EKSISTENSI SUPREMUM DAN INFIMUM DENGAN TEOREMA CANTOR DEDEKIND

In this paper, we will try to proof existence of supremum and infimum with Cantor Dedekind theorem. Before we discuss this material, necessary to introduce several basic concepts, especially Cut Dedekind and Supremum and Infimum concepts. The method we are presenting here is due to Richard Dedekind (1831-1916) whose work entitled What are and what should be numbers?. Cantor Dedekind theorem very important to show that nothing gap at real numbers system

Pemberdayaan Perangkat Desa Dalam Penyusunan Database dan Potensi Desa Berbasis Spasial di Desa Windu Kecamatan Biau Kabupaten Gorontalo Utara

Kegiatan KKN Tematik Desa Windu Kecamatan Biau Kabupaten Gorontalo Utara dengan Program Utama Penyusunan Basisdata spasial berupa peta citra batas desa, peta sarana dan prasarana desa dan pet potensi desa dilaksanakan selama 45 hari dengan melibatkan aparat desa. Keterlibatan aparat desa dalam kegiatan pengabdian ini adalah penentuan batas desa windu. Selain itu masyarakat juga dilibatkan untuk mengetahui mata pencaharian dan kegiatan masyarakat yang terkait dalam kehidupan sehari-hari. Pada akhir kegiatan mahasiswa yang didampingi oleh pembimbing Lapangan menyerahkan secara resmi Peta Potensi Desa Windu yang disaksikan oleh Kepala Desa, Sekretaris Desa, serta Tokoh Agama dan Masyarakat

MENYELESAIKAN PERSAMAAN DIFERENSIAL OSILATOR NON LINEAR DENGAN METODE KRYLOV BOGOLIUBOV

During a century and half of development and refinement of techniques, calculus consisted of these paired operations and their applications, primarily to physical problems. Newtons theory of fluxions, which was based on an intuitive idea of limit, would be familiar to any modern student of differential calculus once some changes in therminology and notation were made. But the vital observation, made by Newton and, independently, by Gottfried Leibniz, was that areas under curves could be calculated by reversing the differentiation process. The exciting technique, one that solved previously difficult area problems with ease, sparked enormous interest among the mathematicians of the era and led to a coherent theory that became known as the differential and integral calculus. This paper will develop the theory of diffentiation. We will assume that the reader is already familiar with the physical interpretations of derivative of a function as described in introductory calculus courses. Consequently, we will concentrate on the mathematical aspects of the derivative and the applications in physics. The first section is devoted to a presentation of the basic form of non-linear differential equations. A discussion of Krylov-Bogoliubov Method is also given. The material is of the greatest importance because this method can determine solution of non-linear differential equations. Keywords : Persamaan Diferensial Non Linear, Krylov Bogoliubo

Peran Media Pembelajaran Matematika sebagai Teknologi dan Solusi dalam Pendidikan Di Era Digitalisasi dan Disruption

Technology makes a very important contribution to mathematics learning. The main requirement for successful integration of technology in learning mathematics is about willingness and commitment to adapt to change through learning design activities by preparing the right learning tools and resources, including media. This study aims to determine the effectiveness of integrating media in mathematics learning in Grade VII of SMP Negeri 11 Gorontalo. The method used is descriptive which examines the teacher's ability to manage learning, student learning activities, responses, and learning outcomes. Based on the descriptive analysis of the results of research on the effectiveness of mathematics learning media as educational technology at SMP Negeri 11 Gorontalo with indicators of the teacher's ability to manage learning, student learning activities, student responses and classical learning outcomes it can be concluded that the teacher's ability to manage learning is categorized as effective, student activity is categorized effective, student responses to learning activities is positive, and classically complete learning outcomes. Thus, the integration of media in learning mathematics in Grade VII of SMP Negeri 11 Gorontalo can be said to be effective

Analisis Kesulitan Pembelajaran Daring pada Mata Pelajaran Matematika di Tengah Pandemi Covid-19

This study aims to describe the difficulties of online learning in mathematics subjects in the midst of the Covid-19 pandemic. This research is a descriptive research with a quantitative approach. The subjects in this study were students of class VIII 3 and VIII 4 at SMP Negeri 4 Gorontalo. Data collection was obtained from data from questionnaires and student interviews. To see student responses in online learning on mathematics subjects in the midst of the Covid-19 pandemic, a questionnaire was given with indicators, namely: (1) Difficulty in accessing the internet network and operating online media during learning, and (2) Difficulty in understanding objects, facts, concepts, principles and mathematical operations. Based on the data obtained from 61 students, there were 8 students in the high category, 41 students in the moderate category and 12 students in the low category. This means that the difficulty level of online learning in mathematics subjects in the midst of the Covid-19 pandemic in class VIII of SMP Negeri 4 Gorontalo is in the Medium category

Pengaruh Model Pembelajaran Student Facilitator And Explaining Terhadap Hasil Belajar Sisiwa Pada Materi Bentuk Aljabar

Telah banyak cara yang dilakukan untuk meningkatkan hasil belajar siswa pada pelajaran matematika. Salah satunya adalah dengan menerapkan berbagai jenis model pembelajaran. Dikarenakan sebagian siswa masih menganggap bahwa matematika sulit untuk dipelajari karena berhubungan dengan angka dan rumus. Pada penelitian ini, peneliti bertujuan untuk mengetahui apakah terdapat perbedaan hasil belajar siswa antara kelas yang menggunakan model pembelajaran student facilitator and explaining dengan kelas yang menggunakan model pembelajaran langsung.  Metode yang digunakan pada penelitian ini yaitu metode eksperimen dengan desain posttest only group design. Penelitian ini, memiliki populasi yaitu seluruh kelas VII SMP N 1 Telaga yang berjumlah 224 siswa. Sampel pada penelitian ini yaitu kelas VII3 dan VII5 yang diambil menggunakan Teknik cluster random sampling. Instrument tes hasil belajar siswa dan dokumentasi merupakan Teknik pengumpulan data yang digunakan. Analisi data dalam mengolah data hasil penelitian menggunakan uji normalitas, uji homogentas dan uji-t yang digunakan untuk menguji hipotesis penelitian. Hasil penelitian menunjukan, data penelitian berasal dari populasi yang berdistribusi normal serta varians dari data penelitian berisfat homogen atau sama. Uji hipotesis yang menggunakan uji-t menunjukan hasil bahwa thitung = 2,27 ≥ ttabel = 2,02. Ini berati, pengaruh dari model pembelajaran student facilitator and explaining lebih baik dari pada model pembelajaran langsung terhadap hasil belajar siswa. Dapat disimpulkan, bahwa  terdapat perbedaan hasil belajar siswa antara kelas yang menggunakan model pembelajaran student facilitator and explaining dengan kelas yang menggunakan model pembelajaran langsung pada materi aljabar kelas VII di SMP N 1 Telaga

Pengaruh Penggunaan Multımedıa Interaktıf Terhadap Hasıl Belajar Peserta Dıdık Pada Materı Sıstem Koordınat

Penelitian ini memiliki tujuan guna untuk melihat pengaruh multimedia interaktif terhadap hasil belajar peserta didik pada materi sistem koordinat. Penelitian ini adalah penelitian eksperimen dengan subjek penelitian yang diklasifikasikan menjadi dua yakni VIII-A selaku kelas eksperimen serta VIII-B selaku kelas kontrol pada populasi MTs Negeri 2 Bolaang Mongondow Utara. Dengan desain penelitian pre-test post-test control group design. Teknik pengumpulan data yaitu melalui instrumen tes setelah proses pembelajaran yang didasarkan pada indikator. Untuk mengukur hasil belajar peserta didik menggunakan pre-test dan post -test. Pengolahan data memakai analisis deskriptif memperlihatkan bahwasannya rata-rata hasil belajar peserta didik kelas eksperimen lebih tinggi jika diperbandingkan kelas kontrol. Adapun hasil analisis inferensial memperlihatkan bahwasannya kedua data berdistribusi normal serta homogen sehingga dilanjutkan dengan uji analisis kovarian (anacova) dan diperoleh hasil ditolak serta  diterima. Sehingga hasil penelitian menunjukkan bahwa hasil belajar peserta didik lebih tinggi setelah dibelajarkan menggunakan multimedia interaktif dibandingkan dengan menggunakan power point

Deskripsi Kemampuan Koneksi Matematis Siswa Pada Materi Teorema Pythagoras

This article discusses the description of students' mathematical connection abilities in solving mathematics on the Pythagorean theorem material. This descriptive research was conducted at SMP Negeri 1 Bolaang Uki in the odd semester of the 2019/2020 school year. The technique of data collection is done by test. Description test to obtain mathematical connection ability data. The results showed that the students' mathematical connection ability to recognize and use connections between mathematical ideas was 45.14%, the indicator of understanding how mathematical ideas were connected and built on one another to produce a coherent whole was 29.63%, and indicators of the introduction and application of mathematics in daily life by 23.61%

Efektivitas Pembelajaran Matematika Menggunakan Multimedia pada Materi Kerucut

This is descriptive research which aims to describe the effectiveness of learning by using multimedia in the cone materials of class IX MTs Al-Khairat Kwandang in the academic year 2019/2020 in terms of (1) the ability of teachers to manage learning, (2) positive student responses to learning, and (3) student learning outcomes test. Based on the analysis and discussion results, it can be concluded that learning mathematics using multimedia on cone material is effective. This is indicated by the ability of teachers to manage to learn has been categorized as very good, student responses in every aspect during the learning process are categorized as very positive, and the completeness of learning outcomes has reached 80% classically

PENGARUH MODEL PENEMUAN TERBIMBING TERHADAP HASIL BELAJAR PADA MATERI PRISMA DAN LIMAS DI SMP NEGERI I TALAGA JAYA

This research aims to look at the influence of guided discovery learning models on students' learning outcomes. The type of research used is experimental research. Sampling in this research was conducted by simple random sampling technique. Data collection was carried out using instruments in the form of observation sheets and tests of learning outcomes. The data obtained is then analyzed descriptively and inferentially. The results of the data analysis showed that the students’ learning outcomes taught by the guided discovery model are higher than students’ learning outcomes taught by conventional models, and the guided discovery model was effective in teaching material surface area and volume of upright and pyramid prisms