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<![CDATA[PEMBELAJARAN STRUKTUR ALJABAR DENGAN MENGGUNAKAN SOFTWARE GAP ]]>
<![CDATA[Carnia, Ema]]>;
<![CDATA[Aisah, Isah]]>;
<![CDATA[Sylviani, Sisilia]]>
<![CDATA[ Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam Vol 19, No 2 (2014): Jurnal Pengajaran MIPA ]]>
Publisher : <![CDATA[Faculty of Mathematics and Science Education, Universitas Pendidikan Indonesia ]]>
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DOI: 10.18269/jpmipa.v19i2.455
<![CDATA[Strukur Aljabar sebagai salah satu mata kuliah wajib yang diberikan di Program Studi Matematika di Indonesia dirasakan sulit oleh sebagian besar mahasiswa. Sebagai salah satu alternatif untuk mengatasi hal itu maka diperkenalkan penggunaan software GAP (Group, Algorithm, and Programming) dalam proses belajar mengajar pada mata kuliah Strukur Aljabar. Selain mendukung dalam proses pembelajaran, penggunaan software GAP ini mendukung pemberlakuan Kurikulum Berbasis Kompetensi (KBK) di Perguruan Tinggi, khususnya di Program Studi Matematika, yang secara tidak langsung menuntut pembelajaran Student Centered Learning (SCL). Pengajaran dengan menggunakan software ini akan diujicobakan di Departemen Matematika FMIPA UNPAD. Dengan demikian diharapkan dapat memberikan motivasi untuk belajar Struktur Aljabar dengan cara yang tidak membosankan yang pada akhirnya dapat meningkatkan pemahaman mahasiswa terhadap mata kuliah tersebut. Penelitian ini baru sebatas kajian teori dan belum diimplementasikanKata kunci: GAP, Struktur Aljabar.]]>
<![CDATA[Kongruensi Unsur Idempoten Ortogonal dalam Aljabar Insidensi Finitary ]]>
<![CDATA[Carnia, Ema]]>;
<![CDATA[Wahyuni, Sri]]>;
<![CDATA[Irawati, Irawati]]>;
<![CDATA[Setiadji, Setiadji]]>
<![CDATA[ Jurnal Natur Indonesia Vol 13, No 2 (2011) ]]>
Publisher : <![CDATA[Lembaga Penelitian dan Pengabdian kepada Masyarakat Universitas Riau ]]>
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DOI: 10.31258/jnat.13.2.89-93
<![CDATA[Let X be a partially ordered set, R is a commutative ring with identity and FININC (X, R) denote finitary incidencealgebra of poset X over R. In this paper it will be seen congruence of two elements that are idempotent orthogonalin FININC (X, R) relative to the modulo Radical Jacobson of algebra. Review of this topic would be useful to examineisomorphism problems of the finitary incidence Algebra.]]>
<![CDATA[A COMPARISON OF CENTRALITY MEASURES IN SUSTAINABLE DEVELOPMENT GOALS ]]>
<![CDATA[Ariesandy, Sena]]>;
<![CDATA[Carnia, Ema]]>;
<![CDATA[Napitupulu, Herlina]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 14 No 3 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan ]]>
Publisher : <![CDATA[MATHEMATIC DEPARTMENT, FACULTY OF MATHEMATICS AND NATURAL SCIENCES, UNIVERSITY OF PATTIMURA ]]>
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DOI: 10.30598/barekengvol14iss3pp309-320
<![CDATA[The Millennium Development Goals (MDGs), which began in 2000 with 8 goal points, have not been able to solve the global problems. The MDGs were developed into Sustainable Development Goals (SDGs) in 2015 with 17 targeted goal points achieved in 2030. Until now, methods for determining the priority of SDGs are still attractive to researchers. Centrality measure is one of the tools in determining the priority goal points on a network by using graph theory. There are four measurements of centrality used in this paper, namely degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality. The calculation results obtained from the four measurements are compared dan analyzed, to conclude which goal points are the most prior and the least prior. Furthemore, in this paper we present other example with simple graph to show that each different centrality calculation possibly resulted different priority node, the calculation of this illustration is done using a Python’s library named NetworkX]]>
<![CDATA[PEMBELAJARAN STRUKTUR ALJABAR DENGAN MENGGUNAKAN SOFTWARE GAP ]]>
<![CDATA[Carnia, Ema]]>;
<![CDATA[Aisah, Isah]]>;
<![CDATA[Sylviani, Sisilia]]>
<![CDATA[ Jurnal Pengajaran MIPA Vol 19, No 2 (2014): JPMIPA: Volume 19, Issue 2, 2014 ]]>
Publisher : <![CDATA[Faculty of Mathematics and Science Education, Universitas Pendidikan Indonesia ]]>
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DOI: 10.18269/jpmipa.v19i2.36174
<![CDATA[ABSTRAKStrukur Aljabar sebagai salah satu mata kuliah wajib yang diberikan di Program Studi Matematika di Indonesia dirasakan sulit oleh sebagian besar mahasiswa. Sebagai salah satu alternatif untuk mengatasi hal itu maka diperkenalkan penggunaan software GAP (Group, Algorithm, and Programming) dalam proses belajar mengajar pada mata kuliah Strukur Aljabar. Selain mendukung dalam proses pembelaja-ran, penggunaan software GAP ini mendukung pemberlakuan Kurikulum Berbasis Kompetensi (KBK) di Perguruan Tinggi, khususnya di Program Studi Matematika, yang secara tidak langsung menuntut pembelajaran Student Centered Learning (SCL). Pengajaran dengan menggunakan software ini akan diujicobakan di Departemen Matematika FMIPA UNPAD. Dengan demikian diharapkan dapat mem-berikan motivasi untuk belajar Struktur Aljabar dengan cara yang tidak membosankan yang pada akhirnya dapat meningkatkan pemahaman mahasiswa terhadap mata kuliah tersebut. Penelitian ini baru sebatas kajian teori dan belum diimplementasikanABSTRACTAs one of the compulsory subjects given in the Mathematical Studies Program in Indonesia, Algebraic Structure is perceived as difficult by most students. One alternative to overcome it is by introducing the use of GAP software (Group, Algorithm, and Programming) in teaching and learning for Algebraic Structure course. In addition to support the learning process, the use of GAP software support the implementation of the Competency Based Curriculum in universities, especially in Mathematics Program, which indirectly requires Student Centered Learning (SCL). Teaching with this software will be tested in Department of Mathematics Faculty of Mathematical and Natural Sciences. Hence the use of it is expected to provide the motivation to learn algebraic structure in a way that is not boring, and will subsequently increase students’ understanding of the course. This research is a theoretical study and has not been implemented yet.]]>
<![CDATA[Karakterisasi Subgrup Sylow Solvable Dari Grup Poin Senyawa Fosfor Pentaklorida ]]>
<![CDATA[Ema Carnia Carnia]]>;
<![CDATA[Sisilia Sylviani]]>;
<![CDATA[Elah Dewia]]>
<![CDATA[ Jurnal Sains Dasar Vol 6, No 2 (2017): October 2017 ]]>
Publisher : <![CDATA[Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta ]]>
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DOI: 10.21831/jsd.v6i2.15295
<![CDATA[Setiap molekul atau senyawa kimia memiliki operasi simetri yang mendeskripsikan keseluruhan karakter dari molekul tersebut. Himpunan dari semua operasi simetri yang berlaku pada suatu senyawa akan membentuk suatu grup. Semua operasi simetri yang berlaku pada senyawa Fosfor pentaklorida membentuk grup poin. Pada paper ini dibahas karakterisasi dari grup poin senyawa Fosfor pentaklorida dilihat dari sudut pandang teori grup. Salah satu hasil yang diperoleh adalah bahwa setiap subgrup Sylow dari senyawa Fosfor pentaklorida merupakan grup solvable.Kata kunci: simetri, grup poin, teori grup, p-subgrup Sylow, solvableCHARACTERIZATION OF SOLVABLE SYLOW SUBGROUP OF POINT GROUP PHOSPHORUS PENTACHLORIDE COMPOUNDPhosphorus pentachloride is a gaseous chemical compound. One of the uses of this compound is a substance that can accelerate the rate of chemical reactions. Phosphorus pentachloride compounds has a molecular geometry shape trigonal bipyramid with a total of 12 symmetry operations. The set of all symmetry operations completed with the operation of the function composition will form a group called the D_3h point group. In this paper discuss the characterization the points group of Phosphorus pentachloride compound from the perspective of group theory. Beginning with point group proofing, then determine all Sylow p-subgroup and normal subgroups of this group.The results obtained were the properties that Sylow 2-subgroup and Sylow 3-subgroup of Phosphorus pentachloride compounds and slices between Sylow subgroups and normal subgroup is solvable groups. Keywords: Phosphorus pentachloride, point group, group theory, Sylow p-subgroup, solvable]]>
<![CDATA[PENGGUNAAN GROUP, ALGORITHM, AND PROGRAMMING (GAP) DALAM PEMBELAJARAN GRUP KUOSIEN ]]>
<![CDATA[Sisilia . Sylviani]]>;
<![CDATA[Ema . Carnia]]>;
<![CDATA[Isah . Aisah]]>
<![CDATA[ KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 1, No 2 (2015): Karismatika ]]>
Publisher : <![CDATA[Universitas Negeri Medan ]]>
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DOI: 10.24114/jmk.v1i2.17067
<![CDATA[ABSTRAK Pada paper ini akan dibahas suatu alternative metode pembelajaran yang dapat digunakan dalam menyampaikan materi Grup Kuosien/ Grup Faktor pada matakuliah Struktur Aljabar. Grup Kuosien sebagai salah satu materi dalam Struktur Aljabar sering kali dirasakan sulit oleh sebagian besar mahasiswa S1 Jurusan Matematika. Untuk itu, diperlukan suatu metoda pembelajaran yang dapat memudahkan mahasiswa untuk memahami materi tersebut. Salah satu alternatif yang dapat dilakukan adalah dengan menggunakan software GAP (Group, Algorithm, and Programming) sebagai alat bantú dalam mempelajar imateri Grup Kuosien. GAP dapat membuat penyajian konsep grup kuosien menjadi lebih menarik. Sehingga, diharapkan dapat lebih memudahkan mahasiswa untuk memahami konsep Grup Kuosien.Keywords: Grup Kuosien, Group algorithm and programming, Struktur Aljabar ABSTRACT This paper will discuss an alternative method of learning which can be used in presenting the Quotient Group/ Factor Group material in Abstract Algebra course. Quotient group as one of the materials in Abstract Algebra is often perceived difficult by most of undergraduate mathematics students. For that, we need a method of learning which can facilitate the students to understand the material. One of the alternatives that can be done is by using GAP (Group, Algorithm, and programming) software as a tool in studying the quotient group material. GAP can make a presentation of the quotient group concept becomes more attractive. Thus, it can be easier for students to understand the concept of quotient group.Keywords: Quotient Group, Group Algorithm And Programming, Abstract Algebra]]>
<![CDATA[Quasi-Associative Algebras on the Frobenius Lie Algebra M_3 (R)⊕gl_3 (R) ]]>
<![CDATA[Henti Henti]]>;
<![CDATA[Edi Kurniadi]]>;
<![CDATA[Ema Carnia]]>
<![CDATA[ Al-Jabar: Jurnal Pendidikan Matematika Vol 12, No 1 (2021): Al-Jabar: Jurnal Pendidikan Matematika ]]>
Publisher : <![CDATA[Universitas Islam Raden Intan Lampung, INDONESIA ]]>
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DOI: 10.24042/ajpm.v12i1.8485
<![CDATA[In this paper, we study the quasi-associative algebra property for the real Frobenius Lie algebra of dimension 18. The work aims to prove that is a quasi-associative algebra and to compute its formulas explicitly. To achieve this aim, we apply the literature reviews method corresponding to Frobenius Lie algebras, Frobenius functionals, and the structures of quasi-associative algebras. In the first step, we choose a Frobenius functional determined by direct computations of a bracket matrix of and in the second step, using an induced symplectic structure, we obtain the explicit formulas of quasi-associative algebras for . As the results, we proved that has the quasi-associative algebras property, and we gave their formulas explicitly. For future research, the case of the quasi-associative algebras on is still an open problem to be investigated. Our result can motivate to solve this problem. ]]>
<![CDATA[The Existence of Affine Structures on the Borel Subalgebra of Dimension 6 ]]>
<![CDATA[Edi Kurniadi]]>;
<![CDATA[Ema Carnia]]>;
<![CDATA[Herlina Napitupulu]]>
<![CDATA[ ComTech: Computer, Mathematics and Engineering Applications Vol. 12 No. 1 (2021): ComTech ]]>
Publisher : <![CDATA[Bina Nusantara University ]]>
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DOI: 10.21512/comtech.v12i1.6581
<![CDATA[The notion of affine structures arises in many fields of mathematics, including convex homogeneous cones, vertex algebras, and affine manifolds. On the other hand, it is well known that Frobenius Lie algebras correspond to the research of homogeneous domains. Moreover, there are 16 isomorphism classes of 6-dimensional Frobenius Lie algebras over an algebraically closed field. The research studied the affine structures for the 6-dimensional Borel subalgebra of a simple Lie algebra. The Borel subalgebra was isomorphic to the first class of Csikós and Verhóczki’s classification of the Frobenius Lie algebras of dimension 6 over an algebraically closed field. The main purpose was to prove that the Borel subalgebra of dimension 6 was equipped with incomplete affine structures. To achieve the purpose, the axiomatic method was considered by studying some important notions corresponding to affine structures and their completeness, Borel subalgebras, and Frobenius Lie algebras. A chosen Frobenius functional of the Borel subalgebra helped to determine the affine structure formulas well. The result shows that the Borel subalgebra of dimension 6 has affine structures which are not complete. Furthermore, the research also gives explicit formulas of affine structures. For future research, another isomorphism class of 6-dimensional Frobenius Lie algebra still needs to be investigated whether it has complete affine structures or not.]]>
<![CDATA[STABILITY ANALYSIS OF TUNGRO DISEASE SPREAD MODEL IN RICE PLANT USING MATRIX METHOD ]]>
<![CDATA[Ati Maryati]]>;
<![CDATA[Nursanti Anggriani]]>;
<![CDATA[Ema Carnia]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 1 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol16iss1pp215-226
<![CDATA[Rice is one of the staple foods produced from the rice plant. Rice productivity is increased by carrying out efforts to control diseases that usually attack rice plants. Tungro is one of the most destructive diseases of rice plants. Mathematical models can help solve problems in the spread of plant diseases. In this paper, the development of a mathematical model for the spread of tungro disease in rice plants with 6 compartments is developed involving rice in the vegetative and generative phases. Furthermore, stability analysis is carried out on the obtained model by using the Basic Reproduction Number ( ) search through the matrix method, especially through the search for transition matrices and transmission matrices. The analytical results show that when 1 the non-endemic equilibrium point is stable and when >1 the endemic equilibrium point is stable. Numerical results showed that rice plants in the generative phase were more infected than rice plants in the vegetative phase.]]>
<![CDATA[Struktur Aljabar Koszul pada Aljabar Lie M_(3,1) (R)⋊〖gl〗_3 (R) ]]>
<![CDATA[Nur Hafizhah]]>;
<![CDATA[Edi Kurniadi]]>;
<![CDATA[Ema Carnia]]>
<![CDATA[ Pythagoras: Jurnal Matematika dan Pendidikan Matematika Vol 17, No 1: June 2022 ]]>
Publisher : <![CDATA[Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY ]]>
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DOI: 10.21831/pythagoras.v17i1.39713
<![CDATA[Dalam penelitian ini dipelajari aljabar Lie affine aff(3) berdimensi 12 yang merupakan jumlah semi langsung dari ruang vektor matriks berukuran 3x1 dan aljabar Lie matriks berukuran 3x3 . Tujuan penelitian ini adalah untuk membuktikan eksistensi dan struktur aljabar koszul pada aljabar Lie aff(3). Aljabar Lie tersebut adalah aljabar Lie Frobenius. Oleh karena itu, terdapat suatu fungsional linear yang mengakibatkan nilai fungsional linear pada matriks strukturnya tidak sama dengan nol. Fungsional linear yang demikian ini disebut fungsional Frobenius. Dalam penelitian ini diberikan juga bagaimana mendapatkan matriks struktur, menghitung determinannya serta memilih fungsional Frobenius yang tepat. Hasil yang diperoleh dalam penelitian ini adalah rumus eksplisit struktur aljabar koszul pada aljabar Lie affine berdimensi 12 melalui induksi pada bentuk simplektik dari fungsional Frobeniusnya. Sebagai bahan diskusi untuk penelitian selanjutnya, hasil yang diperoleh dapat dikembangkan untuk menentukan struktur aljabar koszul pada aljabar Lie affine berdimensi n(n+1). Structure of Koszul Algebra in Lie Algebra M_(3,1) (R)⋊〖gl〗_3 (R)AbstractIn this research, we study the affine Lie algebra aff(3) of 12 dimension which is the semi-direct sum of the vector space of a matrix of 3x1 and Lie algebra of a matrix of 3x3. The research aims to prove the existence and structure of koszul algebras on the affine Lie algebra aff(3) . Since its Lie algebra is Frobenius then there exists a linear functional whose values in the matrix structure are not equal to zero. Such a linear functional is called a Frobenius functional. Furthermore, in this study, it is also given how to obtain the structure matrix, to calculate its determinants, and to choose the right Frobenius functional. The results obtained in this study are explicit formulas for the structure of the koszul algebra on 12-dimensional Lie affine algebra through induction in the symplectic form of its Frobenius functional. As a discussion material for further research, the results obtained can be developed to determine the structure of koszul algebra in affine Lie algebra of dimension n(n+1).]]>
