Fields Of Mathematics Research Articles

The Title of the Growth of New Dynasties in Spain Maghrib and Iran

This research aims to examine the birth and development of new dynasties in the regions of the Spanish Maghrib and Iran after the collapse of major powers such as the Umayyad Caliphate in Spain and the Abbasid Caliphate in Iran. Employing a literature research approach, this study traces the background of the emergence, expansion processes, consolidation of power, as well as the contributions of these dynasties to the intellectual and cultural development in the regions they ruled. In the Spanish Maghrib, the Almoravid and Almohad Dynasties emerged as new powers after the fall of the Umayyad Caliphate. Both dynasties succeeded in uniting the regions of Spain and the Maghrib, albeit with different methods and ideologies. Meanwhile, in Iran, the Ilkhanid, Jalayirid, Timurid, and Safavid Dynasties rose after the collapse of the Abbasid Caliphate, each exerting significant influence and contributions to the political, cultural, artistic, and scientific development. The research findings indicate that the birth and development of these new dynasties not only brought about political changes but also contributed significantly to intellectual and cultural advancements in both regions. The periods under their rule are known as golden ages in the fields of art, architecture, literature, mathematics, astronomy, philosophy, and other sciences. These dynasties fostered the exchange of ideas among various ethnic and religious groups and created a conducive environment for the growth of knowledge and creativity. Overall, this study highlights the importance of the new dynasties in the dynamics of history and civilization, as well as their contributions in shaping new political landscapes and catalyzing the growth of rich knowledge, art, and culture.

The Impact of Immersive Virtual Reality on Knowledge Acquisition and Adolescent Perceptions in Cultural Education

Understanding local history is fundamental to fostering a comprehensive global viewpoint. As technological advances shape our pedagogical tools, Virtual Reality (VR) stands out for its potential educational impact. Though its promise in educational settings is widely acknowledged, especially in science, technology, engineering and mathematics (STEM) fields, there is a noticeable decrease in research exploring VR’s efficacy in arts. The present study examines the effects of VR-mediated interventions on cultural education. In greater detail, secondary school adolescents (N = 52) embarked on a journey into local history through an immersive 360° VR experience. As part of our research approach, we conducted pre- and post-intervention assessments to gauge participants’ grasp of the content and further distributed psychometric instruments to evaluate their reception of VR as an instructional approach. The analysis indicates that VR’s immersive elements enhance knowledge acquisition but the impact is modulated by the complexity of the subject matter. Additionally, the study reveals that a tailored, context-sensitive, instructional design is paramount for optimising learning outcomes and mitigating educational inequities. This work challenges the “one-size-fits-all” approach to educational VR, advocating for a more targeted instructional approach. Consequently, it emphasises the need for educators and VR developers to collaboratively tailor interventions that are both culturally and contextually relevant.

Circling the Square with Straightedge & Compass in Euclidean Geometry

There are three classical problems remaining from ancient Greek mathematics which are extremely influential in the development of Geometry. They are Trisecting an Angle, Squaring the Circle, and Doubling the Cube problems. I solve the Squaring the Circle problem, of which paper is published in the International Journal of Mathematics Trends and Technology (Volume 69, June 2023). Upstream from this method of exact “Squaring the Circle”, we can deduce, conversely/inversely, to get a new Mathematical challenge "CIRCLING THE SQUARE" with a straightedge & a compass in Euclidean Geometry. This study idea came from my exact solution “Squaring the Circle by Straightedge & compass in Euclidean Geometry”, published by IJMTT in June 2023 at https://ijmttjournal.org/Volume-69/Issue-6/IJMTT-V69I6P506.pdf for this ancient Greek Geometry problem. In this research, I adopt the ANALYSIS method to prove the process of solving this new challenge problem, which has not existed in the Mathematics field till today. The process is an inverse/converse solution solving the ancient Greek Geometry challenge problem of “Squaring the Circle”, using a straightedge & a compass. I hereby commit that this is my own personal research project.

Elementary proof of Funahashi's theorem

Funahashi established that the space of two-layer feedforward neural networks is dense in the space of all continuous functions defined over compact sets in $n$-dimensional Euclidean space. The purpose of this short survey is to reexamine the proof of Theorem 1 in Funahashi \cite{Funahashi}. The Tietze extension theorem, whose proof is contained in the appendix, will be used. This paper is based on harmonic analysis, real analysis, and Fourier analysis. However, the audience in this paper is supposed to be researchers who do not specialize in these fields of mathematics. Some fundamental facts that are used in this paper without proofs will be collected after we present some notation in this paper.

LINEAR ALGEBRA AS THE MATHEMATICAL FOUNDATION OF ARTIFICIAL INTELLIGENCE: CONCEPTS, APPLICATIONS, AND FUTURE PROSPECTS

Linear algebra, a fundamental tool in the field of mathematics, plays an essential part in the mathematical foundation of the groundbreaking arena of Artificial Intelligence (AI). This mathematics branch offers immense possibilities for capturing complex relationships within datasets through matrices and vectors. These mathematical tools facilitate the concise representation of large volumes of data, contributing to efficient data analysis between them, bringing immense value to AI algorithms and models. This research paper investigates the pivotal role of linear algebra as the fundamental mathematical framework underpinning artificial intelligence. This paper also explores the foundational concepts of linear algebra and its direct applications in various AI algorithms, demonstrating how matrices, vectors, and transformations provide the essential mathematical scaffolding for the development and optimization of intelligent systems.

ДОСЛІДЖЕННЯ МЕТОДУ ФРАКТАЛЬНОГО СТИСНЕННЯ ЗОБРАЖЕНЬ З МЕТОЮ ПОКРАЩЕННЯ ЯКОСТІ СТИСНЕННЯ

The development of the Internet, along with the availability of increasingly powerful computers and other digital devices, cameras, scanners and printers, has led to the wide-spread use of digital images. In this regard, interest in improving data compression algo-rithms, such as images, is growing. Data compression is important for both transfer speed and storage efficiency. In addition to many commercial uses, compression technologies are also of interest in the military industry, such as applications for processing telemetry data from missile inter-ceptors or for archiving terrain image data for defense simulations. Solving the problem of image compression, or, more generally, image coding, has used advances and stimulated the development of many fields of engineering and math-ematics. The article examines fractal image compression — a data compression method based on the use of self-similar patterns in an image. This method allows you to achieve a high degree of compression while preserving image details. Fractal image compression is a unique and efficient approach to data compression based on the mathematical theory of fractals. Nowadays, it has important applications and advantages that make it a valuable tool in image processing. The main advantages include: 1. Preservation of details during compression. One of the key advantages of fractal compression is its ability to preserve a high degree of image detail in a relatively small amount of storage. This is especially important in situations where image quality must be preserved with limited storage and data transfer resources. 2. Efficiency of transmission through the network. Fractal compression allows for compact images, making it suitable for image transmission over a low-bandwidth network. This is especially true for mobile devices, the Internet of Things, and other scenarios where high bandwidth is not always available. 3. Adaptive compression for different resolutions. Fractal compression allows you to adapt the level of compression depending on the resolution and details of the image. This means that it can be used to compress various image sizes without significant loss of quality. 4. Data archiving and storage. Fractal compression can be useful for archiving and long-term storage of images, as it allows you to effectively reduce the amount of data without losing important information. This is especially important for libraries, archives, research databases and other data repositories. Fractal image compression remains a relevant and valuable tool in today's envi-ronment, thanks to its ability to efficiently compress, preserve details, and adapt to dif-ferent usage scenarios. Therefore, the study of its efficiency, the optimization of the soft-ware code to obtain a faster and better compression result, is an urgent task.

Overstaying our welcome: On the rise of women's seniority in the academy

AbstractIssues surrounding gender equality are—and should be—front and centre in the water resources community, and other science, technology, engineering and mathematics (STEM) fields. Very necessarily, the focus tends to be on recruitment, offering support for students and early career academics. The leaky pipeline concept used to describe the incremental loss of women from STEM fields with career duration describes a disproportionate loss of senior women, creating a parallel problem where highly qualified, top tier academics are lost from the system after significant financial and personnel investment by institutions. Ultimately, the leaky pipeline undermines the extensive investment of the hydrology and other STEM communities in equity, diversity, inclusion and accessibility (EDIA) recruitment and retention programmes by cutting short career ambitions and the trajectories of diverse top performing individuals, resulting in no net benefit of EDIA policy investments and a lack of diversity with seniority. Addressing this critical gender gap requires the attention and support of the hydrology community of practice with specific focus on generating opportunities for advancement, confronting systemic and structural biases and improving education around allyship. Institutions and professional organizations need to consciously grow diversity in leadership and recognize and outwardly manage the perception of academic excellence around slow research and education that attracts increased diversity. Supporting allyship, reducing competitiveness among community members and reinforcing collaboration will not only attract, but retain, a higher proportion of diversity in the hydrology community, academia and STEM professions in general. It is time for the water resources (and other STEM) communities to demand broader accountability and recognition of the barriers to women, implement and reward more diverse definitions of research excellence, and offer allyship training to the community of practice at large.

Lighting pathways to success in STEM: a virtual Laboratory Meeting Programme (LaMP) mutually benefits mentees and host laboratories.

Developing robust professional networks can help shape the trajectories of early career scientists. Yet, historical inequities in science, technology, engineering, and mathematics (STEM) fields make access to these networks highly variable across academic programmes, and senior academics often have little time for mentoring. Here, we illustrate the success of a virtual Laboratory Meeting Programme (LaMP). In this programme, we matched students (mentees) with a more experienced scientist (mentors) from a research group. The mentees then attended the mentors' laboratory meetings during the academic year with two laboratory meetings specifically dedicated to the mentee's professional development. Survey results indicate that mentees expanded their knowledge of the hidden curriculum as well as their professional network, while only requiring a few extra hours of their mentor's time over eight months. In addition, host laboratories benefitted from mentees sharing new perspectives and knowledge in laboratory meetings. Diversity of the mentees was significantly higher than the mentors, suggesting that the programme increased the participation of traditionally under-represented groups. Finally, we found that providing a stipend was very important to many mentees. We conclude that virtual LaMPs can be an inclusive and cost-effective way to foster trainee development and increase diversity within STEM fields with little additional time commitment.

EMOTIONAL TRAINING FOR PROSPECTIVE TEACHERS IN SCIENCE EDUCATION

Cognitive and affective interrelationships are increasingly gaining importance in educational literature, assigning emotions a prominent role in the teaching and learning process. This study aims to promote awareness among prospective teachers of their emotional vulnerability and the influence of affective and emotional aspects in the teaching of natural sciences, mathematics, and social sciences. The research had a dual purpose: to analyse the beliefs, attitudes, and emotions of prospective teachers regarding the teaching of these disciplines and to examine the impact on their beliefs and emotions after undergoing specific training. The study topic is justified by the growing attention emotions are receiving as decisive factors in learning processes and the persistent substantial gap in scientific education research, particularly in the realm of online teacher training. To address and analyse this gap, a descriptive quantitative survey study on beliefs, attitudes, and emotions towards the teaching of these courses before and after participation in a training program was designed. The analysis of the data revealed results consistent with previous studies. Specifically, the results demonstrated that prospective teachers showed more negative emotions, beliefs, and attitudes towards the teaching of natural sciences and mathematics compared to the teaching of social sciences. However, in all cases, improvements were observed after receiving specific training. These findings highlight the need to incorporate emotional improvement projects into online teacher training, particularly in the fields of natural sciences and mathematics. Keywords: distance education, emotional teaching, pre-service teachers, science education

Defining quantitative rules for identifying influential researchers: Insights from mathematics domain

In the midst of a vast amount of scientific literature, the need for specific rules arise especially when it comes to deciding which impactful researchers should be nominated. These rules are based on measurable quantities that can easily be applied to a researcher's quantitative data. Various search engines, like Google Scholar, Semantic Scholar, Web of Science etc. Are used for recording metadata such as the researcher's total publications, their citations, h-index etc. However, the scientific community has not yet agreed upon a single set of criteria that a researcher has to meet in order to secure a spot on to the list of impactful researchers. In this study, we have provided a comprehensive set of rules for the scientific community within the field of mathematics, derived from the top five quantitative parameters belonging to each category. Within each categorical grouping, we meticulously selected the five most pivotal parameters. This selection process was guided by an importance score, that was derived after assessing its influence on the model's performance in the classification of data pertaining to both awardees and non awardees. To perform the experiment, we focused on the field of mathematics and used a dataset containing 525 individuals who received awards and 525 individuals who did not receive awards. The rules were developed for each parameter category using the Decision Tree Algorithm, which achieved an average accuracy of 70 to 75 percent for identifying awardees in mathematics domains. Moreover, the highest-ranked parameters belonging to each category were successful in elevating over 50 to 55 percent of the award recipients to positions within the top 100 ranked researchers' list. These findings have the potential to serve as a guidance for individual researchers, who aimed on to making it to the esteemed list of distinguished scientists. Additionally, the scientific community can utilize these rules to sift through the roster of researchers for a subjective evaluation, facilitating the recognition and rewarding of exceptional researchers in the field.

Methods of Automatic Analysis of Information Presentation Dynamics in Texts Based on Adaptable Dictionaries of Scientific Terms

The paper proposes a method for determining the dynamics of aspectual content of scientific texts. The problems arising in the automatic processing of scientific texts are discussed, approaches to the creation of a combined method of aspect-oriented analysis of scientific texts are proposed. The results of experiments of aspect analysis of scientific publications in the field of mathematics are given. The algorithm of aspect analysis is built on the basis of processing both the semantic domain graph formed as a result of automatic extraction of information from the text of the mathematical encyclopedia and the weighted semantic graph of the publication. Weighting functions for calculating the dependence of links between professional terms of the semantic domain graph are proposed. During the processing the text of a scientific publication, the semantic domain graph is transformed into the semantic graph of the publication, the two-phase processing algorithm of which forms semantic dependencies between text fragments.

Identity Trajectories of Faculty Members through Interdisciplinary STEAM Collaboration Paired with Public Communication

Faculty members in science, technology, engineering, and mathematics (STEM) fields are accustomed to presenting their research findings through journal publications, conference presentations, textbooks, and other academic mediums. However, the audience for these traditional forms of communication are other researchers, which raises concerns about how science research and knowledge are communicated to audiences who have less expertise on these topics. We sought to understand how faculty members develop their identities through collaborative professional development opportunities aimed at growing communication skills to communicate with audiences less familiar with research through interdisciplinary science, technology, engineering, arts, and mathematics (STEAM) activities. We conducted a qualitative, longitudinal study with sixteen STEAM faculty members to explore their identity trajectories as their interdisciplinary cohorts participated in various collaborations to engage with public audiences about their research. Through our analysis, we found that each faculty member’s dominant identity played a significant role in their identity trajectory through their professional development. We observed a significant growth in faculty members’ communication skills, such as learning new presentation techniques to engage others in their research areas of expertise and in their understanding of interdisciplinary STEAM collaboration. Our results provide insights into the identity trajectories of faculty members and how their identity development through these interdisciplinary STEAM collaborations will impact their formal education roles as researchers and teachers moving forward.

Literature Review: Study of the Use of Interactive Multimedia in Mathematics and Natural Sciences Learning in Indonesia

The use of information and communication technology (ICT) in teaching has become an important issue in recent years in order to improve the quality of education. One use of ICT is as a learning tool, namely in the form of interactive multimedia. Learning using interactive multimedia develops on the basis of conventional learning which cannot meet students' learning needs. This interactive multimedia can be a supplement and complement to learning which represents learning resources. Interactive multimedia is multimedia that is equipped with a controller that can be operated by the user, so that the user can choose what they want for the next process. Interactive multimedia has been widely created and used in Mathematics and Natural Sciences learning in Indonesia. In this paper, a literature review study will be carried out on the use of interactive multimedia in learning in the fields of mathematics and natural sciences, to see developments, development methods, weaknesses and the results that have been achieved. On this occasion, the author provides observation results based on evidence through a literature review regarding the extent of multimedia use in learning, especially in the field of exact sciences such as mathematics and natural sciences.

Independence Number of Order Prime Graph

Objective: To explore the algebraic structures inherent in groups and their relationship to graph theory, particularly focusing on the process of converting a group into a graph. Method: Let be a group. The Order Prime Graph of is a graph with and two distinct vertices and are adjacent in if and only if In this paper, we characterize the structure of order prime graphs of some groups and also we find the independence number and clique number of the order prime graph. Finding: In the present article, we characterized the structure of order prime graphs of some groups and also we found the independence number and clique number of the order prime graph. Novelty: Introducing innovative methods for converting groups into graphs, departing from existing approaches, could be a key novelty. This might involve novel ways of encoding group elements as vertices and group operations as edges, potentially leveraging insights from other mathematical fields or computational techniques. Keywords: Order Prime graph, Finite group, Clique number, Independence number, Prime number

Nanomaterials Research at a Primarily Undergraduate Institution: Transforming Nanorods, Undergraduate Research Communities, and Infrastructure.

Undergraduate research transforms student's conceptions of themselves as scientists and encourages participation and retention in science, technology, engineering, and mathematics (STEM) fields. Many barriers exist to carrying out scientifically impactful undergraduate research in nanomaterials at primarily undergraduate institutions (PUIs). Here, we share several practices and design principles that demonstrate pathways to overcome these barriers. Design of modular research projects with low entry barriers is essential. Postsynthetic transformation of nanoparticles is a field that enables such design and has been used successfully to advance nanoscience research while being achievable within undergraduate laboratories. Relatively large, inclusive research communities can be supported through the creation of opportunities with peer- and near-peer mentoring. We also share emerging strategies for enabling routine undergraduate access to transmission electron microscopy, which is one of the most mainstream characterization techniques in nanoscience yet is frequently absent from the infrastructure at undergraduate-focused institutions.

Core competency oriented problem-solving teaching ----Taking "Solving Application Problems with a System of Equations" as an Example

The teaching of Mathematical problem-solving is one of the three key teaching points in junior high school mathematics. Solving applied problems through equations (systems) is an important component of the first module of teaching content, "Numbers and Algebra", and holds a very important position. It is a key focus in junior high school mathematics problem-solving teaching. At present, under the premise of the implementation of the new curriculum reform in the field of mathematics in China, based on the recent publication of compulsory education curriculum standards,the teachers of mathematics should focus on cultivating excellent mathematical core literacy among junior high school students, and ensuring that they can independently cope with and solve problems in the math teaching of junior high school. Based on the above background, the author focuses on the newly published mathematics curriculum standards in 2022, and studies the teaching design of "solving application problems for systems of equations". In this paper, we explore the mathematical core literacy elements contained in the teaching of solving applied problems in equations, study the improvement path of mathematical problem-solving teaching, share the teaching design practice and thinking based on core literacy oriented problem-solving teaching, and the important role that this teaching design can play in cultivating students' core literacy .

Lesson Plan Design Process Develops STEM Design Thinking Through Science Grade 4

Within the context of fundamental STEM education, the primary objective of this article is to investigate the process of developing lesson plans specifically for the aim of fostering students' capacity for design thinking in the field of science. When it comes to the process of document gathering and analysis, the qualitative research approach is utilized. The outcomes of the study indicate that design thinking makes a substantial contribution to the development of students' creative activities and their ability to engage in problem-solving activities. In addition, it has been demonstrated that design thinking is an extremely efficient method for supporting students in their educational pursuits. Education in the fields of mathematics, science, technology, and engineering are all equally important. while it comes to the field of STEM education, it is essential to adhere to a particular method while developing lesson plans to encourage the growth of design thinking in students. In order to improve the efficiency of STEM education and to provide recommendations regarding areas that need additional research on the subject matter, the purpose of this article is to supply academics and teachers with resources that are pertinent to the subject matter.

Experiences of female early-career professionals in male-dominated STEM companies in Kazakhstan

ABSTRACT After the collapse of the Soviet Union, Kazakhstan put forward elaborate initiatives to address gender segregation in the labour market. However, female professionals are still heavily underrepresented in the fields of science, technology, engineering and mathematics. Considering conflicting cultural influences on the role of women in the country and guided by the social cognitive theory, the present study explores the early career experiences of female professionals working in STEM companies in Kazakhstan. The thematic analysis of 24 semi-structured interviews with early-career female professionals showed that social structural challenges with recruitment and promotion, organization integration and work-life balance prevent women from building successful careers in STEM. It was also found that to counterbalance these challenges, female professionals develop a variety of coping strategies such as projecting a professional image and adopting a masculine interaction style, conforming to the existing status quo and challenging gender discrimination and stigmatization. Drawing from the social cognitive theory, this study revealed that conflicting gender role expectations based on traditional, Western and Soviet cultural values might disempower and undermine women’s agency in transitioning to employment in STEM.

Determinating the STEM Education Compentencies of Pre-Service Teachers

With solely academic knowledge, it appears challenging for today's students to find a place for themselves in the business world where they will operate in the future. Therefore, it is crucial to provide students with a variety of abilities, such as problem-solving, critical thinking, creativity, collaboration, and analytical thinking, in addition to academic knowledge. The STEM education approach is one of the approaches that aims to equip students with the knowledge and abilities they need in the fields of science, technology, engineering, and mathematics while also educating them as persons with 21st-century competencies. In this context, it is the teachers who will provide students with these knowledge and skills and apply STEM education. In this sense, it is thought that teachers' knowledge and competencies in STEM teaching are significant. In this study, it was aimed to determine the STEM teaching competencies of pre-service teachers studying in the last year of education faculties. The case study design, one of the qualitative research methods, was used in the research. The study group of the research consists of 45 final year science and classroom teaching students studying at 21 different universities in Turkey. The data of the research was obtained by the "STEM Teaching Competencies Questionnaire" developed by the researchers. The obtained data were analyzed simultaneously by three different researchers using content analysis. During the analysis process, codes, categories and themes were created. As a result, it can be claimed that pre-service teachers have theoretical knowledge of STEM education, but they do not think of themselves as highly competent. They require more hands-on education and wish to use it when they begin their careers, but they need practice-based education for this

Using GeoGebra with Van Hiele’s Model in Geometry Classroom: An Experience with Prospective Teacher

Various advances in technology, communication, and information have provided great benefits to all users around the world, especially in digital communication and learning mathematics in the classroom. However, without a systematic and clear model, the use of technology becomes vague and ineffective in cultivating students' interest and understanding in the field of Science, Technology, Engineering, and Mathematics (STEM). This study aimed to explore prospective teachers’ (PT) understanding and experience using GeoGebra with van Hiele’s model in the geometry classroom. The research employed a qualitative approach, specifically a case study design, which included semi-structured one-on-one interviews and classroom observations. Additionally, dynamic GeoGebra task completion, digital objects, tests, and electronic surveys were also administered. The bottom-up data analysis process was conducted inductively by reading the collected data and forming segments, determining the codes, and filtering overlapping codes until themes were identified. The results showed PTs' sequential understanding using GeoGebra occurred enthusiastically in a supportive environment. This understanding was evidenced when students engaged in activities such as examining, analysing, doing, comparing, identifying, explaining, recognising, distinguishing, and solving tasks. Furthermore, the experience of PTs using GeoGebra involved a collaborative environment, motivation to learn, awareness of various technologies, and independent learning. In conclusion, the transformation of PT’s comprehension using GeoGebra in Mathematics is actively demanded with the use of a guidance process such as van Hiele’s model. It provides greater chances for students’ engagement while delivering more appropriate and meaningful learning.