Dimensi Metrik dari Graf Jaring Laba-Laba

Dimensi metrik dari graf terhubung G adalah kardinalitas dari himpunan pembeda minimum dari G, dimana W disebut himpunan pembeda dari G jika  r(v|W) berbeda untuk setiap v elemen V(G) . Penelitian ini bertujuan untuk menentukan dimensi metrik dari graf jaring laba-laba R_(m,n). Graf jaring laba-laba dikonstruksi dari graf bintang S_n  sebanyak  1 dan graf sikel C_n  sebanyak m. Konstruksi graf tersebut melibatkan definisi dari C_n(m) yang menyatakan graf sikel C_n ke-m , dengan V(C_n(m))={a_(m1), a_(m2), a_(m3), ..., a_(mn)} dan V(S_n)={u, a_(m1), a_(m2), a_(m3), ..., a_(mn)}   dengan  u sebagai titik pusatnya, dimana m elemen N dan n>3 . Dari hasil penelitian, diperoleh  dimensi metrik dari graf jaring laba-laba R_(m,n) adalah 3

Analisis Kesalahan Mahasiswa dalam Menyelesaikan Soal Persamaan dan Pertidaksamaan pada Mata Kuliah Kalkulus I

Tujuan dari penelitian ini adalah untuk memberikan deskripsi mengenai kesalahan yang mahasiswa lakukan dalam menyelesaikan soal persamaan dan pertidaksamaan pada mata kuliah kalkulus I. Metode yang digunakan dalam penelitian ini adalah kualitatif dan subjek yang digunakan dalam penelitian ini adalah mahasiswa semester 1 program studi Tadris Matematika STAI Muhammadiyah Probolinggo. Teknik yang digunakan untuk mengumpulkan data adalah ujian dan wawancara. Berdasarkan hasil penelitian, diperoleh kesimpulan bahwa terdapat 8 kesalahan yang subjek lakukan dalam menyelesaikan soal persamaan dan pertidaksamaan pada mata kuliah kalkulus I, yaitu kesalahan dalam menuliskan tanda sama dengan , menuliskan kata penghubung atau , menyamakan penyebut dari suatu persamaan linier, memindahkan suatu bilangan dari suatu ruas ke ruas yang lain pada persamaan linier, menuliskan tanda kurung kurawal , menentukan situasi dari pembilang dan penyebut dari bilangan pecahan kurang dari nol, menuliskan tanda interval dan kurang dari , dan kesalahan dalam menuliskan himpunan penyelesaian. Kata Kunci: analisis kesalahan, persamaan, pertidaksamaan, kalkulu

Eksplorasi Etnomatematika pada Masjid Raya Bandung

Etnomatematika merupakan pembelajaran matematika yang diperoleh melalui budaya. Penelitian ini bertujuan untuk melakukan eksplorasi etnomatematika pada Masjid Raya Bandung. Metode pada penelitian ini berupa studi kepustakaan, observasi, dan dokumentasi. Data yang telah diperoleh dilakukan analisis dengan cara reduksi data, yaitu pengolahan data melalui tahap pemilahan, pemusatan, dan penyederhanaan. Berdasarkan hasil penelitian, ditemukan beberapa bangun bidang pada bangunan dan ornamen dari Masjid Raya Bandung, yaitu persegi panjang, lingkaran, persegi, segitiga, jajargenjang, segilima, layang-layang. Selain itu, juga ditemukan beberapa bangun ruang pada bangunan dan ornamen dari Masjid Raya Bandung, yaitu bola, balok, dan tabung.Kata Kunci: Etnomatematika, Masjid Raya Bandung, geometr

Characterizations of 2-Primal Ternary Semiring using Special Subsets of Ternary Semiring

This research aims to determine the characterizations of 2-primal ternary semiring using special subsets of ternary semiring. We use literature review method to achieve these aims. We define O^' (P) and O_P^', the special subsets of ternary semiring then we determine some properties of them. We also determine the condition for O(P) and O_P in order to the special subsets are ideals of S. The last, the special subsets of ternary semiring will be used to determine the characterizations of 2-primal ternary semiring. As the results, some the characterizations were S must be a commutative super nilpotent ternary semiring and O(P)=(O(P) ) ̅ for each prime ideal P of S. Besides that, O(P)=O_P=N(P) and O_P^' must has the IFP for each prime ideal P of S. Keywords: prime ideal; ternary semiring; 2-primal ternary semirin

ANALISIS KESALAHAN MAHASISWA DALAM MENYELESAIKAN SOAL KESEIMBANGAN PASAR PADA MATA KULIAH MATEMATIKA KEUANGAN DAN BISNIS

This research aims to give the description about the mistakes by students in solving market balance problems in financial and business mathematics course. The method in this research is a qualitative descriptive method and the subjects in this research were semester 2 students of the Islamic Economics study program at STAI Muhammadiyah Probolinggo. The techniques for data collection are exams and interviews, while the technique for data analysis in this research uses the formula P=  f/N ×100%. Based on the results of the research, it was concluded that there were 5 errors by the subjects in solving market balance problems in financial and business mathematics course, namely errors in writing Q_s notation, doing the calculation process, moving numbers or variables from one segment to another, multiplying both sides with a number to eliminate the denominator on a side, and errors in determining the offered price after tax

ANALISIS KESALAHAN MAHASISWA DALAM MENYELESAIKAN SOAL TEORI HIMPUNAN PADA MATA KULIAH HIMPUNAN DAN LOGIKA

This research aims to describe some of the mistakes made by students in solving set theory problems in the set and logic course. The method used in this research is descriptive qualitative. The subjects in this study were students of Tadris Mathematics STAI Muhammadiyah Probolinggo Semester I for the academic year 2021/2022. Data collection techniques used in this study were exams and interviews. Based on the results of the study, it can be concluded that the subject made 9 types of errors, namely errors in determining the value of a quadratic equation, registering members of a set, writing mathematical notation, writing down sets, writing down members of Cartesian product, determining the intersection of two sets, determining the Cartesian product of two sets, determining the difference of the two sets, and determining the value of a quadratic inequality

INVERS MOORE-PENROSE SEBAGAI REPRESENTASI MATRIKS PROYEKSI ORTHOGONAL

The inverse of matrix is one of the important properties of matrix. This properies, especially singular matrix, has been developed by Moore and continued by Penrose. Then, this inverse called Moore-Penrose inverse. The Moore-Penrose invers criteria can represent a projection on a vector space V along W with V and W are orthogonal to each other or can written with W=V^⊥ which is called orthogonal projection matrix on V. This research will present lemmas and theorems related to the Moore-Penrose invers construction of the multiplication matrix. Then, a square matrix is an orthogonal projection matrix on a vector space V if and only if it satisfies two conditions, that are idempotent and symmetric. These two properties are satisfied by matrices I-A^+ A and I-AA^+ which respectively are orthogonal projection matrices on Ker(A) and Ker(A^' ). As a result, the Moore-Penrose inverse A^+ can be constructed from a square matrix A which is an multiplication of several matrices and fulfills certain properties

Analisis Kesalahan Mahasiswa Dalam Menyelesaikan Soal Persamaan dan Pertidaksamaan Pada Mata Kuliah Kalkulus I

The goal of this research is to give description about the various errors that students make in solving equations and inequalities in the calculus I subject. The method in this research is qualitative and the subjects in this research were semester 1 students of Tadris Mathematics study program STAI Muhammadiyah Probolinggo. The techniques to collect the data were examinations and interviews. Based on the results of the study, it was concluded that there were 8 errors by the subjects in solving equations and inequalities in the calculus I course, namely errors in writing the equal sign , writing the conjunction or , equating the denominator of a linear equation, moving a number from one side to another in the equation linear, writing curly brackets , determining the situation of the numerator and denominator of fractions less than zero, writing down the interval sign and less than , and errors in writing the solution set.Keywords: Error Analysis, Equation, Inequality, Calculu

THE INFLUENCE OF REALISTIC MATHEMATICS EDUCATION ON YEAR 8 STUDENTS' SPATIAL ABILITY OF CUBOIDS AND CUBES

This study aims to determine the effect of RME on the spatial abilities of Year 8 students concerning cuboids and cubes. Geometry problems often experienced by junior high school students, such as difficulty knowing the difference between cuboids and cubes, difficulties showing elements of cuboids and cubes, and difficulty imagining cuboids and cubes in the case of rotation. The teacher should not underestimate it because it will impact the next level of learning. Besides, spatial abilities are closely related to other mathematical concepts. One alternative is using RME. This research employed the quasi-experimental method, and samples were selected using purposive sampling techniques. The two classes were selected as samples in this study: the experimental and the control classes. Before conducting the main analysis test, the pre-test score students were tested with the t-test. The initial conclusion was that there was no difference in the spatial ability of the experimental class and the control class. The main analytic test in the post-test was done using U-test. The post-test results show that the average score of the experimental class is higher than the control class; RME positively influences students' spatial abilities