In this thesis we discuss the diagram forms of semigroup presentations and . The discussion starts with the word-word outlines of semigroup presentations and . Then it is proceeded to make a diagram of word-word description obtained. All of characteristics are expressed in the form of a semigroup diagram theorem. The discussion in this article refers to Guba, V. & M. Sapir. 1996. Diag…
This research purposed to produced the mathematics learning devices based on problem based learning on social arithmetic material for VII grade students of SMP/MTs. Learning devices in this research are syllabus, Lesson Plans, and Student’s Worksheet. The research method used is the 4D models which consists of the stage define, design, development dan disseminate, but in this research only ca…
This research is motivated by the limited mathematics learning tools that are in accordance with the 2013 Curriculum. The purpose of this study is to produce products in the form of learning tools that are Syllabus, RPP, and Student Activity Sheet (LAS) by using discovery learning models in the material of Quadrilateral and Triangle VII class of SMP/MTs . The development model used in this stud…
The background of this research is the difference between the expected achievement and the achieved by students of class VIII4 SMP Negeri 8 Pekanbaru. The proposes of this research are to improve the learning process, to increase mathematics achievement from the students, and to increase student percentage that reaches Minimum Mastery Criteria (MMC) with applied problem based learning model. Th…
This final project discusses the predator-prey model with three-order interactions using the Routh-Hurwitz criteria. This model uses a nonlinear differential equation system from the classical predator-prey model. The observed model consists of four equilibrium points. Analysis for the model is carried out at the non-negative equilibrium point using the Routh-Hurwitz criteria. Then simulat…
This final project studies the global asymptotic stability of a Holling-Tanner predator-prey model using Holling type II. The global asymptotic stability is investigated using the Lyapunov method based on the equilibrium point that has been obtained. This final project is a review of articles of Lisena [Mathematical Methods in the Applied Sciences, 41 (2017), 1-12]. Keywords: Predator-prey…
This research is a class action research that aims to improve the learning process and mathematics learning outcomes through the implementation of the Problem Based Learning (PBL) model. The subjects of this research were VIII.7 grade students of SMP Negeri 5 Pekanbaru in the academic year 2019/2020, which total of participants are 38 students, consists of 20 male students and 18 female student…
This research was conducted due to limited mathematics learning devices that corresponds to The 2013 Curriculum. This research aims to produce learning devices by Problem Based Learning (PBL) model on Linear Program material of class XI. The development model used is 4-D that consist of define, design, develop, and disseminate. The research instrument used is validity device and practicality de…
Penelitian ini dilatarbelakangi oleh rendahnya kemampuan pemecahan masalah matematis (KPMM) siswa SMA Negeri 8 Pekanbaru. Tujuan penelitian ini adalah: (1) mendeskripsikan perbedaan KPMM siswa yang mengikuti pembelajaran melalui model Problem Based Learning (PBL) dengan siswa yang mengikuti pembelajaran biasa dengan pendekatan saintifik; (2) mengetahui peningkatan KPMM siswa yang mengikuti pemb…
The background of this research is the low ability of mathematical problem solving skill of students class X SMA Negeri 8 Pekanbaru. The purposes of this research are 1) to describe the difference of mathematical problem solving skill of students who study through PBL model with student who study through conventional learning with scientific approaching; 2) to examine the improvment of mathemat…
This final project discusses the epidemic model of chickenpox disease with vaccination (SVEIR) which has two equilibrium points, namely disease-free and endemic equilibrium points. Analysis of the global stability of the equilibrium points is carried out using the Lyapunov function which shows that the spread is determined by basic reproduction numbers. Then the simulation is performed usi…
Analysis of predator-prey acarine models in trophic level is discussed in this final project. The system of differential equation of the predator-prey acarine model is used in each population. The model consists of three observed equilibrium points. The stability of the system around the equilibrium point is determined by the linearization method in order to obtain the characteristic equati…
The background of this research is the difference between the expected achievement and the achieved by students of class XI MIA 1 MA Muhammadiyah Pekanbaru. The proposes of this research are to improve the learning process and to increase mathematics achievement from the students with applied discovery learning model. The form of this research is a class action research which is carried out in …
This research is a classroom action research (CAR) that aims to find out the improvement of mathematics learning outcomes through the application of Think Pair Square (TPS) Type Cooperative learning. The subjects of this study were Class VII-A students of SMP Negeri 1 Bangkinang Kota in the odd semester of the academic year 2019/2020, with a total of 30 students, consisting of 13 men and 17 wom…
The learning process is seen as one of the main factors that influence learning outcomes so that this research aims to improve learning process and students’ mathematics learning achievement by applying Discovery Learning model. This research is a classroom action research with two cycles. The research instruments used are mathematical learning instruments (Syllabus, Lesson Plans, and Activit…
This final project discusses Winter’s Smoothing model and ARMA(p, q) model with numerical computation. Both of these models are used to predict the availability of rice stock at BULOG Pekanbaru in 2015 by considering the seasonal factor from time series span data. Then a comparison is carried out for both forecasting models to select the right forecasting model with minimum Mean Square E…
This nal project discusses the stability analysis in Lotka-Volterra model of the three species consisting of two predators and one prey introduced by Hadziabdic et al. [Technology Education Management Journal, 6 (2017), 132-136]. The analysis was conducted on the stability of the equilibrium point based on eigen- values. This model has three equilibrium points of which one is unstable, a…
This final project discusses the use of shifted Jacobi polynomials to solve Abels integral equations of the second type. The process begins by approaching the integral that appears with the shifted Jacobi polynomials. Then a system of linear equations is formed, which their solutions are constants to be used as the coefficients to form a linear combination of the shifted Jacobi polynomials …
This thesis discusses alternative definitions of triangular fuzzy numbers to be positive and negative based on the area comparison, and given alternative arithmetic for triangular fuzzy numbers. Next, these definitions are applied to solve the fully fuzzy linear system using the decomposition method. Keywords: Triangular fuzzy numbers, alternative arithmetic, fully fuzzy linear system, decom…
This research is classroom action resesarch that aim to improve the mathematics learning outcomes with applied the learning cooperative model of Numbereds Heads Together (NHT)type. The research consist of two cycles, each cycles has four stages, which are planning, implementation, observation, and reflection. The subject of this research is students of class VIIA SMP Negeri 35 Pekanbaru in acad…