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All Journal Jurnal Fourier International Journal on Emerging Mathematics Education Journal of Mathematics UNP Jurnal Matematika Integratif
Uha Isnaini
Universitas Gadjah Mada
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering Transportation

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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.
Co-Authors Afit Istiandaru Agung Aldhi Prastya Burhanudin Arif Nurnugroho Fadhlan Zhaahiran Naelufa Syifna Wifaqotul Muna Puguh Wahyu Prasetyo, Puguh Rully Charitas Indra Prahmana