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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.
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Articles 21 Documents
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Search results for , issue "Vol 8, No 2 (2024): April" : 21 Documents clear
An Inclusive Distance Irregularity Strength of n-ary Tree Wijaya, Kristiana; Aulia, Safira Nur; Halikin, Ikhsanul; Kusbudiono, Kusbudiono
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20549

Abstract

An inclusive distance vertex irregular labelling of a simple graph G is a function of the vertex set of  to positive integer set such that the sum of its vertex label and the labels of all vertices adjacent to the vertex are distinct. The minimum of maximum label of the vertices is said to be inclusive distance irregularity strength of G, denoted by dis(G). The purpose of this research is showing that dis(T_{n,2})= (n^2+2)/2 where T_{n,2} is a complete n-ary tree to level two.
Domination Numbers in Graphs Resulting from Shackle Operations with Linkage of any Graph Saifudin, Ilham; Widiyaningtyas, Triyanna; Rhomdani, Rohmad Wahid; Dasuki, Moh.
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19675

Abstract

The domination number is the number of dominating nodes in a graph that can dominate the surrounding connected nodes with a minimum number of dominating nodes. This domini number is denoted by γ(G). In this research, we will examine the domination number of the distance between two graphs resulting from the shackle operation with any graph as linkage. This differs from previous research, namely the domination of numbers at one and two distances. This study emphasizes how the results of operations on the shackle are connected to the shackle graph as any graph connects the copy. Any graph here means all graphs are connected and generally accepted. The method used in this research is pattern recognition and axiomatic deductive methods. The pattern detection method examines patterns where a graph's number of dominating points can dominate the connected points around it with a minimum number of dominating nodes. Meanwhile, axiomatic deductive is a research method that uses the principles of deductive proof that apply to mathematical logic by using existing axioms or theorems to solve a problem. The Result of graph S_n with t copies and S_m as linkage, then the two-distance domination number in the graph resulting from the shackle operation is γ_2 (Shack(S_n,S_m,t) )=t-1; graph S_n with t copies and C_m as linkage, then the two-distance domination number in the graph resulting from the shackle operation is γ_2 (Shack(S_n,C_m,t) )={■(t,for 3≤m≤6@⌈n/5⌉(t-1),for m≥7)┤; graph C_n with t copies and S_m as linkage, then the two-distance domination number in the graph resulting from the shackle operation isγ_2 (Shack(C_n,S_m,t) )={■(t-1,for n=3@t,for 4≤n≤5@⌈n/5⌉t,for n≥6)┤ This research provides benefits and adds to research results in the field of graph theory specialization of two-distance domination numbers in the result graph of shackle operation with linkage any graph.
Super (a,d)-P_2⨀P_m-Antimagic Total Labeling of Corona Product of Two Paths Yatin, Bela Zainun; Awanis, Zata Yumni; Wardhana, I Gede Adhitya Wisnu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20065

Abstract

Graph labeling involves mapping the elements of a graph (edges and vertices) to a set of positive integers. The concept of an anti-magic super outer labeling (a,d)-H pertains to assigning labels to the vertices and edges of a graph using natural numbers {1,2,3,...,p+q}. The weights of the outer labels H form an arithmetic sequence {a,a+d,a+2d,...,a+(k-1)d}, where 'a' represents the first term, 'd' is the common difference, and 'k' denotes the total number of outer labels, with the smallest label assigned to a vertex. This study investigates the super (a,d)-P_2⨀P_m-antimagic total labeling of the corona product P_n⨀P_m, where n and m are both greater than or equal to 3. We define the labeling functions for vertices and edges based on the partitioning of labels into three subsets. Using k-balanced and (k,δ)-anti balanced multisets, we demonstrate that for m being odd, P_n⨀P_m is super (9m^2 n+4mn+m-n+3,1)-P_2 ⨀▒P_(m ) -antimagic, and for m being even, P_n⨀P_m is super (9m^2 n+4mn+m-2n+5,3)-P_2 ⨀▒P_(m ) -antimagic. The labeling scheme is illustrated through examples. For the case when m is odd, an antimagic total labeling of P_3 ⨀▒P_3    forms a super (282,1)- P_2 ⨀▒P_(3 )  -antimagic labeling. In the case of even m, an antimagic total labeling of P_3 ⨀▒P_(4 ) results in a super (483,3)- P_2 ⨀▒P_(4 )  -antimagic labeling. Both of these examples provide insights into the antimagic properties of corona products.
Rainfall Forecasting Using an Adaptive Neuro-Fuzzy Inference System with a Grid Partitioning Approach to Mitigating Flood Disasters Fauzi, Fatkhurokhman; Erlinda, Relly; Arum, Prizka Rismawati
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20385

Abstract

Hydrometeorological disasters are one of the disasters that often occur in big cities like Semarang. Hydrometeorological disasters that often occur are floods caused by high-intensity rainfall in the area. Early mitigation needs to be done by knowing about future rain. Rainfall data in Semarang City fluctuates, so the Adaptive Neuro-Fuzzy Inference System (ANFIS) method approach is very appropriate. This research will use the Grid Partitioning (GP) approach to produce more accurate forecasting. The data used in this research is daily rainfall observation data from the Meteorology Climatology Geophysics Agency (BMKG). The membership functions used are Gaussian and Generalized Bell. The two membership functions will be compared based on the RMSE and MAPE values to get the best one. The data used in this research is daily rainfall data. Rainfall in Semarang City every month experiences anomalies, which can result in flood disasters. The ANFIS-GP method with a Gaussian membership function is the best, with an RMSE value of 0.0898 and a MAPE of 5.2911. Based on the forecast results for the next thirty days, a rainfall anomaly of 102.53 mm on the thirtieth day could cause a flood disaster. 
The Development of Students’ Worksheets Based on Combinatoric Reasons in Elementary School Aini, Nurul; Suryowati, Eny
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20214

Abstract

This study was motivated by the many shortcomings of students’ worksheets so far, including the incapability in developing students’ scientific skills and high-level thinking. Meanwhile, the learning objectives of the elementary school level get students to think reasonably and solve problems. Therefore, developing students’ worksheets based on combinatoric reason is the solution, as it drills students to have sustainable thinking. This study aimed to see the validity, practicality, and effectiveness of students’ worksheets based on combinatoric reason. It is a Research and Development study with the Plomp model. The plomp model consists of preliminary investigation; design;  realization/construction; and test, evaluation, and revision. The research instruments were students’ worksheets, validation form, questionnaire, and test form. The subject involved 40 students in the sixth grade of elementary school. The data analysis used is descriptive qualitative and descriptive quantitative.  It resulted in 91,5% for the validity (very valid), 90,9% for the practicality (very practical), and 92,5% for the effectiveness (very effective). Thus, it indicates that students’ worksheets based on combinatoric reason are valid, practical, and effective, which are proper for elementary school. So, it is recommended that mathematics teachers use it in learning, because it trains students to use combinatorial reasoning. As a result, students become flexible and logical in determining strategies, as well as being systematic in solving problems. As a result, elementary school students' Problem-solving and higher order thinking abilities become better.
Projection of PT Aneka Tambang Tbk Share Risk Value Based on Backpropagation Artificial Neural Network Forecasting Result Haris, M. Al; Setyaningsih, Laras Indah; Fauzi, Fatkhurokhman; Amri, Saeful
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20267

Abstract

PT Aneka Tambang Tbk (ANTAM) received an award as the most sought-after stock issuer in Indonesia in 2016. That stock continued to attract investors in 2022 due to a 105% increase in net profit and a 19% increase in sales from the previous year. Despite the upward trend, investors still had doubts due to the fluctuating movement of ANTAM's stock prices. Therefore, forecasting was needed to determine the future movement of stock prices. The Backpropagation Neural Network method had good capabilities for fluctuating data types. However, this method has the disadvantage of a lengthy iteration process. To handle this limitation, The Nguyen-Widrow weighted setting was applied to address this constraint. The expected Shortfall (ES) method used the forecasting results to measure investment risk. This research uses ANTAM stock closing price data from May 2, 2018, to May 31, 2023. Based on the analysis results, the best architecture was obtained with a configuration of 5-11-1, using Nguyen-Widrow weight initialization and a combination of a learning rate of 0.5 and momentum of 0.9. This architecture yielded a prediction error based on the Mean Absolute Percentage Error (MAPE) of 1.9947%. Risk measurement with the ES method based on the prediction for the next 60 periods showed that at a 95% confidence level, the risk value was 0.002181; at a 90% confidence level, it was 0.002165; at an 85% confidence level, it was 0.002148, and at an 80% confidence level, it was 0.002132.
Algorithm for Constructing Total Graph of Commutative Ring Meinawati, Rima; Kurniawan, Vika Yugi; Kurdhi, Nughthoh Arfawi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19850

Abstract

Let R be a commutative ring. The total graph of R, denoted by TΓ(R) is a graph whose vertices are all elements of the ring R and every i,j∈R with i≠j, then i and j vertices are connected by edges if and only if i+j∈Z(R), where Z(R) is the set of zero-divisors in R with 0∈Z(R). Python programming is code that is easy to learn, read, understand, and helpful in explaining problems regarding graphs and algebra. In this paper, we determine an algorithm to construct the total graph of ring Z_n using Python. The research methods in this paper is a literature studies. The results generated by the algorithm can be utilized to observe the characteristic patterns displayed by the graph. Based on the algorithm’s constructed graph pattern, several properties of TΓ(Z_n ) can be inferred. For instance, if n is a prime number, then TΓ(Z_n ) is a disconnected graph. On the other hand, if n is a prime number and n≥3, then TΓ(Z_2n ) and TΓ(Z_4n ) is a connected graph, regular graph, Hamiltonian graph, and has a girth gr(TΓ(〖Z〗_n ))=3. In this paper we creating an algorithm to construct total graphs from commutative rings streamlines the construction process, enhances accessibility and utilization of total graphs, and supports parameter variation exploration and application in problem-solving. 
Forecasting Maximum Water Level Data for Post Sangkuliman using An Artificial Neural Network Backpropagation Algorithm Mislan, Mislan; Dani, Andrea Tri Rian
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20112

Abstract

Neural Network (NN) is an information processing system that has characteristics similar to biological neural networks. One of the algorithms in NN is Backpropagation Neural Network (BPNN). BPNN is an excellent method for dealing with complex pattern recognition problems. In this research, maximum water level forecasting was carried out at Sangkuliman Post using a Backpropagation Neural Network. This research aims to obtain modeling for forecasting maximum water level, as well as forecasting results using the best model. The research results show that the best model is five neurons in hidden layer 1 and 3 neurons in hidden layer 2 with the backpropagation algorithm, the activation function used is binary sigmoid, the learning rate is 0.001, and the maximum iteration is 10,000,000 with the smallest RMSE result being 1.816. The forecast results for the following 12 periods are 1.672, 1.779, 1.523, 1.271, 1.752, 1.692, 1.335, 1.479, 1.750, 1.779, 1.340, 1.269, and 1.754. Forecasting results can be used by various parties in decision-making and planning in multiple fields, as an example to see the patterns of biological and vegetable life around Sangkuliman Post. Based of forecasting results, certain months show an increase in maximum water levels. 
The Impact of Differences in Attitudes of Male and Female Prospective Teachers in Understanding Statistics Judijanto, Loso; Lumbantoruan, Jitu Halomoan
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20396

Abstract

Universities have understood the gender gap of prospective teachers towards attitudes in facing statistics lessons is increasingly growing. However, the understanding of universities about gender in influencing prospective teachers' attitudes toward statistics lessons is still minimal. This is urgent to be studied because there is a gap between expectations in universities and facts in the field, so this study aims to analyze differences in attitudes towards statistics based on gender and identify factors that influence attitudes towards statistics. The research method used is a quantitative survey type. The research sample was 395 prospective mathematics teachers from 18 universities that prepare prospective mathematics teachers in Jakarta and the sample was selected randomly. The data collection technique was a survey using an instrument. The instrument was developed and validated. The instrument was distributed with a rating scale from point 1 to point 5. Data were collected with the help of Google. The data analysis technique used was descriptive statistics with the help of SPSS Version 25.0, assessing the mean, variance, standard deviation, and the t-test. The results found that prospective teachers have a positive attitude towards statistics and the female gender has a significant and more positive influence on attitudes towards statistics lessons. The conclusion is that gender is important in shaping prospective teachers' attitudes towards statistics lessons. The research implies that higher education needs to pay attention to gender factors in implementing the curriculum and provide training to prospective teachers to increase interest in learning statistics.
Novel Distance-Based Molecular Descriptors for Styrene Butadiene Rubber Structures Chidambaram, Natarajan; Kamran, Muhammad; Balasubramanian, Deepa; Hameed, Shahzaib; Mehmood, Saba; Raza, Wasim; Khan, Aamir Hussain; Iqbal, Zainab
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20037

Abstract

Styrene-butadiene rubber (SBR) is a general-purpose rubber produced from a copolymer of styrene and butadiene.  It is used largely in automobile and truck tires. In general, it is considered to be an abrasion-resistant replacement for natural rubber.  In this article, we compute a set of recently introduced distance-based topological descriptors namely, Zagreb connection indices and reformulated Zagreb connection indices for the SBR structures. Zagreb indices and Reformulated Zagreb indices  were applied to forecast numerous molecular properties through QSAR studies of boiling point, Molar volume and bioactivity. These indices offer a quick and effective measure of molecular complexity and features of their composition resulting in approximate molecular behavior.

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