Sets and Numbers

This chapter covers set theory. The topics include set algebra, relations, orderings and mappings, countability and sequences, real numbers, sequences and limits, and set classes including monotone classes, rings, fields, and sigma fields. The final section introduces the basic ideas of real analysis including Euclidean distance, sets of the real line, coverings, and compactness.

Preface

International Conference on Mathematical and Statistical Sciences (ICMSS) 2021 Study Program of Mathematics and the Study Program of Statistics Faculty of Mathematics and Natural Sciences Universitas Lambung Mangkurat Banjarbaru - Indonesia, 15 - 16 September 2021 The International Conference on Mathematical and Statistical Sciences (ICMSS) 2021 was organized through a collaboration between the Study Program of Mathematics and the Study Program of Statistics, Faculty of Mathematics and Natural Sciences - Universitas Lambung Mangkurat (ULM). The theme raised was “Mathematical and Statistical Sciences in Multidisciplinary Research”, with the aims are to acknowledge, learn, share, and transfer the results of scientific knowledge and research among academia and practitioners who have used or implemented Mathematical and Statistical Sciences to solve real-world problems and improve the quality of life. The scopes of our conference are Mathematical modeling, Artificial intelligence, Mathematical physics, Algebra and its applications, Statistics and its applications, Computational fluid dynamics, Data mining and its applications, Dynamical nonlinear systems, Mathematics Educations, Financial mathematics, Mathematical biology, Numerical methods and analysis, Operation research and optimizations, and Real analysis. On behalf of the committee, we would like to thank the Rector of Universitas Lambung Mangkurat, the Dean of Faculty of Mathematics and Natural Sciences, Coordinator of the Study Program of Mathematics and Coordinator of the Study Program of Statistics, advisory board, steering committee, all committee members, reviewers, presenters, and participants. We also would thank the Indonesian Mathematical Society (IndoMS), The Indonesian Algebra Society (IAS), and The Forum Pendidikan Tinggi Statistika (Forstat). Special thanks are also given to the Journal of Physics: Conference Series. We, on behalf of the ICMSS 2021 committee, would like to thank all parties for their participation in supporting this publication. We hope to see you all at the next conference. Kind regards, Dr. Muhammad Ahsar Karim Chair of the ICMSS 2021 List of Organizing Committees, Photographs and Peer review statement are available in this pdf.

ANALISIS KEMAMPUAN BERPIKIR TINGKAT TINGGI MAHASISWA DALAM MENGKONSTRUKSI REPRESENTASI BINER BILANGAN REAL

Higher-order thinking skills (HOTS) are needed to determine the student's ability to construct an answer. In this study, researchers analyzed the higher-order thinking skills of students of the Mathematics Education Study Program in constructing one of the test answers, namely constructing a binary representation of real numbers in the Introduction to Real Analysis course. Fifty-two students taking the Introduction to Real Analysis course in the odd semester 2020/2021 are the subjects of this research. Data was collected using a test that was analyzed based on the indicator of higher-order thinking ability created (C6). It was revealed that the students' higher-order thinking skills were in the sufficient category. This means that most students have not been able to construct and analyze information into the right strategy. The results of this study are expected to be a reference for the lecture process where students are familiarized with giving HOTS-oriented questions during exams and practice questions for lectures to help develop higher-order thinking skills.Keywords: Bloom's taxonomy-C6; higher order thinking skill; binary representation Kemampuan berpikir tingkat tinggi diperlukan untuk mengetahui kemampuan mahasiswa mengkonstruksi suatu jawaban. Pada studi ini, peneliti menganalisis kemampuan berpikir tingkat tinggi mahasiswa Program Studi Pendidikan Matematika dalam mengkonstruksi salah satu jawaban tes yaitu mengkonstruksi representasi biner bilangan real pada mata kuliah Pengantar Analisis Real. Lima puluh dua mahasiswa yang sedang mengambil mata kuliah Pengantar Analisis Real pada semester ganjil 2020/2021 sebagai subjek penelitian ini. Data dikumpulkan dengan tes yang dianalisis berdasarkan indikator kemampuan berpikir tingkat tinggi create (C6). Terungkap bahwa kemampuan berpikir tingkat tinggi mahasiswa berada pada kategori cukup. Ini berarti sebagian besar mahasiswa belum mampu mengkonstruksi dan menganalisis informasi menjadi strategi yang tepat. Hasil penelitian ini diharapkan menjadi acuan untuk proses perkuliahan dimana mahasiswa dibiasakan dengan pemberian soal yang berorientasi HOTS baik itu pada saat ujian maupun latihan-latihan soal perkuliahan untuk membantu mengembangkan kemampuan berpikir tingkat tinggi.Kata Kunci: taksonomi Bloom-C6; kemampuan berpikir tingkat tinggi; representasi biner

On two kinds of the reverse half-discrete Mulholland-type inequalities involving higher-order derivative function

By means of the weight functions, Hermite–Hadamard’s inequality, and the techniques of real analysis, a new more accurate reverse half-discrete Mulholland-type inequality involving one higher-order derivative function is given. The equivalent statements of the best possible constant factor related to a few parameters, the equivalent forms, and several particular inequalities are provided. Another kind of the reverses is also considered.

Mathematical-Analytical Thinking skills: The Impacts and Interactions of Open-ended Learning Method & Self-Awareness (Its Application on Bilingual Test Instruments)

Analytical thinking is a skill to unite the initial process, plan solutions, produce solutions, and conclude something to produce conclusions or correct answers. This research aims to 1) determine whether there are differences in students' mathematical, analytical thinking skills between classes that use the Open-ended learning method and classes that use the lecturing method, 2) to find out whether there are mathematical, analytical thinking skills differences between students with high, moderate, and low self-awareness criteria, and 3) to find out whether there is an interaction between Open-ended learning method and self-awareness toward students' mathematical-analytical thinking skills. This research employs a quasi-experimental design. Based on the data and data analysis, this research is mixed-method research, and the design used in this research is the posttest control group design. This research was conducted on students who have studied the Real Analysis Courses. Based on the results of hypothesis testing, it was found out that, first, there are differences in students' mathematical-analytical thinking skills between the class that uses the Open-ended learning method and the class that uses the lecturing method. Second, there are mathematical-analytical thinking skills differences between high, moderate, and low self-awareness criteria. Third, there is no interaction between the Open-ended learning method with self-awareness of students' mathematical-analytical thinking skills.

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

In this paper, using weight functions as well as employing various techniques from real analysis, we establish a few equivalent conditions of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel. To prove our results, we also deduce a few equivalent conditions of two kinds of Hardy-type integral inequalities with a homogeneous kernel in the form of applications. We additionally consider operator expressions. Analytic inequalities of this nature and especially the techniques involved have far reaching applications in various areas in which symmetry plays a prominent role, including aspects of physics and engineering.