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In the current scenario Programming in Python plays a vital role in research arena as it preserves much of the man power. Converting the research work into the format of coding helps any researcher across the globe as it serves as a ready reckoner. Topology is one of the main branches of Mathematics. A Polish Mathematician named Kazimierz Kuratowski defined essential axioms in Topology with the aid of a closure operator named after him. In this paper, we have developed a Python program to find the closure and interior for the subsets of the given set. We will be using dictionary in Python with each subset as the key and the respective closure as its value. Subsequently we will be finding int(cl(A)), cl(int(A)), int(cl(int(A))), cl(int(cl(A))), for any subset A of the given set. [ABSTRACT FROM AUTHOR]

In recent years, with the increase of online learning platforms, obtaining learning behavior data from students, are becoming easy. However, analyzing the data to extract meaningful information remains challenging due to the data volume and complexity. Here, we apply Self-organizing Maps (SOM) to visualize the learning characteristics of many elementary students over many online assignments in mathematics class. As a case study, this research used the data log of MONSAKUN, a digital learning environment that focuses on exercising arithmetic using story-based questions by using a problem-posing approach with the integration of mathematical sentences. Our primary objective is to give intuitive understanding to the teachers regarding the students' performance that subsequently allows the teachers to generate meaningful advices. Here, SOM generates a two-dimensional map that preserved the topological order of high-dimensional learning characteristics data, in which students with similar learning characteristics are located close to each other, while students with significantly different characteristics are distanced from each other. We are interested especially in locating low-performing students, as they are the most important to be given advice by the teachers. By locating the low-performing students and other students in their vicinity on the map, the teacher may be able to use other students as references for improving the low-performing students' performances. The idea is to mimic the learning characteristics of the students designated as references. Due to the learning characteristics similarity, the low-performing students do not need to make drastic changes in their learning styles. It can be expected that by iterating this process over many assignments, the students' performances will gradually be improved. In this paper, we utilized a digital learning platform MONSAKUN, for learning arithmetic used in Japan. In this paper, we present our preliminary results in the form a learning-visualization of characteristics students of analytical and advisory tools and described our future goals for building a more flexible and general tool that can be deployed in Indonesia. [ABSTRACT FROM AUTHOR]

In the digital era, most of the human work is now been performed using the computer system. The computer's capacity to detect and understand meaningful Handwriting input from sources such as touch screens, pictures, paper documents, and other sources is referred to as handwriting character recognition. The diversity in people's handwriting style increases the complexity of handwritten characters. Also, grading academic answer sheets manually and providing an unbiased genuine grade is a challenging task. The aim of the work is to create handwriting character recognition system that will be used to read handwriting notes and solve mathematical equations. The ultimate goal is to show that neural networks can solve equations from a handwritten source effectively. In this paper, we present a web application-based equation solver that uses a camera image of an equation to display the solution. The program has the ability to solve simple arithmetic equations (addition, subtraction, multiplication) and up to two systems of linear equation variables handwritten or typed in a computer font. [ABSTRACT FROM AUTHOR]

This paper showcases an example of how mathematics was utilized to debunk a suspected anomaly in election returns in the aftermath of the Philippine national elections last May 2022. Initial results of the automated elections yielded numbers that the public deemed suspicious. In response to a call for experts' opinions on the matter, we processed and analyzed large samples of preprocessed data to which we have been given access. Using data analytics techniques, we examined transmission arrivals of election returns and compared them against the total votes transmitted, with the analysis performed at different aggregation levels. Our analyses showed that the seemingly suspicious numbers can be explained by examining the distributions of the transmission arrivals of election returns and analyzing those distributions using different levels of aggregation. From the perspective of critical mathematics education (CME) particularly, focusing on mathematics for critical citizenship, we highlight the importance of mathematics to help fight disinformation and spread of unfounded rumors. The paper concludes with recommendations for enriching students' mathematical experiences that could pave the way for a responsive and engaged citizenry in our country. [ABSTRACT FROM AUTHOR]

In this paper, a new operator was defined μ m , k j. v f (w)) : A → A. Associated with Hadamard product of the Komatu Integral operator [MATH] and the Dziok-Srivastava operator [MATH]. And done use the method of differential subordination to derive certain properties of the differential operator μ m , k j. v f (w)). And aim of this paper is to use the relation (α 1 k + 1) μ m , k j + 1 , v f (w) = w (μ m , k j , v f (w)) ' + α 1 k (μ m , k j , v f (w)) [ABSTRACT FROM AUTHOR]

The soft set is a concept which is considered as a common mathematical tool to deal the unpredictability in all the fields that deals mathematics. The problems that trouble the theoretical approaches are solved using soft set. The soft topology is formulated using soft sets. Based on variable values, soft topology induces topology. Using soft topological spaces soft tritopological spaces are framed. This research paper deals some new definitions of trio open soft b cover, trio compact soft b. Also investigates trio compact soft b spaces properties in soft tritopological spaces. In further studies the outcome of this research paper can be done on soft tritopological spaces. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to study and investigate new notion of separated sets namely, δ-ß-Separated sets by using δ-ß- open sets. Moreover, with this notion we introduce new classes of connected spaces which are called strongly δ-ß-connected spaces and study some essential properties concerning of δ-ß- connected spaces. Several characterizations and fundamental properties concerning of such these classes of connected spaces with some δ-ß- Separtion axioms and compact spaces are obtained. The behavior of δ-ß- connected spaces with respect to several types of well-known mappings is discussed. Also, the digital spaces in the context of these new concepts are examined. Mathematics Subject Classification: 54B05, 54B10 ,54C10 ,54D18,90D42. [ABSTRACT FROM AUTHOR]

Graph theory is a branch of mathematics which is quit rich and interesting. The study of domination is one of the fastest growing area in graph. There are different types of domination such as connected domination, independent domination, total domination, paired domination, secure domination , etc. "The secure dominating set S of a graph G is a dominating set with the property that each vertex u∈V\ S is adjacent to a vertex v∈S such that (S\ v) Uu is a dominating set. The minimum cardinality of such a set is called the secure domination number and denoted by γs(G)". In this paper we discuss about the secure domination for some special graphs. [ABSTRACT FROM AUTHOR]

A teacher, who is the provider of the proven educational knowledge, should be adequately competent in terms of expertise, trust, dedication, positive attitude, effective communication and patient listening. All these attributes can surely be inculcated in pupil teacher but only if the training is provided with maximum commitment, with specified objectives, taking into account the needs of todays' educational scenario and the needs of students. This paper emphasize on the system of training being provided to pre-service Mathematics' teachers, to develop their teaching skills. It includes the use of some creative teaching concepts to increase the interest, level of satisfaction and the outcome of their targeted Mathematics' students. Several studies, researches have shown that the students, who have been studying Mathematics since their childhood, are unable to perform simple calculations and are unable to solve simple numerical problem of their everyday life. This study will conclude with some suggestive facts that pre-service trainees should be trained in a way that other than the prescribed curriculum/syllabus, they should spend time to improve quantitative skills using some innovative techniques in regular class practice. As an example, the inventive methodology will also be discussed. And the second highlight will be the the emphasis on continual and rigorous assessment of the trainees during teaching practice, so that they can resolve the dearth and can go ahead with a handful of approaches to serve the purpose of fruitful teaching and learning. [ABSTRACT FROM AUTHOR]

STEM education is one of the primary priorities in the Malaysian Education Blueprint (PPPM) 2013-2025, in line with the relevance of STEM at the global level. In keeping with the educational needs of 21st-century learning, the use of technology in education is also highly encouraged. Unfortunately, the Malaysian government's goal of producing one million experts in Science, Technology, Engineering, and Mathematics (STEM) by 2020 was not met because the 60:40 STEM: non-STEM policy failed to meet the goal. Students' interest in different STEM disciplines has been linked to their interest in integrated STEM in previous studies. Students' lack of interest in STEM fields appears to have an impact on their low mathematics achievement at the international assessment level, including in the field of geometry. Geometry is one of the most important branches of mathematics, and spatial thinking goes hand in hand with it. This paper presents the results of a critical review as well as a brief overview of ongoing research targeted at developing a model for the formation of interest among secondary school students in STEM through geometry learning based on augmented reality (AR) technology and visual-spatial abilities. The first part of the paper provides an in-depth review of these matters based on rather limited resources. The review revealed various difficulties and limitations in piquing students' interest in STEM and mathematics. The second part describes research being conducted by the researchers to examine the implementation of using AR in geometry learning based on visual-spatial abilities. For the pilot and main stages of the study, pre-and post-test, observations, and semi-structured interviews will be conducted. The data will be analysed quantitatively and qualitatively, and the theory of change approach will be applied. The findings will be used to develop a model for the formation of interests among students as a result of geometry learning. The model aims to provide some relevant information for technology-assisted mathematics instruction, and it aligns with national STEM policy goals of increasing the number of students selecting STEM disciplines in secondary and higher education. [ABSTRACT FROM AUTHOR]

Isabelle/HOL is a generic proof assistant. Using an Isabelle/HOL requires insight into procedures as well as into the concepts involved. In addition, the way computer manages the procedures can affect mathematical concepts. We can clearly understand mathematical concepts and can minimize the burden of operation opportunities. "Foundations of Geometry" is a book of mathematics written by Hilbert in 1899. The book is famous as the most rigorous study of the axiom system of Euclidean geometry by axioms and formalism. The purpose of this paper is to complement the axiom system by theorizing a part of the problems in this book. [ABSTRACT FROM AUTHOR]

This research aims to analyze gender difference in cryptarithmetic problem-solving with "funtastic" battle math game. The respondent 29 student of the 4th graders in the elementary school, 16 female and 13 male students. The research approach was qualitative and quantitative. The data were collected through paper and pencil test, observation, and interview. The data were analyzed by descriptive and effect size methods. The results showed the average score of male students is lower than female students, however effect size on male students is higher than female. The findings are then elaborated using some related theories to justify the results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the concept of a parametric b-2 Metric space, which is a nonlinear version of the parametric b-metric, as well as to establish several fixed point theorems in these spaces. Before extending the finding of O. Ege and I. Karaca [Azerbaijan Journal of Mathematics, 7(1), 2017] to parametric b-2 metric spaces, some basic definitions and notions of parametric b-2 metric space are provided. We also present an example to show how our findings are applicable. [ABSTRACT FROM AUTHOR]

In physics and mathematics educational environments, meaningful learning paths should be balanced interactive explorations of the different epistemological and cognitive phases of the modelling cycle. Our approach in this context involves sequences of interactive engagement learning activities with computational modelling that explore the different kinds of modelling, progressively introduce scientific computation, generate, and resolve cognitive conflicts in the understanding of physics and mathematics, and comparatively analyze complementary mathematical model representations. In this work we present a learning sequence about light polarization for intermediate science, technology, engineering, and mathematics (STEM) university courses during which students can create and explore in the computer relevant mathematical physics models and animations that help and complement the learning processes in theoretical lectures and problem-solving paper and pen activities. [ABSTRACT FROM AUTHOR]

The field of numerical mathematics is one of the basic mathematical areas of training of future mathematicians. It plays an important role in the sense of connecting theoretical knowledge with practice. At the same time, it is one of the courses that specifically applies students' computer knowledge in solving mathematical problems. As a number of mathematical software and programming languages are emerging with the rise of IT technology, the question arises as to how to build the concept of teaching numerical mathematics. Models that have been used for a long time are already proving to be non-functional and significant innovation is needed. The paper will describe the structure of teaching numerical mathematics at the University of Ostrava, its innovations and teaching experience. [ABSTRACT FROM AUTHOR]

Mathematical representation is one of the fundamental abilities used in mathematics to build the connection between abstract ideas and logical thinking to understand and solve mathematics problems. The level of student representation ability will affect the way students convey the idea of solving mathematics problems. This shows how important this ability is in mathematics. But in fact, the ability of mathematical representation is felt to be less comprehensively mastered. This is indicated by the large number of students having difficulty conveying their ideas in solving mathematics problems. This paper describes students' abilities in mathematical representation to solve math problems. The indicators for mathematical representation ability in this research are classified as verbal representation (written text), visual representation (picture, diagram, graph, or table), and symbolise representation (mathematical statement, numerical/algebra symbol, mathematical notation). The subject of this research was 8-grade students of one of the junior secondary schools at Bukittinggi. The results showed that 22 out of 34 students have difficulty in conveying their ideas to solve math problems, while the rest feel quite good about it. [ABSTRACT FROM AUTHOR]

This paper aims to describe mathematics teachers' perception of mathematical proof. Proving in mathematics for the teacher is crucial as the foundation of developing students' skills in generating correct proof to some conjectures which require good mathematical reasoning. It has been highlighted in some works of literature that mathematical reasoning which is closely related to proving in mathematics also contributes to the development of a chosen set of 21st-century skills. A total number 152 of Indonesian in-service mathematics teachers were given a survey concerning their perception of mathematical proving. The description of the result consists of five important categories including the process of mathematical proof, thinking ability in mathematical proof, appropriate school level in learning proof, topic, and understanding in a mathematical proof. It is found that Indonesian in-service mathematics teachers had a positive attitude towards mathematical proof as a teaching approach in their classrooms, as the opportunity for students to improve helped students improve their thinking ability. [ABSTRACT FROM AUTHOR]

In Graph theory, colouring is the best and most well-considered amplitude. The four-colour problem has contributed to great change in the world of mathematics. Graph colouring has become an essential of interest in graph theory. This often includes its disparate theoretical conclusions, its unconcluded issues and its several utilizations. Throughout this paper, the Conjecture Steinberg is studied with a counter example. Conjecture Steinberg states that "Each planar graph except cycles of length four or five is 3-colourable". Whereas an example by which there exists a planar graph with four or five cycle is 3-colourable is encountered for the Steinberg conjecture. [ABSTRACT FROM AUTHOR]

This paper aims to examine the learning of mathematics using philosophy-based teaching materials for high school students. Philosophy-based teaching materials are in the form of Student Activity Sheets (LKPD) consisting of LKPD based on Anthology, LKPD based on Epistemology, and LKPD based on Axiology. [ABSTRACT FROM AUTHOR]

The goal of this study is to outline the outcomes of analysis on the creation of useful math learning resources during the COVID-19 pandemic. The issue is that goods from the creation of math learning resources are required to counteract an acceleration in learning following the COVID-19 epidemic. Many of the results of development research, however, are only kept as study materials and are only preserved in Study Program documents or on Google Drive. The study was conducted utilizing the survey methodology, questionnaire data collection strategies, and development research outcomes papers completed by students of the Mathematics Education Study Program FKIP UPGRI Palembang during the COVID-19 epidemic. strategies for analyzing quantitatively described data. The outcomes of the development research take the form of products for math learning devices, with PBL/PBM, RME, CTL, and mathematics software being the most widely utilized learning models and methods. E-modules, LKPD/LKS, learning media in the form of video, and PPT are the most common product kinds. Algebra, Geometry, Calculus, trigonometry, statistics, and Arithmetic are among the mathematics topics covered throughout the development. The development's validity yields a product quality of 87.19%, while its practicality comes in at 85.48% and its potential impact is at 83.48%. According to the development research's findings, it should be given some thought if mathematics instruction is to be changed following the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

This paper aimed to describe the implications mathematics education in finance. Calculation of interest rates, discounts, profits, taxes, GDP growth requires basic arithmetic skills such as percentages. By imbuing financial literacy in math learning, not only do students know firsthand the use of percent in financial situations, but they are also increasingly knowledgeable about finance. Financial literacy in our study spans three dimensions: content, context, and process. By using the proportion and equation approach as well as two types of construction, namely the bar model and the circle model, we present the learning situation of monthly salary allocation table. Through this situation, students are expected to be able to construct fractional material and financial knowledge on salary and income content. [ABSTRACT FROM AUTHOR]

This paper aims to develop a valid and practice the development of PISA-Like Mathematics Problems and produce a potential effect on creative thinking skills of 7th grade junior high school students in solving the development of PISA-Like Mathematics Problems in the context of Palembang tourism. This research is type of qualitative research. The result of this research is the development of PISA-Like Mathematics Problems with the characteristics of creative thinking skills using Merdeka curriculum, which in the curriculum is related to number material. In content using Quantity content. In context using a social context, namely "Wisata Sungai Musi". In terms of difficulty level categorized as application level. To conclude, the development of PISA-Like Mathematics Problems can teach students to learn mathematics and at the same time introduce students to the culture and tourism of Palembang. [ABSTRACT FROM AUTHOR]

The effectiveness of Game-based Learning (GBL) in fostering students' motivation to learn mathematics is examined in this systematic review. Nine related papers published between 2018 and 2022 were found after an extensive search of the electronic databases of ERIC. A systematic review methodology was used to analyze the studies, and the results were then synthesized and summarized. None of the research in this review found evidence of a negative impact of GBL on students' motivation to learn mathematics; instead, all studies found evidence of a positive impact. It benefits students' motivation for several reasons, including the engaging and dynamic learning environment, the quick feedback and rewards, and the demanding and goal-oriented learning experience that games may give. The game's design, degree of difficulty, student autonomy, use of feedback and rewards, and other factors play significant roles in determining how effective GBL is at encouraging students' motivation to learn mathematics. However, this effectiveness is not guaranteed. The design and implementation of GBL in the mathematics classroom should consider these elements seriously. Generally, the results of this review point to GBL as a potentially successful strategy for increasing students' motivation to learn mathematics. Game-based Learning (GBL) is a strategy educators should consider employing to engage students and increase their interest in and love of mathematics. However, the game's design and other elements that may affect it must be carefully considered. More research is required to completely comprehend GBL's potential in mathematics education and develop efficient implementation methods. [ABSTRACT FROM AUTHOR]

COVID-19 pandemic requires professional teachers to use digital technology, but some students experience obstacles in technology so that it has an impact on their low critical thinking abilities. This paper aims to analyze mathematical critical thinking abilities between students who carry out learning models eliciting activities assisted by Edmodo and conventionally assisted by WhatsApp based on prior knowledge of mathematics. The research method used a quasi-experimental, non-equivalent pretest-posttest control group design. The sample was selected through a homogeneity test from 4 parallel classes of one junior high school in Bandung Indonesia, two classes were selected, namely class VIII A as the experimental class and VIII D as the control class. The instrument uses an initial mathematical ability test and critical thinking abilities. Data analysis uses: Two-way ANOVA test. Findings: There is a difference in the improvement of mathematical critical thinking abilities between experimental class and control class students. There are differences in the achievement of mathematical critical thinking abilities based on prior knowledge of mathematics in the smart, medium and weak categories. Learning models eliciting activities assisted by Edmodo can facilitate the process of construction, interaction and reflection so as to improve students' critical thinking abilities. [ABSTRACT FROM AUTHOR]

In this paper proposed, a novel subclass of meromorphic univalent functions has been introduced and defined. 풥(a, ℷ, A, B, μ) using convolution operator in U*. We have obtained some properties, like, coefficient inequality, growth and distortion bounds, radii of starlikeness and convexity, linear combination, closure theorems and extreme points. Mathematics Subject Classification: Primary 30C45 [ABSTRACT FROM AUTHOR]

This paper attempts to provide information about designing digital holographic learning media especially in teaching and learning mathematics at University. To be detail, this study was conducted to provide educators at university information towards things need to be considered in designing such instrument. In this case, we depict several activities in making holograms to deliver mathematical insights for students for Calculus course. The study was carried out through developmental steps ADDIE, such as Analysis, Design, Development, Implementation, and Evaluation. This study was conducted at Mathematics Education Program, Medan State University, especially for students who enrolled Calculus course. The activities were described explicitly in each phase. The results of this study show that it takes time to make holographic digital media in teaching and learning process of mathematics, including university. In this case, there are several aspects that need to be considered in designing the media, such as (1) the learning topics; (2) contents; (3) object video/animation; (4) hologram application. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a result on the existence of fixed points for a system of mappings which generalizes the results of Edelstein (J. London Math. Soc. 37 (1962), 7479), Suzuki (Nonlinear Anal. 71 (2009), 11, 53135317.), Matkowski (Bull.Acad.Polon.Physics. 21 (1973), 323324) and many others. As an application, we establish a result on the existence of common fixed points for two systems of mappings, which supports our main finding. In addition, we also have an example to validate our main finding. [ABSTRACT FROM AUTHOR]

Education for children with special needs, especially with mild intellectual disabilities, has not received much attention from researchers and practitioners. The education of intellectual disabilities children also has the same right to develop according to the needs of the times as regular children's education in general. The changing and evolving needs of the times should also be followed by changes in the curriculum used, considering that one of the learning goals in special schools for intellectual disabilities children is to make the children who can live independently. In special schools for intellectual disabilities children in Indonesia, mathematics learning is combined with other lessons to discuss specific themes in everyday life. Based on an extensive literature search on the mathematics curriculum in special schools for intellectual disabilities children, this paper aims to review the literature involving two things: (1) mathematics education curriculum in special schools for intellectual disabilities children in Indonesia, and (2) mathematics curriculum in special education in Australia and Singapore. A view is also provided. This paper concludes that: (1) learning in special schools for intellectual disabilities children in Indonesia uses thematic learning where mathematics learning is focused on its usefulness in everyday life, (2) numeracy is the focus of education in Australia, not least for intellectual disabilities children, and learning Mathematics for mild intellectual disabilities children in Singapore includes the concepts of numbers, spaces, arithmetic procedures, problem solving and measurement. [ABSTRACT FROM AUTHOR]

Students' pattern of learning that does not involve active thinking will make it difficult for them to master the elements of higher order thinking skills (HOTS) in mathematics. Therefore, more effective learning methods need to be implemented to help students deal with this problem. This paper presents the results of a study after a cooperative method through paired learning was conducted on a selection of Year 6 students for the subject of Mathematics. The purpose of the study was to see the effectiveness of paired learning methods in the teaching and learning process of mathematics that apply the elements of HOTS. A total of twenty-eight Year 6 students from a school in Penang were selected as the sample for this study. Students' performance was tested before and after treatment to see if there was a difference between their performances. After that, a questionnaire was given to see the level of students' motivation and identify the factors contributing to their difficulties in mastering HOTS. From the results of this study, all students (100%) have shown an improved performance in the post-test. The mean scores from the questionnaire responses also indicated that students had a positive perception of the paired learning method. [ABSTRACT FROM AUTHOR]

Prior to the COVID-19 pandemic, majority of universities in Malaysia commonly implement the teaching and learning practices on physical face to face basis. However, the pandemic had drastically changed the norm of the teaching and learning practices into online teaching and learning as one of the measures to curb the spread of the virus among the community. The drastic move had greatly affected the academic communities particularly the students. Some of the possible factors influencing online learning difficulties faced by the students include poor internet accessibility, lack of self-motivation, lack of active interaction with lecturers and peers, lack of conducive learning environment and poor time management. In this paper, the technique of Fuzzy DEMATEL is employed in analyzing the level of influence and relationships of the aforementioned factors in contributing to learning difficulties particularly among fifty mathematic students at a public university in Shah Alam, Selangor, Malaysia. The cause-and-effect analysis that take into consideration the interactions or interrelationships between factors discovered that poor internet accessibility was classified in the cause group whereas the remaining factors which are lack of self-motivation, lack of active interaction with lecturers and peers, lack of conducive learning environment and poor time management were in the effect group. The results indicate that poor internet accessibility has the highest degree of relation in terms of influencing other factors. Based on the prominence value, the lack of self-motivation turns out to be the leading factor contributing to online learning difficulties. [ABSTRACT FROM AUTHOR]

Teaching and Learning Mathematics in the 21st centuries highly related to the digital technology used in the classroom. Mathematics is the best practice in the standard teaching and learning (T&L) process where the teacher and student physically attend the class. There is where the interaction and discussion on subject matter happened. However, due to the COVID-19, the practice needs to be changed drastically in which both sides of teacher and student are not allowed to have a physical class to avoid any contact. The learning process must proceed and adapt well to the current situation. A Learning Management system must be developed as a platform to digitally organize educational material. Due to that, this paper aims to illustrate the development of a website that is beneficial in T&L Mathematics courses. The content of the mathematics course chosen is Linear Algebra. There are various learning management systems, but the one that customizes the purpose and requirement of our class content can be developed by ourselves. Google offers a good package where google sites can be easily set up for that purpose. The content is arranged according to based on topics. In addition, the interactive learning environment is also embedded in developing the system to attract the student's attention during class hours. Live chat is also provided for the student to ask questions at their convenience time. Developing a customized learning management system can be an alternative for teachers to provide a digital environment to their students so that the process of T&L can be continued. Our website has been introduced to students, and their feedback is recorded. The result shows that students show positive responses while describing the website [ABSTRACT FROM AUTHOR]

The mode of assessment is one of the most important factors influencing learning as it affects how students organize their time and what subjects they focus on. It is well known fact that students may exhibit different abilities in different forms of assessment. In this paper, we show how e-assessment with the Halomda educational platform can enhance students' learning experiences. In addition, we present how technology-assisted math education can help students study at home and in the classroom, as well as support teachers in their routine work of checking student assignments. Results from teaching courses with Halomda demonstrate not only high student learning outcomes on the final exam, but also a good correlation between exam marks and weekly assignment marks. [ABSTRACT FROM AUTHOR]

Lie algebras appeared in mathematics at the end of the 19th century in connection with the study of Lie groups. A Lie algebra is a vector space over some field together with a bilinear multiplication is called the bracket which satisfies two simple properties: skew symmetric and Jacobi identity. The universal property of tensor product for representations of Lie algebras is a supporting conjugate of tensor product, which guarantees obtaining a linear map from a bilinear map. The main objective of the paper is to obtain results in representations for Lie algebra through the new structure consisting of four and five representations, by action of representation for Lie algebra. As well as obtaining new generalizations using dual action of representation for Lie algebra. [ABSTRACT FROM AUTHOR]

Nowadays, the need of ICT as a learning aid has potential role at the global scope. However, it sounds contradicts with the teaching and learning habit of the boarding schools or pesantren environment. It is an educational institution with strong and large cultural products, but reluctant to see the urgency of ICT implementation. This article aimed to examine students' learning experiences in mathematics at the role of ICT. The study was conducted using a qualitative approach with phenomenological methods. Research data were obtained through interviews and observations. Furthermore, triangulation of sources and triangulation of theory using Dale's classification or "the Cone of Experience" was carried out with regard to student learning experiences. The results showed that at this place: 1) the learning experience symbolically dominated the implementation of mathematics learning; 2) the iconic and enjoyable learning experience was only experienced by some students; 3) ICT had an important role in creating a symbolic, iconic, and enjoyable learning experience for students. This study provides strategic recommendations on how it can adapt the positive impact of ICT to support the learning process. While it deems impossible to stem the flow of ICT developments, this paper can serve as a reminder and a form of wake-up call to keep up with the demands and developments of the times. When ICT integration has not been implemented in mathematics learning, teachers should be able to create concrete learning experiences for students. [ABSTRACT FROM AUTHOR]