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All Journal Jurnal Matematika UNAND Journal for Lesson and Learning Studies
Arief Budiman, Muhammad
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Computer Science & IT Education Mathematics Other

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KEEFEKTIFAN MODEL PEMBELAJARAN THINK TALK WRITE DENGAN MEDIA PUZZLE TERHADAP KEMAMPUAN MEMBACA PERMULAAN PESERTA DIDIK KELAS II SDN REJOSARI 03 SEMARANG Nizma, Syecha Nurun; Asri Untari, Mei Fita; Arief Budiman, Muhammad
Journal for Lesson and Learning Studies Vol 3, No 1 (2020): April
Publisher : Universitas Pendidikan Ganesha

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23887/jlls.v3i1.24266

Abstract

Keefektifan Model Pembelajaran Think Talk Write Dengan Media Puzzle Terhadap Kemampuan Membaca Permulaan Peserta Didik Kelas II SDN Rejosari 03 Semarang. Penelitian ini bertujuan untuk mengetahui keefektifan Model Think Talk Write (TTW). Jenis penelitian yang digunakan pada penelitian ini adalah kuantitatif, dengan desain penelitian yaitu One-Grup Pretest-Posttest design. Berdasarkan hasil analisis yang telah dilakukan rata-rata skor yang diperoleh saat pretest mencapai 62,86 dan posttest mencapai 85,36. Berdasarkan hasil pada uji t diperoleh harga thitung>ttabel yaitu 10,127 > 1,703, maka H0 ditolak dan Ha diterima. Sehingga dapat disimpulkan bahwa Model Think Talk Write (TTW) dengan Media Puzzle Efektif Terhadap Kemampuan Membaca Permulaan Kelas II SDN Rejosari 03 Semarang.Kata Kunci: Keefektifan, Model Pembelajaran, TTW, Think Talk Write, Kemampuan membaca permulaan.
Analysis of the Brownian Motion on the Matrix Lie Group SO(2) for Determining a Short-Term Interest Rate Model: A Simulation Approach Arief Budiman, Muhammad; Kurniadi, Edi; Sukono
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.132-149.2026

Abstract

In this paper, we observe the special orthogonal matrix Lie group containing of all 2x2 real matrices, denoted by SO(2), which can be geometrically visualized as the one-dimensional torus S1 which is nothing but the unit circle. A Brownian motion on SO(2) can be constructed and represented by a stochastic differential equation defined over a dynamic state space. The research aims to derive a short-term interest rate model on SO(2) through Brownian motion analysis which is a geometric approach. We employ a qualitative methodology, including a literature review of Brownian motion, stochastic differential equations, and dynamical state-space techniques on SO(2). Firstly, we prove the isomorphism SO(2) is isomorphic to S1, secondly, we determine Brownian motion on SO(2) and its equivalent, and thirdly, we formulate the corresponding stochastic differential equation, and the last, determine the short-term interest rate equation on SO(2). In this study, it is confirmed Lim and Privault’s work that the interest rate equation on SO(2) is given by rt = beta + 2 gamma cos(Wt) with beta, gamma is constant and Wt is standard Brownian motion. To clarify the obtained results, this study also gave a quantitative approach that is Python simulation of interest rate calculation using the matrix Lie group interest rate and other equations. The interest rate equation uses the matrix Lie group SO(n) with n greater than or equal to three still open to further research that can be applied to long-term interest rates.
Co-Authors Edi Kurniadi Mei Fita Asri Untari Nizma, Syecha Nurun Sukono