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<![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).]]>
<![CDATA[Aljabar Semiprima Mendasar dan Aplikasinya pada Protokol Autentikasi ]]>
<![CDATA[Khurul Wardati]]>;
<![CDATA[Muhammad Zaki Riyanto]]>
<![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.v17i1.48982
<![CDATA[Library research dengan pendekatan deduksi-induksi ini bertujuan untuk mengkaji kesemiprimaan mendasar aljabar tak bebas yang dibangun secara hingga atas ring komutatif unital. Tujuan secara praktis penelitian ini adalah mengaplikasikan suatu contoh aljabar semiprima mendasar yang non-komutatif pada protokol autentikasi berdasarkan masalah dekomposisi. Di samping itu, aljabar semiprima mendasar lebih umum dari aljabar semiprima, hal ini ditunjukkan dengan suatu contoh penyangkal. Hasil utama dari penelitian ini adalah suatu aljabar yang dibangun secara hingga bersifat semiprima mendasar jika dan hanya jika ideal dasar nol merupakan irisan dari semua ideal dasar prima. Lebih lanjut ideal dasar nol merupakan satu-satunya ideal dasar nilpoten. Syarat perlu dan cukup ini serupa dengan sifat aljabar semiprima, dan pembuktian sifat-sifat ini pada keduanya memerlukan konsep annihilator. The basically semiprime algebra and its application on authentication protocolAbstractThis library research is conducted with a deductive-inductive approach. The aim of this study is to explore the basically semiprimeness of the finitely generated non-free algebra over a commutative unital ring. The basically semiprime algebra is more general than a semiprime algebra, which is proven by a counterexample. In theory, Theorem 12 is the main result of the study. The finitely generated algebra over a commutative unital ring is basically semiprime, if and only if, the zero basic ideal is the intersection of all prime basic ideals, if and only if, the zero basic ideal is the only nilpotent basic ideal. These necessary and sufficient conditions are analogous to the properties of a semiprime algebra, and proving these properties in both requires a concept of annihilator. The practical aim of this research is to apply an example of non-commutative basically semiprime algebra in an authentication protocol based on the decomposition problem.]]>
<![CDATA[Specialized Content Knowledge Lower Secondary School Teachers on Quadrilaterals ]]>
<![CDATA[Sadrack Luden Pagiling]]>;
<![CDATA[Khumaeroh Dwi Nur'aini]]>
<![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.v17i1.42446
<![CDATA[The teachers' knowledge of specific content has a positive relationship with the students' mathematics achievement. Mathematics teachers must have an appropriate level to ensure mathematics learning effectively. The quadrilateral is one of the essential contents in geometry. However, many teachers did not successfully deliver and teach this content in classroom instruction. Therefore, this qualitative study explores the specialized content knowledge of lower secondary teachers in defining and classifying quadrilaterals. Four teachers, two male and two female teachers, were recruited to become participants in this work. All participants have similar teaching experience and do not hold an educator certificate. A test and semi-structured interviews were assigned to obtain specialized content knowledge of the teachers on quadrilaterals. The interview data were analyzed in three stages: data condensation, data presentation, and conclusion drawing. The findings show that only one teacher understands hierarchically in defining and classifying quadrilaterals, two teachers are at the partial prototype level because they cannot see the hierarchical relationship between the quadrilaterals, and another teacher is at the prototype understanding level because it relies on the prototype of quadrilaterals' shape. These findings suggest that lower secondary teachers' special content knowledge of quadrilateral needs to be strengthened through workshops and training professional development.]]>
<![CDATA[Problem Solving Videos sebagai Media Teknologi Asistif untuk Memfasilitasi Mahasiswa Tunarungu di Kelas Inklusif ]]>
<![CDATA[Sugiman Sugiman]]>;
<![CDATA[Emi Pujiastuti]]>;
<![CDATA[Ziyana Endah Khairun Nisa']]>
<![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.v17i1.48637
<![CDATA[Beberapa Perguruan Tinggi sekarang ini membuka kesempatan bagi siswa disabilitas misalnya tunarungu untuk menjadi mahasiswa di kelas inklusif. Oleh karena itu, penulisan artikel ini bertujuan untuk membahas: (1) Cara memberikan peran kepada mahasiswa tunarungu di kelas insklusif agar dapat ikut berpartisipasi dalam kegiatan ilmiah berupa diskusi dalam kelompok kecil mahasiswa. (2) Cara menyediakan media teknologi asistif berupa problem solving videos untuk memfasilitasi mahasiswa tunarungu di kelas inklusif dalam diskusi ilmiah. Langkah untuk mencapai tujuan tersebut dilakukan dengan cara: (1) pelatihan dan pendampingan mahasiswa dalam berbahasa isyarat, (2) mixed method yang menggabungkan R D dan pendekatan kualitatif. R D untuk menemukan keabsahan media teknologi asistif berupa problem solving videos, sedangkan pendekatan kualitatif untuk mengungkap aspek tanggapan subjek penelitian terhadap pemakaian media teknologi asistif berupa problem solving videos. Hasil yang diperoleh adalah: (1) Setelah dilaksanakan pelatihan dan pendampingan dalam berbahasa isyarat pada semua mahasiswa di kelas inklusif, mahasiswa tunarungu dapat terlibat pada kegiatan diskusi pada materi perkuliahan. (2) Semua subjek penelitian memberikan tanggapan positif dan mendukung ketersediaan media teknologi asistif berupa problem solving videos untuk memfasilitasi mahasiswa tunarungu di kelas inklusif dalam melakukan diskusi ilmiah.Problem Solving Videos as Assistive Technology Media to Facilitate Deaf Students in Inclusive ClassAbstractSeveral universities currently open opportunities for students with disabilities, such as the deaf to become students in inclusive classes. Therefore, the purpose of this article is to discuss: (1) how to give roles for deaf students in the class to be able to participate in scientific activities as discussion in small student groups; (2) how to provide assistive technology which is the problem-solving videos to facilitate deaf students in scientific discussion in the inclusive class. To achieve the purposes carried out: (1) training and monitoring students in sign language, (2) mixing the method by combining R D method and qualitative approaches. R D to find the validity of assistive technology media in the form of problem solving videos, while the qualitative approach is to reveal aspects of research subjects' responses to the use of assistive technology media in the form of problem solving videos. The results from this research are: (1) After training and assistance in sign language have been carried out for all students in the inclusive class, deaf students can be involved in discussion activities on lecture material. (2) All research subjects gave positive responses and supported the availability of assistive technology media in the form of problem solving videos to facilitate students with hearing impairment in the inclusive class in scientific discussions.]]>
<![CDATA[Model Identifikasi Singkong Berdasarkan Warna untuk Tepung Mocaf Berbasis Citra Digital ]]>
<![CDATA[Sri Andayani]]>;
<![CDATA[Ega Noviastuti]]>
<![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.v17i1.34994
<![CDATA[Penelitian ini bertujuan menghasilkan model untuk mengidentifikasi mutu singkong berdasarkan warna sebagai bahan pembuatan tepung mocaf dengan berbasis citra digital. Metode yang digunakan meliputi beberapa tahap pengolahan citra digital antara lain preprocessing dan ekstraksi ciri. Preprocessing meliputi cropping, resizing, dan grayscaling, sedangkan ekstraksi ciri meliputi segmentasi threshold dan binerisasi. Data penelitian menggunakan 118 citra singkong yang dibagi menjadi 72 citra data latih dan 46 data uji. Hasil penelitian berupa model identifikasi yang mendasarkan pada dua hal berikut: a) menggunakan ekstraksi ciri yang meliputi segmentasi threshold dengan nilai ambang 170 dan binerisasi dengan nilai ambang 75; dan b) penentuan mutu singkong dilakukan berdasarkan perbandingan luas piksel putih hasil segmentasi threshold dengan luas piksel putih hasil binerisasi. Singkong dikatakan bermutu baik jika citranya yang memiliki persentase luas piksel warna putih lebih besar atau sama dengan 65%. Model yang dihasilkan memberikan akurasi sebesar 94% terhadap 72 data latih dan sebesar 95% terhadap 46 data uji. Cassava Identification Model Based on Color for Mocaf Flour Using Digital ImageAbstractThis study aims to produce a model to identify the quality of cassava-based on color as an ingredient for making mocaf flour based on digital images. The procedure includes preprocessing and feature extraction among other steps of digital image processing. Preprocessing includes cropping, resizing, and grayscaling, while feature extraction includes threshold segmentation and binaryization. The data are 188 cassava images consisting of 72 training data images and 46 test data. The result of the study is an identification model based on the following two things: a) utilizing feature extraction that uses threshold segmentation with a threshold value of 170 and binaryization with a threshold value of 75; and b) determining of the quality of cassava is carried out based on the ratio of the area of white pixels produced by threshold segmentation to the area of white pixels produced by binaryization. If 65% or more of the pixels in the image are white, the cassava has a good quality. The resulting model provides an accuracy of 94% for 72 training data and 95% for 46 test data.]]>
<![CDATA[Development of Mathematics E-Book on Pythagorean Theorem Material ]]>
<![CDATA[Dyah Shinta Lintang Intyassandy]]>;
<![CDATA[Destiniar Destiniar]]>;
<![CDATA[Ety Septiati]]>
<![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.v17i1.44968
<![CDATA[This study aims to determine the response and potential effects of using a mathematics e-book on the Pythagorean theorem material. The method used in the development of this ebook is ADDIE. The research data was obtained through student response questionnaires, and student learning outcomes test The subjects used were 15 grade VIII students of SMP Negeri 3 Mesuji Raya, Kab. Ogan Komering Ilir, South Sumatra. Based on the results of data analysis, student responses about practicality obtained the criteria of "very practical" with an average percentage of 86.22%. While the potential influence aspect is stated to have "potential influence" with an average percentage of 86.66% of the student learning outcomes test. The Pythagorean theorem mathematics e-book is suitable for students to use and can be developed on other materials.]]>
<![CDATA[Algoritme Migrating Birds Optimization dan Algoritme Particle Swarm Optimization: Penyelesaian Masalah Knapsack 0-1 ]]>
<![CDATA[Bib Paruhum Silalahi]]>;
<![CDATA[Mohamad Novanto]]>;
<![CDATA[Prapto Tri Supriyo]]>
<![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.v17i1.35660
<![CDATA[Permasalahan knapsack merupakan salah satu masalah optimisasi. Masalah knapsack merupakan suatu permasalahan bagaimana memilih objek dari beberapa objek yang akan dimasukkan ke media penyimpanan dengan masing-masing objek memiliki bobot dan total bobot dari objek yang dipilih tidak boleh melebihi kapasitas media penyimpanannya, sehingga diperoleh nilai yang maksimal. Ketika objek yang dimasukkan ke dalam media penyimpanan bersifat harus dimasukkan semua atau tidak sama sekali, permasalahan ini dikenal dengan nama knapsack 0-1. Salah satu metode penyelesaian masalah knapsack 0-1 adalah dengan menggunakan metode meta-heuristic. Terdapat beberapa metode meta-heuristic seperti algoritma migrating birds optimization dan particle swarm optimization. Paper ini membahas bagaimana algoritma migrating birds optimization dan particle swarm optimization digunakan dalam menyelesaikan permasalahan knapsack 0-1. Kemudian dilakukan perbandingan kinerja kedua algoritma tersebut berdasarkan nilai fungsi tujuan untuk beberapa studi kasus. Berdasarkan hasil penelitian ini algoritme migrating birds optimization mempunyai nilai hasil fungsi objektif yang lebih baik dibandingkan dengan algoritma particle swarm optimization.Migrating Birds Optimization Algorithm and Particle Swarm Optimization Algorithm: Knapsack problem solving 0-1AbstractThe knapsack problem is one of the optimization problems. The knapsack problem is a problem of how to select objects from several objects to be inserted into the storage with each object having a weight and the total weight of the selected object must not exceed the capacity of the storage so that the maximum value is obtained. When objects that are inserted into the storage have the character of having to be included all or nothing, this problem is known as the 0-1 knapsack. One of the methods of solving the 0-1 knapsack problem is by using the meta-heuristic method. There are several meta-heuristic methods such as the migrating birds optimization algorithm and particle swarm optimization. This paper discusses how migrating birds optimization and particle swarm optimization algorithms are used to solve the 0-1 knapsack problem. Then the performance of the two algorithms is compared based on the objective function values for several case studies. Based on the results of this study, the migrating birds optimization algorithm has better objective function values than the particle swarm optimization algorithm.]]>
<![CDATA[Tinjauan Matematis Waktu Tundaan pada Model Covid-19 dengan Vaksinansi ]]>
<![CDATA[Fitriana Yuli Saptaningtyas]]>;
<![CDATA[Ahmadi Ahmadi]]>
<![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.v17i1.49372
<![CDATA[Artikel ini membahas pemodelan matematika penyebaran Covid-19 dengan vaksinasi yang melibatkan waktu tundaan. Waktu tundaan merepresentasikan waktu individu mengalami penurunan kekebalan tubuh sehingga kembali rentan terhadap Covid-19 setelah sembuh. Kita tahu bahwa individu yang dinyatakan sembuh dari Covid-19 dapat terinfeksi kembali. Penelitian ini menganalisa titik ekuilibirum beserta kestabilannya, menentukan bilangan reproduksi dasar untuk melihat penyebaran penyakit, menentukan jenis bifurkasi yang muncul yang diakibatkan oleh waktu tundaan, dan melakukan simulasi numerik untuk melihat perilaku penyebaran penyakit. Di samping itu juga dilakukan kajian analitik untuk menentukan bilangan reproduksi dasar dan analisa perbandingan kestabilan lokal untuk model tanpa waktu tundaan dan dengan waktu tundaan. Hasil dari analisis terhadap model didapat dua titik ekuilibrium, yakni satu bebas penyakit dan satu endemik. Pada model dengan waktu tundaan diperoleh bahwa waktu tundaan tertentu dapat menyebabkan munculnya solusi periodik artinya akan terjadi fluktuasi banyaknya individu yang terinveksi pada periode waktu tertentu. Simulasi numerik dengan mengubah ubah parameter waktu tundaan dan tingkat vaksinasi menunjukkan pada kondisi endemik model dengan waktu tundaan akan menyebabkan lebih banyak individu yang terinveksi dari pada model tanpa waktu tundaan. Mathematical Overview of Time Delay on Covid 19 Models with VaccinationAbstractThis article discusses the mathematical modeling of the spread of Covid-19 with vaccination which involves a time delay. The time delay is represented when an individual experiences a decreased immune system so that he is declared susceptible to Covid-19 after recovering. Because we know that individuals who are declared cured of Covid-19 can be reinfected, this study analyzes the equilibrium point of the model and its stability, determines the primary reproduction number to see the spread of the disease, determines the type of bifurcation that appears due to the time delay, and performs numerical simulations. To see the behavior of the spread of the disease. In addition, analytical studies were carried out to determine the primary reproduction number and local stability comparison analysis for models without time delay and with time delay. The model analysis results obtained two equilibrium points, one free of disease and one endemic. In the time-delayed model, the value of the time-delay parameter is obtained, which causes the emergence of a periodic solution, meaning that there will be fluctuations in the number of individuals infected in a certain period. Numerical simulations by changing the time delay parameters and vaccination rates show that in endemic conditions, models with time delays will cause more individuals to be infected than models that do not use time delays.]]>
