Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika
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Implementasi Game Theory Dalam Penentuan Strategi Bersaing Pada Produk Sepeda Motor
No full textCompetition in the business world, especially land transportation equipment, is currently getting tighter with its use in people\u27s lives, one of which is motorbikes. Its use is very easy and very helpful in everyday life, causing many people to be interested in it. This research aims to determine competitive strategies in motorbike product competition by applying mathematical methods, namely Game Theory. The research results obtained show competition between Honda motorbike products and Yamaha motorbike products with Honda\u27s optimal strategy being product quality, while the optimal strategy for Yamaha motorbike products to compete with Honda motorbike products is model and spare parts
Unveiling The Hidden Mathematics In Traditional Indonesian Culinary Art: An Exploration of Knot Theory And Alexander Polynomial in Ketupat Telur
No full textThis research delves into the intriguing relationship between mathematical concepts and traditional Indonesian cultural heritage, particularly in the context of ketupat telur. By applying the theory of knots (knot theory) as a field of topology, the study aims to identify geometric patterns that underlie the making of ketupat telur, as well as to understand the role of symmetry in the formation of knots. The main focus of this research is the ketupat telur knot diagram with 13 points of intersection and Alexander polynomial calculations, as an alternative method for obtaining knot polynomials. The results of the geometric structure analysis of ketupat telur with Alexander polynomial calculations yield:
Ak=-t3+7t2-18t+23-18t-1+7t-2-t-3
This finding produces a polynomial that reflects its geometric and structural properties. This illustrates how fundamental mathematical concepts such as knots and polynomials can be applied to culture to achieve a deeper understanding of both
Aplikasi Metode Entry Age Normal dan Projected Unit Credit untuk Asumsi Tingkat Kenaikan Gaji Dalam Menentukan Manfaat Pensiun
No full textAbstrak. Dana Pensiun adalah badan hukum yang mengelola dan menjalankan program yang menjanjikan manfaat pensiun. Penelitian ini bertujuan untuk mengetahui besar kewajiban aktuaria dan iuran normal dana pensiun dalam asumsi tingkat kenaikan gaji manfaat pensiun menggunakan metode Entry Age Normal dan Projected Unit Credit kemudian mempertimbangkan metode yang lebih menguntungkan antara keduanya. Dalam hal ini menggunakan data guru pegawai negeri sipil (PNS) berjenis kelamin laki-laki dan perempuan. Total iuran normal menggunakan metode EAN salah satu peserta sebesar Rp 59.155.658,93 dan metode PUC salah satu peserta sebesar Rp 139.183.314,55 dan Total kewajiban aktuaria menggunakan metode EAN salah satu peserta sebesar Rp 4.273.776.585,00, dan metode PUC salah satu peserta sebesar Rp 3.427.911.903,77. Hasil perhitungan menunjukkan besar iuran normal dengan asumsi tingkat kenaikan gaji menggunakan metode Entry Age Normal pada pegawai laki-laki dan Perempuan adalah konstan setiap tahunnya. Akan tetapi dengan menggunakan metode Projected Unit Credit pada pegawai pria dan wanita nilai iuran normalnya meningkat dengan pertambahan masa kerja. Jumlah kewajiban aktuaria dengan asumsi tingkat kenaikan gaji yang dihitung menggunakan metode Entry Age Normal lebih besar daripada metode Projected Unit Credit pada pertengahan tahun kepesertaan.
Kata kunci: Asumsi Kenaikan Gaji; Iuran Normal; Kewajiban Aktuaria; Entry Age Normal; Projected Unit Credit
Abstract. A Pension Fund is a legal entity that manages and runs a program that promises pension benefits. This study aims to determine the amount of actuarial obligations and normal contributions of pension funds in assuming the level of salary increase in pension benefits using the Normal Entry Age method and Projected Unit Credit then consider a more profitable method between the two. In this case, using data on civil servant (PNS) teachers are male and female. The total normal contribution using the EAN method of one of the participants is IDR 59,155,658.93 and the PUC method of one of the participants is IDR 139,183,314.55 and the total actuarial obligation using the EAN method of one of the participants is IDR 4,273,776.58 ,, and the PUC method of one of the participants is IDR 3,427,911,903.7 7.. The calculation results show the amount of normal contributions assuming the rate of salary increase using the Normal Entry Age method for male and female employees is constant every year. However, by using the Projected Unit Credit method for male and female employees, the value of contributions normally increases with the increase in length of service. The amount of actuarial liabilities assuming the salary increase rate calculated using the Normal Entry Age method is greater than the Projected Unit Credit method in the middle of the membership year.
Keywords: Salary Increase Assumption; Normal Dues; Actuarial Obligations; Normal Entry Age; Projected Unit Credit
 
Peningkatan Pemahaman Konsep Matematika Siswa Kelas XI-2 SMAN 2 Bantul dengan Pendekatan Culturally Responsive Teaching (CRT) Berbantuan Google Sites
No full textKurangnya pemahaman konsep matematika dapat menghambat kemampuan siswa dalam memecahkan masalah matematika yang lebih kompleks dan mempersiapkan mereka untuk tantangan di dunia nyata. Tujuan penelitian ini adalah untuk mendeskripsikan peningkatan kemampuan pemahaman konsep matematika siswa dengan pembelajaran dengan pendekatan Culturally Responsive Teaching (CRT) berbantuan google sites. Penelitian ini dilakukan menggunakan metode PTK (Penelitian Tindakan Kelas) dengan subjek 36 Siswa kelas XI-2 SMA N 2 Bantul. Hasil tes pemahaman konsep matematika siswa XI-2 SMA N 2 Bantul dengan pendekatan CRT berbantuan google sites setelah dilaksanakan di siklus I memiliki nilai rata-rata 68,61 dengan nilai tertinggi 90 dan terendah 30. Dari 36 siswa hanya 13 siswa (36,11%) yang mencapai nilai KKM dan 23 siswa (63,88%) yang belum mencapai nilai KKM. Dari siklus I yang nilai rata-ratanya 68,61% meningkat menjadi 90,69%. Dari total 36 siswa, 33 siswa (91,67%) diantaranya berhasil mencapai KKM dan yang belum mencapai KKM ada 3 siswa (8,3%). Secara keseluruhan, hasil penelitian ini dapat disimpulkan bahwa pemahaman konsep matematika siswa kelas XI-2 SMA N 2 Bantul dengan Pendekatan CRT berbantuan Google sites berhasil mengalami peningkatan
Peramalan Penerimaan Pajak Kendaraan Bermotor Menggunakan Metode Triple Exponential Smoothing di Sumatera Utara
No full textAt this time, motorized vehicles have become a primary need. Therefore, it is necessary to take into account revenues for motor vehicle taxes so that the government has a good motor vehicle tax calculation produce is one aspect of revenue management that is very helpful in achieving the goals set by the government. Therefore, it is necessary to estimate motor vehicle tax revenues correctly so that it can be seen how much revenue will be managed properly. The purpose of this research is to get the forecast value of motor vehicle tax revenue for the next year with a low MAPE. The method used is the Triple Exponential Smoothing method with a constant alpha = 0,3 and obtains a MAPE of less than 10 % which means it is very good. The results of this study there are several districts / cities that experienced a decrease in motor vehicle tax revanues
Penggunaan Model Pembelajaran Knisley Berbasis Kontruktivisme dalam Meningkatkan Self Confidence Mahasiswa
No full textMathematics education plays a crucial role in the cognitive and affective development of students, including self-confidence in understanding the material. This study aims to evaluate the impact of the Knisley learning model based on constructivism on students\u27 self-confidence. The Knisley learning model provides direct experiences, group collaboration, and individual reflection, which is presumed to enhance students\u27 self-confidence in mathematics learning. This research employs a quantitative approach with an experimental design. The study population consists of 34 fourth-semester students from IAIN Tadris Matematika, divided into two groups: experimental and control. The instrument used in this study is a self-confidence questionnaire. Data collected from the questionnaires distributed to both groups were analyzed to determine the difference in average self-confidence scores between the experimental group using the Knisley constructivism-based model and the control group not using this model. The results indicate that the experimental group had a higher average self-confidence score (45.52) compared to the control group (61.05). The significant value obtained from SPSS testing is 0.0000, which is smaller than the significance level (α = 0.05), indicating that H1 is accepted. Therefore, it can be concluded that students\u27 self-confidence using the Knisley constructivism-based learning model is better than that of students not using the Knisley model, meaning there is an effect of implementing the Knisley constructivism-based learning model on the self-confidence of Tadris Mathematics students. The Knisley constructivism-based model in mathematics learning provides relevant learning contexts, encourages active interaction, and facilitates reflection that supports the development of self-confidence. Thus, the application of this learning model has proven to be effective in enhancing students\u27 self-confidence in mathematics learning
Pengembangan Media Pembelajaran Matematika Berbasis Android pada Materi Sistem Persamaan Linear di Kelas X SMK Negeri 1 Ketapang
No full textPenelitian ini bertujuan untuk mengembangkan aplikasi Android sebagai media ajar matematika pada materi sistem persamaan linear untuk siswa SMK kelas X Ketapang yang mencapai tingkat kevalidan, kepraktisan, dan keefektifan. Metode penelitian yang digunakan dalam penelitian ini adalah Metode Pengembangan (Research and Development/ R & D). Rancangan penelitian yang digunakan dalam penelitian ini adalah model ADDIE yang terdiri atas lima tahapan pokok, yaitu analisis, rancangan, pengembangan, implementasi dan evaluasi. Subjek dalam penelitian ini adalah siswa kelas X SMK sebanyak 30 siswa dan 3 orang ahli media dan materi. Instrumen yang digunakan dalam penelitian ini adalah lembar validasi ahli media dan ahli materi, angket respon guru dan respon siswa, dan soal post-test. Hasil penelitian validasi aplikasi berbasis android yaitu validasi media dengan nilai rata-rata dari ketiga ahli sebesar 93,33% dalam kriteria sangat valid. Sedangkan hasil penelitian validasi materi diperoleh skor rata-rata 97,14% dalam kriteria sangat valid. Yang kedua adalah nilai kepraktisan, dilihat dari nilai angket yang diisi guru dan seluruh siswa yang diakumulasikan sehingga diperoleh persentase sebesar 92,01,% dengan kriteria sangat praktis. Selanjutnya keefektifan, dilihat dari nilai hasil pengerjaan post-test siswa dengan jumlah siswa yang tuntas sebanyak 22 orang dari 30 orang dengan persentase 73,33% dan nilai rata-rata siswa yang dihitung dengan rumus skor rata-rata dan dipersentasekan dengan keseluruhan nilai siswa sehingga diperoleh nilai sebesar 78,2 dengan berpatokan pada nilai KKM sekolah yaitu 70, maka rata-rata hasil tes siswa memiliki kriteria tuntas dan tergolong sangat efektif
Exploring The Future of Health Through The SELR Mathematical Model with Time Delay on The Risk of Diabetes Among Mathematics Students of FMIPA UNM Due to Unhealthy Lifestyles
No full textThis study aims to build a SELR model with a time delay in diabetes cases, analyze the model, and conduct simulations to predict the incidence of diabetes. This study is a combination of theoretical and application studies. The analysis of the SELR model with a time delay is focused on diabetes cases, while the simulation is carried out using Maple Software. The study population was active students of FMIPA UNM, with a sample size of 1,000 students obtained using the Slovin technique. This study produces a mathematical model of SELR with a time delay for diabetes cases represented as a system of differential equations. Model analysis shows the existence of an equilibrium point free from diabetes cases and a stable endemic equilibrium point. In addition, the results of this study found the basic reproduction number (R₀) for cases without a solution of 25.97333855, which means that one individual can affect 25-26 people in the FMIPA UNM environment. However, if the solution is applied, the R₀ value decreases to 0.7502918529, indicating that there is no psychological spread, where each individual does not affect other individuals
SOLUSI PERMASALAHAN PHUBBING REMAJA AKIBAT KECANDUAN SMARTPHONE MELALUI PENERAPAN NILAI SIPAKATAU, SIPAKAINGE, SIPAKALEBBI DENGAN ANALISIS MODEL MATEMATIKA DI KOTA MAKASSAR
No full textPhubbing is a social problem caused by various factors, one of which is smartphone addiction. This research aims to build a SEAR mathematical model of phubbing problems among adolescents due to smartphone addiction, analyse and simulate the model to predict the number of phubbing cases in Makassar City, and find parameter solutions to this problem. The population in this study consists of adolescents aged 10-14 years in Makassar City, with a sample size of 399 people. The research stages carried out were: building a SEAR model of the phubbing problem, determining the equilibrium point, analysing the stability of the equilibrium point, determining the value of the basic reproduction number , carrying out model simulations using Maple, and interpreting the simulation results. In this paper, it is obtained a SEAR mathematical model for the problem of phubbing; two equilibrium points, namely the phubbing-free and the phubbing equilibrium point; stability of the phubbing-free and phubbing equilibrium point; and the basic reproduction number 3.459 which shows that phubbing cases occur in adolescents with a percentage increase of 1.3% every year. Based on the model simulation, the results obtained show that the parameter solutions in the form of applying the 3S values can reduce the rate of phubbing due to smartphone addiction among adolescents in Makassar City
Mathematical Topology Meets Tradition: Alexander Polynomial Analysis of Sidalungguh Ketupat Weaving Patterns
No full textThis research aims to describe the relationship between mathematics and culinary culture, specifically focusing on ketupat, particularly the Sidalungguh Ketupat. Using knot theory applications, this study examines how mathematics and culinary culture are interconnected. This analysis was conducted by comparing the knots in the ketupat with knot theory literature, leading to the creation of knot diagrams. Through identification using Alexander polynomials, the following result was obtained:
This research was conducted to explore the scientific potential in examining mathematics through traditional food.
This research aims to describe the relationship between mathematics and culinary culture, specifically focusing on ketupat, particularly the Sidalungguh Ketupat. Using knot theory applications, this study examines how mathematics and culinary culture are interconnected. This analysis was conducted by comparing the knots in the ketupat with knot theory literature, leading to the creation of knot diagrams. Through identification using Alexander polynomials, the following result was obtained:
This research was conducted to explore the scientific potential in examining mathematics through traditional food