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JTAM (Jurnal Teori dan Aplikasi Matematika)
Published by Universitas Muhammadiyah Mataram
ISSN : 25977512     EISSN : 26141175     DOI : 10.31764/jtam
Core Subject : Education,
Mathematics
Jurnal Teori dan Aplikasi Matematika (JTAM) dikelola oleh Program Studi Pendidikan Matematika FKIP Universitas Muhammadiyah Mataram dengan ISSN (Cetak) 2597-7512 dan ISSN (Online) 2614-1175. Tim Redaksi menerima hasil penelitian, pemikiran, dan kajian tentang (1) Pengembangan metode atau model pembelajaran matematika di sekolah dasar sampai perguruan tinggi berbasis pendekatan konstruktivis (PMRI/RME, PBL, CTL, dan sebagainya), (2) Pengembangan media pembelajaran matematika berbasis ICT dan Non-ICT, dan (3) Penelitian atau pengembangan/design research di bidang pendidikan matematika, statistika, analisis matematika, komputasi matematika, dan matematika terapan.
Arjuna Subject : -
Articles 565 Documents
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Perbandingan Metode Halley dan Olver dalam Penentuan Akar-akar Penyelesaian Polinomial Wilkinson Darmawan, Randhi Nanang; Zazilah, Auda Nuril
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 3, No 2 (2019): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (113.93 KB) | DOI: 10.31764/jtam.v3i2.991

Abstract

Abstrak: Root finding adalah salah satu topik dalam metode numerik dalam menentukan akar suatu persamaan , biasanya persamaan tersebut dalam bentuk rumit dan sulit diselesaikan secara analitik. Dalam artikel ini suatu polinomial berderajat tinggi yaitu polinomial Wilkinson akan digunakan untuk menguji perbandingan akurasi metode Halley dan Olver, yang mana metode tersebut jarang digunakan karena kalah populer dengan metode Newton-Raphson, akan tetapi kedua metode tersebut memiliki kinerja yang cukup bagus dan lebih cepat konvergen dengan iterasi lebih sedikit. Berdasarkan hasil simulasi metode Halley pada iterasi ke-4 mendapatkan persentase galat 0,0029%, Metode Olver pada iterasi ke-5 mendapatkan persentase galat 0,0004% sedangkan metode Newton-Raphson membutuhkan iterasi ke-7 untuk mendapatkan persentase galat 0,0098%.Abstract:  Root finding is one of the topics in numerical methods for determaining roots of an equation  , usually that equation in the form of complicated and it will be difficult to be solved analytically. In this paper, high order polynomial like Polynomial Wilkinson will be used to test comparison the accuracy on Halley and Olver methods, which is those methods are rarely used for losing popular than Newton-Raphson method, but both methods had powerful performance and faster converging with less iteration.  Based on the simulation, Halley method on 4th iteration got percentage error  0,0029%, Olver method on 5th iteration got percentage error  0,0004%, while Newton-Raphson method are need  7th iteration got percentage error  0,0098%.
Analisis Pemodelan dan Simulasi Matematika Pengendalian Epidemi Toksoplasmosis Meri Hari Yanni; Zulfahmi Zulfahmi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 3, No 2 (2019): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (199.03 KB) | DOI: 10.31764/jtam.v3i2.1030

Abstract

Abstrak: Toksoplasmosis merupakan suatu penyakit pada manusia dan hewan yang disebabkan oleh parasit toksoplasma gondi. Penyebaran toksoplasmosis dapat dilakukan secara vertikal maupun horizontal. Penyebaran vertikal terjadi melalui ibu kepada anak sedangkan horizontal melalui lingkungan dan memakan makanan yang mentah. Lingkungan yang sanitasinya kurang memadai  serta kebiasaan masyarakat memakan daging yang mentah mengakibatkan individu terinfeksi toksoplasmosis. Kebiasaan masyarakat Aceh dalam mengkonsumsi daging menjadi salah satu potensi terinfeksinya toksoplasmosis sehingga diperlukan sosialisasi dan kajian terkait pengendalian epidemi toksoplasmosis. Penelitian ini bertujuan untuk mengkonstruksi model matematika epidemi toksoplasmosis yang mengacu pada masyarakat di wilayah Lhokseumawe. Model matematika dikonstruksi kedalam bentuk persamaan diferensial tak linier kemudian dianalisis kestabilan dari masing-masing titik kesetimbangan serta dilakukan penentuan bilangan reproduksi dasar untuk melihat tingkat penyebaran penyakit. Simulasi model menunjukkan bahwa ketika tidak adanya penyebaran penyakit toksoplasmosis maka tidak ada individu yang terinfeksi sedangkan ketika terjadinya penyebaran toksoplasmosis mengakibatkan jumlah populasi yang terinfeksi meningkat dan kemudian menurun dikarenakan jumlah populasi terkontrol ikut meningkat sehingga penyakit toksoplasmosis dapat hilang dari lingkungan. Abstract:  Toxoplasmosis is a disease in humans and animals which is caused by the parasite called toxoplasma gondi. The spread of toxoplasmosis can be done vertically or horizontally. Vertical spread occurs through mother and child, while horizontally through the environment and eating raw food. The inadequate sanitary environment and the community's habit of eating raw meat make the people infected by toxoplasmosis. The Acehnese habit in consuming meat is one of the potential infections of toxoplasmosis, so it is necessary to disseminate information and studies related to epidemic control of toxoplasmosis. This study aims to construct system differential non linear an epidemic mathematical model of toxoplasmosis that refers to people in Lhokseumawe area. The mathematical model constructed then analyzed the stability of each model equilibrium point and carried out the determination of basic reproduction numbers to see the extent of the spread of the disease. Simulation shows that when there is no spread of toxoplasmosis, no individual is infected. Whereas when the spread of toxoplasmosis happened, so the number of infected population increases and then decreases because the controlled population increases and toxoplasmosis can be disappeared from the environment.
Learning Mathematics with Contextual Approach to Improve Outcomes Learning Maths in Vocational High School Masruroh, Ani Ainun; Oktaviani, Rani; Kulsum, Sri Islami; Afrilianto, M.
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (837.995 KB) | DOI: 10.31764/jtam.v4i1.1870

Abstract

This research aims to improve student learning outcomes on mathematics learning by using a contextual approach. This research is a Class Action Research (CAR) conducted at one of the vocational schools (SMK) in X-class areas of focus on Automation of Governance and Office 3. The research instruments used in this study are (1) tests consisting of pre-test and post-test of the concept of Sigma notation and infinite series; and (2) the use of an observation sheet for teachers and students as a condition of measuring action execution. The procedure of the study consists of (1) planning, (2) The implementation of Action, (3) observation, (4) evaluation, and (5) reflection. The test results showed that there was an increase in pre-test and post-test results of 19.33%. Obviously, this shows that students ' learning outcomes on math learning are increasing after learning using a contextual approach.
Realistic Mathematics Education in Indonesia and Recommendations for Future Implementation: A Meta-Analysis Study Tamur, Maximus; Juandi, Dadang; Adem, Angela Merici G.
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (826.178 KB) | DOI: 10.31764/jtam.v4i1.1786

Abstract

This meta-analysis study aims to investigate the effectiveness of applying realistic mathematics education (RME) in Indonesia to students' mathematical abilities. This study analyzes 95 effect sizes from 72 studies that have been published in national and international journals or proceedings from 2010 to 2019. Comprehensive Meta-Analysis (CMA) software is used to aid analysis. As a result of the study, the overall effect size was 1.104, with a standard error of 0.065 according to the random-effects model. These results indicate that the average person who is ranked 13th in the experimental group is equivalent to those who are ranked 4th in the control group. This research was carried out by considering four characteristics, resulting in significant differences in terms of sample size and duration of treatment. Thus the application of RME in Indonesia is very effective in improving students' mathematical abilities by considering the sample size and duration of treatment.
Implementation of Art and Technology in Batik Purwakarta Ratnadewi, Ratnadewi; Pandanwangi, Ariesa; Prijono, Agus
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (207.662 KB) | DOI: 10.31764/jtam.v4i1.1872

Abstract

Indonesia is dominated by cities that have a history of batik, but Purwakarta does not have a history of batik. But thanks to the persistence of policy holders, Purwakarta currently has batik obtained by elevating the local wisdom of the city of Purwakarta. After surveys and interviews, several batik motifs were designed. The batik motif shape, size and position will be studied which will formulate mathematical equations based on basic geometric shapes such as circles, arches, lines, rectangles, which are implemented into the form of computer graphics (turtles) graph and explained in the form of an algorithm (pseudocode) computer programming to make autogenerative motifs on Purwakarta batik that did not exist before. Batik design is inspired by food and tourist locations which form the basis of the formation of typical Purwakarta batik motifs. Jatiluhur Dam, Datura Metel L. Flower, Sate Maranggi, Mangosteen Fruit is a local wisdom owned by the city of Purwakarta. The results of the morning glory batik design and Jatiluhur dew through mathematical and turtle charts are then formulated so that the batik motif design can be saved by documenting the mathematical equation or the pseudocode of the batik motif. With the results of digital motifs, the process of repeating patterns, duplicating and storing data becomes easier.
Application of Historical Burn Analysis Method in Determining Agricultural Premium Based on Climate Index Using Black Scholes Method Ariyanti, Devi; Riaman, Riaman; Irianingsih, Iin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v4i1.1799

Abstract

Farmers often suffer losses due to crop failure. The failure of the harvest is influenced by one of them is flooding, especially in Bandung which is quite frequent rain. Therefore one of the government's efforts to minimize losses from crop failures is the existence of an agricultural insurance program. The insurance system used is climate index insurance where the climate index is not plant insurance. This study aims to get a large premium to be paid by farmers using the Black-Scholes method. Meanwhile, to determine the climate index using the Historical Burn Analysis method. The results of this study are getting a variety of trigger values and exit values as well as the amount of premium that must be paid by farmers every planting season. Trigger values represent the minimum full payment limit. The exit value represents the maximum limit for no payment. The premium value obtained based on the selected trigger value also varies and is large enough so that it can be considered by farmers in choosing an agricultural insurance policy. Therefore, the method used must still be investigated to adjust to farmers, especially in Bandung.
Forecasting of Poverty Data Using Seasonal ARIMA Modeling in West Java Province Silalahi, Desri Kristina
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (753.518 KB) | DOI: 10.31764/jtam.v4i1.1888

Abstract

The government continues to carry out poverty reduction strategies in Indonesia, especially in West Java Province. West Java Province is a province that has the most populous population in Indonesia. This will affect the level of welfare and the amount of poverty. The strategy undertaken is inseparable from accurate poverty data and is available from year to year. Even from the available data, the government can forecast the number of poor people in the coming years. Seasonal Autoregressive Integrated Moving Average (SARIMA) method is one of forecasting methods. SARIMA is the development of the ARIMA model which has a seasonal effect. Based on the results of the study, that poverty data forecasting in the province of West Java using the SARIMA method obtained SARIMA model (0,1,1) (1,1,1)4. This model is the best model for forecasting data with an R-Squared value of 98%, Mean Square Error is 7.705.5800.000 and Mean Absolute Percentage Error IS 2,81%. It’s means this SARIMA model is very good in predicting poverty data in West Java Province.
Comparison of Logistic Regression Model and MARS Using Multicollinearity Data Simulation Wibowo, Ananto; Ridha, M. Rismawan
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (904.62 KB) | DOI: 10.31764/jtam.v4i1.1801

Abstract

There are several statistical methods used to model the effect of predictor variables on categorical response variables, namely logistic regression and Multivariate Adaptive Regression Splines (MARS). However, neither MARS nor logistic regression allows multicollinearity on any predictor variables. This study applies the use of both methods to the simulation data with principal component analysis as an improvement in multicollinearity to find out which regression has better performance. The result of the analysis shows that MARS is very powerful in modeling research simulation data. Besides, based on the criteria of the number of significant major components, accuracy, sensitivity, and specificity values, MARS has more appropriate performance than logistic regression.
Inquiry Co-Operation Model: An Effort to Enhance Students’ Mathematical Literacy Proficiency Malasari, Putri Nur; Herman, Tatang; Jupri, Al
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v4i1.1894

Abstract

The urgency and proficiency of students’ mathematical literacy in Bandung that have not been optimal are the basis of this study. The aim of this study is to explain the enhancement of students' mathematical literacy proficiency due to the implementation of the inquiry co-operation model (experimental class) and conventional learning (control class) in terms of basic mathematical proficiency. This study is a quasi-experimental study with a non-equivalent control group design, and the research subjects were seventy students of class VIII of Bandung that were selected through a purposive sampling technique. The research data was obtained through mathematical literacy tests of material in a polyhedron. The results of the data analysis showed that: (1) the enhancement in mathematical literacy proficiency of the experimental students class was better than the control studentsclass in terms of the basic mathematical proficiency (high and medium); (2) there is no significant difference in the increase of mathematical literacy proficiency in experimental students class in terms of the basic mathematical proficiency. It can be concluded that inquiry co-operation model espouses the enhancement of students' mathematical literacy proficiency.
Power Domination Number On Shackle Operation with Points as Lingkage Saifudin, Ilham
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 4, No 1 (2020): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (847.237 KB) | DOI: 10.31764/jtam.v4i1.1579

Abstract

The Power dominating set is a minimum point of determination in a graph that can dominate the connected dots around it, with a minimum domination point. The smallest cardinality of a power dominating set is called a power domination number with the notation . The purpose of this study is to determine the Shackle operations graph value from several special graphs with a point as a link. The result operation graphs are: Shackle operation graph from Path graph , Shackle operation graph from Sikel graph , Shackle operation graph from Star graph . The method used in this paper is axiomatic deductive method in solving problems. Understanding the axiomatic method itself is a method of deductive proof principles that applies in mathematical logic by using theorems that already exist in solving a problem. In this paper begins by determining the paper object that is the Shackle point operations result graph. Next, determine the cardinality of these graphs. After that, determine the point that has the maximum degree on the graph as the dominator point of power domination. Then, check whether the nearest neighbor has two or more degrees and analyze its optimization by using a ceiling function comparison between zero forching with the greatest degree of graph. Thus it can be determined ϒp minimal and dominated. The results of the power domination number study on Shackle operation graph result with points as connectors are , for  and ; , for  and ; , for  and .

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