UNIVERSITAS NEGERI PADANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/unpjomath.v8i1.14255

Abstract

A partition of a positive integer n is a non-increasing sequence of finite positive integers such that the sum is equal to n. One thing that is studied by some researchers in integer partition is binary partition. A binary partition of a positive integer n is a non-increasing sequence of finite positive integers that are powers of 2 and sum to n. The number of binary partitions of n is denoted by b(n) and is called the binary partition function. In this study, we provides a combinatorial interpretation of a congruence of binary partition functions modulo 2. The interpretation involves dividing all binary partitions of n into two sets with the same cardinality using a bijective function that maps binary partitions satisfying certain conditions to binary partitions satisfying other conditions.
Residu b_{4,6}(n) terhadap modulo 2 dan 3 Fadhlan Zhaahiran; Uha Isnaini
Journal of Mathematics UNP Vol 8, No 1 (2023): Journal Of Mathematics UNP
Publisher : UNIVERSITAS NEGERI PADANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/unpjomath.v8i1.14329

Abstract

Integer partition is a branch of number theory that is still developing today. A partition of a positive integer n is a way to express   as a sum of positive integers without counting the order. Let   denote the number of partitions of  . We discover arithmetic properties of   which is the number of partitions of an integer n where the parts are not multiple by 4 or 6.
Bukti Alternatif Beberapa Fungsi Pembangkit pada Partisi dengan Penjumlah Ditandai Naelufa Syifna Wifaqotul Muna; Uha Isnaini
Jurnal Matematika Integratif Vol 17, No 1: April 2021
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (289.49 KB) | DOI: 10.24198/jmi.v17.n1.31528.43-49

Abstract

Partisi bilangan bulat merupakan salah satu cabang ilmu yang berkembang sangat pesat di bidang teori bilangan. Suatu partisi dari bilangan bulat positif n adalah barisan tak naik atas bilangan bulat positif sedemikian hingga jumlahnya adalah n. Beberapa kelompok peneliti mengkaji partisi dengan tambahan sifat tertentu. Salah satu kelompok tersebut adalah Andrews, Lewis dan Lovejoy yang memperkenalkan partisi dengan penjumlah ditandai. Suatu partisi dari bilangan bulat  tak negatif  disebut partisi dengan penjumlah ditandai jika setiap penjumlah dari partisi tersebut ditandai tepat satu. Selanjutnya PD(n) menyatakan banyaknya partisi dari  dengan penjumlah ditandai. Kelompok lain, yaitu Chen, Ji, Jin dan Shen, mengkaji 3-diseksi dari PD(n) menggunakan sifat-sifat pecahan kubik kontinu Ramanujan. Di paper ini ditunjukkan bukti alternatif dari 3-diseksi dari PD(n) yang diperoleh oleh kedua kelompok tersebut.
Training and development of flipbook learning resources for Master Bimbel in Malang Regency Fitria Khasanah; Uha Isnaini; Eko Pujiati; Marsono Marsono; Syarifah Inayati
Community Empowerment Vol 9 No 3 (2024)
Publisher : Universitas Muhammadiyah Magelang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31603/ce.10342

Abstract

Master Tutoring aims to help students study at home since the Covid-19 pandemic, when learning at school had to be done online. To realize innovative guidance, there is a system for using learning media, control cards for student progress reports, and regular learning evaluations for tutoring teachers. Apart from that, Master Tutoring plans to package teaching materials that will attract students' interest so that they are more motivated in learning. Thus, the aim of the IndoMS Serving activity is to improve the ability of Master Bimbel tutors in packaging teaching materials in the form of flipbook learning resources. The method used is Master Bimbel tutor training activities, which are carried out in several stages, including: 1) coordination, 2) training on the use of Canva and Heyzine, and 3) flipbook development. The results of this activity show an increase in the knowledge and skills of Master Bimbel tutors in developing teaching materials in the form of flipbook learning resources, which have been applied to Master Bimbel students.
Bukti Alternatif Sifat Simetri Fungsi Partisi Crank Dyson-Andrews-Garvan Prastya, Agung Aldhi; Jituprasojo Hatma, Carolus Pasha Lazuardi; Isnaini, Uha
Jurnal Matematika Integratif Vol 20, No 1: April 2024
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v20.n1.53676.47-62

Abstract

Partisi dari suatu bilangan bulat positif n adalah barisan tak naik atas bilangan bu-lat positif berhingga sehingga jumlahnya adalah n. Salah satu hal yang dikaji olehbeberapa peneliti dalam partisi bilangan bulat adalah fungsi crank. Untuk setiap bi-langan bulat positif n dan partisi x dari n, crank dari x didefinisikan sebagai penjum-lah terbesar di x jika x tidak memuat penjumlah 1; sebagai selisih antara banyaknyapenjumlah yang lebih dari banyaknya penjumlah 1 di x dan banyaknya penjumlah 1di x. Didefinisikan fungsi crank M(m, j, n) yang menyatakan banyaknya partisi darin dengan crank kongruen m modulo j. Pada penelitian ini, dibahas terkait buktialternatif sifat simetri fungsi partisi crank, yaitu M(m, j, n) = M(−m, j, n). Buktidiberikan menggunakan interpretasi kombinatorial melalui konstruksi fungsi bijektifyang memetakan partisi dengan syarat tertentu ke partisi dengan syarat tertentulainnya.
Learning With Error for Digital Image Encryption Setiawan, Aisyah Nooravieta; Wijayanti, Indah Emilia; Isnaini, Uha
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 2 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i2.21073

Abstract

Learning With Error (LWE) is one of the development of a system linear equation that add some noise or error. These problems have good potential for cryptography, especially for the development of Key Exchange Mechanism (KEM). Moreover, the question is whether LWE can be applied for digital image security or not. The digital image consists of hundreds of pixels that can be interpreted as a matrix. Each Pixel is encrypted with LWE so that the image becomes unidentified or cipher.
Co-Authors Afit Istiandaru Afit Istiandaru, Afit Agung Aldhi Prastya Ali, Saifullah Burhanudin Arif Nurnugroho Fadhlan Zhaahiran Fauzi, Prastudy Fitria Khasanah Handayani, Annisa Dini Indah Emilia Wijayanti Jituprasojo Hatma, Carolus Pasha Lazuardi Marsono Marsono Muna, Naelufa Syifna Wifaqotul Naelufa Syifna Wifaqotul Muna Prastya, Agung Aldhi Puguh Wahyu Prasetyo, Puguh Pujiati, Eko Rully Charitas Indra Prahmana Setiawan, Aisyah Nooravieta Syarifah Inayati Wijaya, Yosua Feri Yeni Susanti