Fields Of Mathematics Research Articles

Empowering Women in Biomedical Engineering: A Departmental Pathway to Inclusion and Support

ABSTRACT The underrepresentation of women in science, technology, engineering, and mathematics (STEM) fields, including biomedical engineering, remains a persistent challenge and emphasizes the need for initiatives that attract and retain more women in the field. Such initiatives should address this gender imbalance and aim to harness the diverse perspectives and talents of all genders. Women in engineering face unique challenges due to the field’s male-dominated nature. Gender bias, stereotypes, and family-unfriendly expectations can significantly affect women’s experiences, hindering their opportunities for recognition and career advancement. A 2021 survey of the Biomedical Engineering Department and Graduate Group at the University of California Davis revealed that women and marginalized individuals experience a different sense of belonging compared with their white male counterparts, frequently encounter challenges related to implicit bias, microaggressions, and a lack of adequate support, mentorship, and opportunities for professional development. Here, we describe and reflect on the efforts by the Biomedical Engineering Health, Equity, and Wellness Committee to begin to address these challenges. We launched the Women+ in Biomedical Engineering Lunch Series, which provides a platform for women, marginalized individuals, and their allies to come together, connect, and share experiences. The lunch series aims to facilitate open dialogue, mentorship, and support and promote networking opportunities to bridge the gender gap in the field. The initial meetings in the Spring quarter of 2023 focused on key topics such as mentoring, mental health and stress management, and the effect of legislation on women’s professional lives. By providing a safe space for discussion, sharing experiences, and addressing these topics, the lunch series aims to break down barriers and build networks, foster a supportive environment, and empower women to thrive in biomedical engineering.

Unveiling Effective CSCL Constructs for STEM Education in Malaysia and Indonesia

The acquisition of knowledge and skills in the fields of Science, Technology, Engineering, and Mathematics (STEM) plays a crucial role in fostering the development of future innovators. These subjects are critical for creating future thinkers. Additionally, it is important to note that there are a lot of job openings in the STEM fields, and this trend is expected to keep growing. However, students don’t seem to be as motivated to study in STEM fields or work in STEM fields. One teaching method that is becoming more popular is computer-supported collaborative learning (CSCL). This is because it can have a big effect on how people learn, especially in STEM subjects. It is very important to set up a CSCL learning environment for STEM schooling right away. However, that there isn’t a good framework and there aren’t many widely used design methods in this area. Without a question, there is a strong need to learn more about design methodologies in the areas of collaborative and technology-enhanced learning to come up with simple methods for CSCL. Because of this, the goal of this study is to investigate the conceptual parts of CSCL methods in STEM education. This will be used to make CSCL educational methods that are good especially for STEM education. STEM academics in Malaysia and Indonesia were surveyed using questionnaires to find the most important parts of CSCL strategies in STEM education, and the results were analysed using the Fuzzy Delphi Method. The results give us a list of CSCL settings used in schools, which can be used as a guide for creating and using CSCL strategies in STEM education.

Empowering Diversity: Policies for Gender Equality in Stem Education and Workforce Progression in North Macedonia

Abstract The enduring global issue of women's underrepresentation in science, technology, engineering, and mathematics (STEM) fields carries significant implications for both societal advancement and economic growth. Despite the rise in women's enrollment in higher education, the persistent gender pay gap can be attributed in part to their limited presence in STEM domains, which tend to offer higher-paying career prospects. This study scrutinizes the impact of national policies on gender imbalances in STEM, focusing on the case of North Macedonia. It assesses existing measures and programs while proposing recommendations to foster gender parity in STEM both national and local scales. Employing a mixed research methodology, the study incorporates desktop research, statistical analysis of gender distribution in STEM fields, policy evaluations of national frameworks, and primary data collection through interviews and surveys.

A Systematic Literature Review of Project-Based Learning on English Writing Skills

Project-based learning (PjBL) is a student-centred approach focusing on experiential learning. The approach has been widely used in the field of sciences and mathematics but not in social sciences, particularly in English writing skills. As PjBL gains popularity as one of the 21st century teaching and learning approaches, there is a need to identify the trends, key authors, significant countries, and findings related to PjBL in writing. This paper presents a systematic literature review (SLR) conducted on 17 articles from the year 2018 to 2023 from the Scopus database following the PRISMA guideline. The study focused on PjBL and English writing, employing a systematic literature review to analyse trends, countries, authors, and journals. The analysis reveals dynamic trends of PjBL in the writing field. While the publication output fluctuated over the years, Indonesia emerged as a major contributor, signifying a global interest. A diverse distribution of articles across journals and countries underscores the global impact of PjBL, with notable contributions from Malaysia, China, and Russia. This paper synthesises the key themes from the literature review, emphasising the improvement in writing skills through PjBL and its challenges. The findings underscore PjBL's potential in transforming English writing education, emphasising the importance of addressing challenges for effective integration. The study contributes to the literature through a systematic analysis, providing insights into the trends and recommendations in PjBL in English writing research. Further research should delve into refining PjBL methodologies to maximize its innovative potential in English writing instruction.

White Racial Framing and White Supremacy Culture in STEM Education: Experiences of Students with Minoritized Identities of Sexuality and/or Gender

Whiteness is prevalent in higher education and therefore permeates science, technology, engineering, and mathematics (STEM) fields. While research shows STEM’s long history of exclusion and marginalization in higher education (Ong et al., 2011), there has been limited research on the ways students with minoritized identities of sexuality and/or gender (MIOSG) in STEM interact with systems of dominance, such as whiteness. Using white supremacy culture (Okun, 2021; Okun Jones, 2001) and the white racial frame (Feagin, 2010) as sensitizing concepts, this paper explores how students with MIoSG are situated in relation to systems of whiteness and white racial dominance in STEM learning spaces. Our findings included three emergent categories: color-evasiveness, desiring diversity in STEM, and the simultaneous invisibility and hypervisibility of Black, Indigenous, and People of Color (BIPOC) in STEM. Findings illuminated the complex ways BIPOC and white students with MIoSG experienced and thought about whiteness and white supremacy in STEM. Data point to the need for intentional anti-racist research, policy, and practice in STEM learning spaces.

Structural Impediments Impacting Early-Career Women of Color STEM Faculty Careers

Women of Color faculty continue to experience many challenges in their careers, especially in the science, technology, engineering, and mathematics (STEM) fields. As such, more research is needed that considers structural issues inhibiting their success. Using structuration theory and critical race feminism as a conceptual framework, we conducted semi-structured interviews with 19 faculty and administrators in STEM departments at higher education institutions to investigate their perceptions of structural impediments impacting early-career Women of Color STEM faculty careers. Our findings revealed the need to establish policies that are clear, documented, and transparent. Additionally, incremental approaches to tenure and promotion evaluations should be reconsidered, especially when this approach may position Women of Color faculty to appear as if they are underperforming, when the opposite may be true. Furthermore, as higher education institutions endeavor to diversify the professoriate, this study is significant in enabling institutions and STEM departments to be aware of systemic issues confronting them to make significant inroads in retaining and advancing Women of Color faculty in these disciplines.

Applications of dynamical systems in physics

Dynamical systems are crucial for defining our comprehension of the physical world, offering a robust structure for examining and representing intricate occurrences. The exploration of dynamical systems in physics traces back to the initial developments of classical mechanics by Newton and Lagrange. Over time, this framework has developed and grown to encompass a broad array of physical phenomena, ranging from the movement of astronomical objects to the actions of subatomic particles. The close relationship between dynamical systems and physical principles has inspired the study and improvement of this mathematical field. This paper delves into the diverse applications of dynamical systems in physics, emphasizing the research background, methodology, main discoveries, and wider ramifications. This study tries to offer a thorough summary of the diverse impacts of dynamical systems on the area of physics by combining several research papers. By utilizing dynamical systems, researchers have gained a deeper understanding of the fundamental order that governs complex dynamics, paving the way for improved predictions, innovative technologies, and a deeper understanding of the underlying principles that govern the universe.

STEM Pathway and College Progression: The Link Between Engineering CTE and Postsecondary Outcomes for Students With Learning Disabilities

Despite growing calls to increase diversity in science, technology, engineering, and mathematics (STEM) fields, students with learning disabilities (SWLDs) remain underrepresented in STEM at the postsecondary level. Considering this call for increased diversity as a means to expand and strengthen STEM success, we used the High School Longitudinal Study of 2009 to explore how participation in engineering career and technical education (E-CTE) links to postsecondary educational outcomes for SWLDs. Particularly, we examined how E-CTE participation relates to postsecondary remedial course taking, enrollment in a 4-year postsecondary institution, and declaration of a STEM major. Results from school fixed-effects estimations suggest that each credit of E-CTE earned is associated with fewer remedial college courses, a higher likelihood of enrolling in a 4-year as opposed to sub-baccalaureate institution, and increased odds of declaring a STEM major. To conclude, we discuss the implications of our findings for both policymakers and practitioners.

Enhancing Spatial Ability: A New Integrated Hybrid Training Approach for Engineering and Architecture Students

Spatial ability (SA) is the mental ability to create, maintain, and manipulate abstract visual representations. Studies have shown that SA is a strong predictor of success in the fields of science, technology, engineering, and mathematics (STEM). More recently, attention has extended to the field of architecture, a discipline where spatial thinking skills are fundamental, yet students in this field have not been extensively examined in terms of their spatial abilities. Therefore, SA skills are essential for students in engineering and architecture during their initial academic phases. This research was conducted within an interdisciplinary academic college and describes in detail a new integrated and hybrid training program that is part of a recent mixed-methods study. This program was built to effectively enhance the SA of first-year undergraduate students in a cost-effective manner, using a multi-method teaching strategy. The training program spanned more than 20 h across four sessions. This article focuses on the training methodology, encompassing four key phases, and serves as a complementary article to the one that was just published separately, describing the effectiveness of this intervention program as measured using SA standard tests. Notably, in certain scenarios, these phases were combined rather than being standalone independent modules. The traditional teaching method (TTM) lays the foundation for SA knowledge via lectures and collaborative interactions. Subsequently, computer-based learning (CBL), using tools such as SketchUp and GeoGebra, facilitates in-depth virtual geometric exploration. Augmented reality (AR) training offers an immersive learning experience, allowing students to interact with 3D objects in real-world environments. Finally, the building real model (BRM) phase transforms 2D designs into tangible 3D structures. This study highlights the comprehensive training approach, emphasizing the robust learning environment facilitated by integrating these phases as part of the full mixed-methods research. The suggested integrated training program was qualitatively explored through post-intervention evaluations to understand participants’ experiences and perceptions.

Women in mathematics: Stories of overcoming

This article explores the remarkable contribution of women to the field of mathematics throughout history. Traditionally underestimated and underrepresented in this field, women have played crucial roles in the advancement of mathematical knowledge. This paper examines the lives and accomplishments of some notable women in mathematics, highlighting their achievements and overcoming gender barriers. The role of women in the history of mathematics is often underestimated, but their contribution is vast and significant. This article explores the beauty of this history, highlighting remarkable women who have defied gender norms to leave a lasting mark on the field. From Hippatia, a 4th century mathematician and philosopher, to Ada Lovelace, history's first programmer, women have played crucial roles in the evolution of mathematics. The article also addresses the long period in which women were excluded from academic institutions, even when they made substantial contributions. The narrative highlights the resilience and determination of women who persisted despite the barriers. The modern era has witnessed an increase in the recognition of women's mathematical work, with figures such as Mary Cartwright and Emmy Noether standing out. The article highlights not only individual achievements, but also collective efforts to promote gender equality in mathematics. By exploring this history, the aim is to inspire a renewed appreciation for the role of women in mathematics and to encourage future generations of women to pursue their mathematical interests, thus contributing to a more inclusive and diverse discipline.

Numerical integration of third-order BVPs using a fourth-order hybrid block method

This research paper introduces a new hybrid block method to solve the third-order boundary value problems (BVPs). The method combines interpolation and collocation and uses a power series polynomial to find an approximate solution to the considered third-order BVPs. Some third-order BVP models are numerically solved to verify the performance and efficiency of the proposed method, and the approximate solution from the proposed method is more efficient when compared to some existing numerical methods. In summary, the proposed method provides reliable and efficient accuracy for solving third-order BVPs, making it a valuable contribution to the fields of numerical analysis and computational mathematics. The advantages of the proposed method include improved computational time efficiency and accuracy in terms of maximum absolute errors for solving third-order BVPs.

Leadership Development Interventions to Reduce Imposter Phenomenon in the STEM Fields in Minorities

Background: There is a significant lack of diversity in the Science, Technology, Engineering, and Mathematics (STEM) fields. Evidence shows that lack of representation can feed into feelings of imposter phenomenon which in turn influences leadership qualities. Objectives: An argument is made that by providing leadership development training to minorities in science, technology, engineering, and mathematics fields, confidence will be boosted, feelings of imposter phenomenon will be reduced, and thus these students will be retained. Approach: Theories explored to explain this challenge include the imposter phenomenon, servant leadership, and transformational leadership. Results: The goal of this article is to demonstrate the need for research into leadership development of minorities in the science, technology, engineering, and mathematics fields. Conclusions: A program proposal is also introduced as a suggested plan of action based on the findings.

Development of an IoT based 3D printed Mobile Robot Platform for training of Mechatronics Engineering Students

The advent of the Internet of Things (IoT) has opened up new opportunities in education, particularly in the field of mobile robotics. Mobile robotics is a fast-growing field, and with the increasing demand for skilled robotics engineers, it is essential to provide students with hands-on experience in designing and developing robots. In this regard, an IoT-based 3D printed mobile robot platform has been developed for students training. STEM (Science, Technology, Engineering, and Mathematics) education has been gaining attention as a means to improve science and engineering education. STEM education aims to foster critical thinking, problem-solving skills, creativity, and innovation among students. It involves an educational policy that aims to develop the next generation of skilled professionals by integrating the fields of Science, Technology, Engineering and Mathematics. The goal of this approach is to provide students in mechatronics, who are assigned to the robotics lab during their studies, an up to date knowledge and experience in research and development activities. Thus, this paper aims to provide education that focuses on the acquisition and application of engineering knowledge, including control engineering, mechanical engineering, electrical and electronic engineering, information engineering, among others, with the main focus on mobile robot research.

Exploring Sex Differences in Numerosity Perception Using Dynamic Visual Stimuli: Insights into Cognitive Processing and STEM

Exploring Sex Differences in Numerosity Perception Using Dynamic Visual Stimuli: Insights into Cognitive Processing and STEM

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.