Topological Properties of Braid-Paths Connected 2-Simplices in Covering Spaces under Cyclic Orientations

In general, the braid structures in a topological space can be classified into algebraic forms and geometric forms. This paper investigates the properties of a braid structure involving 2-simplices and a set of directed braid-paths in view of algebraic as well as geometric topology. The 2-simplices are of the cyclically oriented variety embedded within the disjoint topological covering subspaces where the finite braid-paths are twisted as well as directed. It is shown that the generated homotopic simplicial braids form Abelian groups and the twisted braid-paths successfully admit several varieties of twisted discrete path-homotopy equivalence classes, establishing a set of simplicial fibers. Furthermore, a set of discrete-loop fundamental groups are generated in the covering spaces where the appropriate weight assignments generate multiplicative group structures under a variety of homological formal sums. Interestingly, the resulting smallest non-trivial group is not necessarily unique. The proposed variety of homological formal sum exhibits a loop absorption property if the homotopy path-products are non-commutative. It is considered that the topological covering subspaces are simply connected under embeddings with local homeomorphism maintaining generality.

PENGEMBANGAN SOAL TES UNTUK MENGUKUR KEMAMPUAN PEMECAHAN MASALAH SISWA PADA MATERI BENTUK ALJABAR

Problem-solving ability became a learned process as well as a goal that must be achieved in learned mathematics so it is important for students to have these abilities, especially in algebraic form material. But in fact, in the material of algebraic forms, the ability was still minimally mastered by students. Based on the results of the interview, it shows that the lack of ability was due to the questions given by the teacher only in the form of routine questions taken from LKS or textbooks that did not require the use of problem-solving skills but only require the used of procedural formulas. Therefore, it was necessary to develop test questions that contain question items that could measure students' problem-solving abilities in the algebraic form of material. This type of research was developed researched using the ADDIE model which stands for analysis, design, development, implementation, and evaluation. Data collection techniques used in this study were validation questionnaires and tests. Meanwhile, the data collection instruments were validation questionnaire sheets and test sheets. The test subjects in this study were class VII C students of MTs Salafiyah Syafi'iyah Seblak Jombang. The results showed that the product developed in the form of a test was declared valid by the expert with an average validity of 3.75 and was in very valid criteria. Meanwhile, the results of the empirical validity test showed that only four of the five items on the test developed were declared valid and of the four items that were valid, the reliability value of 0.786 with high criteria was obtained. The research findings prove that the developed test contains only four items that were valid both theoretically and empirically and reliably so that they could be used to measure students' problem-solving abilities on the algebraic form of material.

Analytical Solution for Longitudinal Dynamic Responses of Long Tunnels under Arbitrary Excitations

In this paper, an analytical solution is proposed for longitudinal dynamic responses of long tunnels under arbitrary excitations. For the derivation, the tunnel is assumed as a Timoshenko beam resting on a visco-Pasternak foundation. The Timoshenko beam theory is employed to consider both effects of the shear distortion as well as the rotary inertia of the tunnel, which are neglected by the Euler–Bernoulli beam. The visco-Pasternak foundation is applied to represent the viscoelastic compressive and shear resistance of soil. The governing equations of motion are transformed from partial differential forms into algebraic forms through integral transformations, and thus the solutions are conveniently obtained. The analytical solutions of the tunnel under several specific dynamic loads, including impulsive loads, moving line loads as well as traveling loads, are presented in detail and verified by comparing to the known degraded solution in literature and finite element results. Several examples are also conducted to investigate the influence of the relative stiffness ratio between the soil and the tunnel structure on the tunnel responses.

KEMAMPUAN BERPIKIR ALJABAR DALAM MENYELESAIKAN SOAL MATERI TEOREMA PHYTAGORAS

This research aims to determine the algebraic thinking skills of students in solving questions on the subject of the Pythagorean theorem in students of SMP Negeri 19 Pontianak. The research method used is descriptive method in the form of case studies. The subjects in this study were six students and the object in this study was the ability to think algebraically in solving problems on the subject of the Pythagorean theorem. The data collection techniques used were test and non-test (interview). In this research, there is one student who achieves generational activities, two students in transformational activities and one student in global meta-level activities. In general, it can be concluded that the ability to think algebra in solving the problem of the Pythagorean theorem in SMP Negeri 19 Pontianak is that students are in transformational activities even though in generational activities students do not entirely write algebraic forms and equations. Students also have not been able to solve problems by writing down the rules used at each step, and not writing conclusions. Keywords : Algebraic Thinking Skills, Solve The Problem, Pythagorean Theorem

Problematika Guru dalam Mengajar Materi Aljabar di Era Pandemik Coronavirus Disease 2019 (Covid-19)

<p class="06IsiAbstrak">Keharusan dalam pelaksanaan pembelajaran <em>online</em> yang disebabkan oleh pandemik Covid-19 menimbulkan munculnya masalah-masalah dalam pembelajaran matematika khususnya materi aljabar. Penelitian ini bertujuan untuk mengetahui problematika yang dihadapi guru dalam mengajarkan materi aljabar di era pandemik Covid-19. Metode penelitian menggunakan penelitian kualitatif deskriptif. Sumber data berasal dari tujuh guru matematika Sekolah Menengah Pertama (SMP) di Kudus dan Tangerang yang memberikan jawaban atas pertanyaan dalam google form. Hasil penelitian ini menunjukkan problematika yang dialami guru dalam mengajar materi aljabar di era pandemik Covid-19 adalah keterbatasan alat penunjang pembelajaran sehingga guru sulit menerangkan penerapan operasi hitung aljabar, soal aplikasi aljabar, dan menyederhanakan bentuk aljabar secara <em>online</em>. Terbatasnya ruang dan waktu, jaringan internet yang tidak stabil serta kuota yang tidak memadai mengakibatkan interaksi antara guru dan siswa tidak dapat optimal dilakukan.</p><p class="06IsiAbstrak"> </p><p class="06IsiAbstrak"><span lang="IN">The necessity of implementing online learning caused by the Covid-19 pandemic has created problems in learning mathematics, especially algebraic material. This study aims to find out the problems faced by teachers in teaching algebra material in the Covid-19 pandemic era. The research method uses descriptive qualitative research. Sources of data came from seven junior high school mathematics teachers (SMP) in Kudus and Tangerang who provided answers to questions in the google form. The results of this study indicate that the problems experienced by teachers in teaching algebra material in the Covid-19 pandemic era are the limitations of learning support tools so that teachers find it difficult to explain the application of algebraic arithmetic operations, algebra application questions, and simplify algebraic forms online. Limited space and time, unstable internet networks, and inadequate quotas have resulted in the interaction between teachers and students not being optimal.</span></p>

Algebraic Structure and Poisson Integral Method of Snake-Like Robot Systems

The algebraic structure and Poisson's integral of snake-like robot systems are studied. The generalized momentum, Hamiltonian function, generalized Hamilton canonical equations, and their contravariant algebraic forms are obtained for snake-like robot systems. The Lie-admissible algebra structures of the snake-like robot systems are proved and partial Poisson integral methods are applied to the snake-like robot systems. The first integral methods of the snake-like robot systems are given. An example is given to illustrate the results.

MODEL PEMBELAJARAN CORE, SCRAMBLE, HASIL BELAJAR, DAN OPERASI HITUNG BENTUK ALJABAR

The learning model has an essential role in student learning outcomes. Each learning model has different contributions, such as the Scramble learning model, which can make students think quickly, and the CORE learning model can train students to think critically. Thus, this study aims to compare students' learning outcomes with the two models, especially in arithmetic operations in algebraic forms. The research method used is quantitative research with a posttest-only group design classified as a quasi-experimental design. The research population was forty-five seventh-grade students, which were divided into two categories. The test instrument used is a description of five questions used to evaluate student learning outcomes. The study results analyzed statistically using the t-test showed that there were differences in student learning outcomes between the two groups of students. Furthermore, the continued test using Pairwise Comparison showed that students taught with the Scramble learning model had better learning outcomes than students acquainted with the CORE learning model.

Identification of Student Errors in Solving Problems on the Limit of Algebra Functions in Class XI SMAN 4 Palangkaraya

This study aims to describe the mistakes of class XI students of SMA Negeri 4 Palangka Raya in solving the limit problem of algebraic functions and their causative factors. This research is a descriptive study with a qualitative approach. Data collection techniques are tests and interviews. The research instrument was a question sheet and interview guidelines. The questions used are in the form of a description consisting of 5 questions. Before being used, the questions were reviewed by 3 raters, namely 2 mathematics education lecturers and 1 mathematics teacher. From the results of the study it was concluded that all questions could be used. Checking the validity of the data was carried out by observing persistence and triangulation of sources. Then the collected data were analyzed using data analysis techniques proposed by Miles and Huberman, namely data reduction, data presentation, and drawing conclusions. The results showed that the errors made by students on the limit of algebraic functions were: (1) Conceptual errors: (a) errors in understanding the concept of limits which consist of formulas, theorems and definitions of limits. (b) the use of formulas, theorems and definitions of limits that are inconsistent with the conditions for the application of the formula; 2) Procedural errors: (a) errors in calculations, (b) inability to write work steps regularly. (c) errors in applying rules, principles or formulas. (d) the inability of students to manipulate algebraic forms based on applicable properties or principles. As for the factors causing students in this study in terms of internal factors of students.