Search results for: electoral mathematics

Authors: Oláh Gál Róbert, Veress Bágyi Ibolya

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The scientific public has relatively little knowledge about the Hungarian János Bolyai, one of the greatest thinkers of all times. Few people know that apart from being the founder of the non-Euclidean geometry he was also interested in sociology, philosophy, epistemology and linguistics. According to the renowned Hungarian psychoanalytic Imre Hermann, who lives in France, János Bolyai was mentally deranged. However, this is incorrect. The present article intends to prove that he was completely sane until the moment of his death.

Keywords: Imre Hermann, insane, János Bolyai, mathematics, non-Euclidean geometry, psyphoanalytic

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Authors: Raphaël Menard, Etienne Fayette, Paul Azzopardi

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This paper presents the method to generate the geometry of an actual glass canopy project in Rennes, France, by architect Bruno Gaudin, with aim to achieve the best structural efficiency possible using only quadrangle meshing. The paper includes equation of the translational surface generated, the level of accuracy in approximating the funicular shape and the method of constructive implementation.

Keywords: funicular shape, glass canopy, glass panels, lowered arches, mathematics, penalization, shell structure

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Authors: Ana Hol

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We live in a constantly changing environment where technology has become an integral component of our day to day life. We rely heavily on mobile devices, we search for data via web, we utilise smart home sensors to create the most suited ambiences and we utilise applications to shop, research, communicate and share data. Heavy reliance on technology therefore is creating new connections between STEM (Science, Technology, Engineering and Mathematics) fields which in turn rises a question of what the STEM education of the future should be like? This study was based on the reviews of the six Australian Information Systems students who undertook an international study tour to India where they were given an opportunity to network, communicate and meet local students, staff and business representatives and from them learn about the local business implementations, local customs and regulations. Research identifies that if we are to continue to implement and utilise electronic devices on the global scale, such as for example implement smart cars that can smoothly cross borders, we will need the workforce that will have the knowledge about the cars themselves, their parts, roads and transport networks, road rules, road sensors, road monitoring technologies, graphical user interfaces, movement detection systems as well as day to day operations, legal rules and regulations of each region and country, insurance policies, policing and processes so that the wide array of sensors can be controlled across country’s borders. In conclusion, it can be noted that allowing students to learn about the local conditions, roads, operations, business processes, customs and values in different countries is giving students a cutting edge advantage as such knowledge cannot be transferred via electronic sources alone. However once understanding of each problem or project is established, multidisciplinary innovative STEM projects can be smoothly conducted.

Keywords: STEM, curiosity, innovation, advancements

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: J. L. Oliver, T. Agryzkov, L. Tortosa, J. Vicent, J. Santacruz

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This paper aims to demonstrate how the use of Network Theory can be applied to a very interesting and complex urban situation: The parts of a city which may have some patrimonial value, but because of their lack of relevant architectural elements, they are not considered to be historic in a conventional sense. In this paper, we use the suburb of La Villaflora in the city of Quito, Ecuador as our case study. We first propose a system of indicators as a tool to characterize and quantify the historic value of a geographic area. Then, we apply these indicators to the suburb of La Villaflora and use Network Theory to understand and propose actions.

Keywords: graphs, mathematics, networks, urban studies

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Authors: M. Rodionov, Z. Dedovets

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This article discusses ways to implement a differentiated approach to developing academic motivation for mathematical studies which relies on defining the primary structural characteristics of motivation. The following characteristics are considered: features of realization of cognitive activity, meaning-making characteristics, level of generalization and consistency of knowledge acquired by personal experience. The assessment of the present level of individual student understanding of each component of academic motivation is the basis for defining the relevant educational strategy for its further development.

Keywords: learning activity, mathematics, motivation, student

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Authors: M. Shaheed Hartley

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There has been increasing pressure on education researchers and practitioners at higher education institutions to focus on the development of South Africa’s rural and peri-urban communities and improving their quality of life. Many tertiary institutions are obliged to review their outreach interventions in schools. To ensure that the support provided to schools is still relevant, a systemic evaluation of science educator needs is central to this process. These prioritised needs will serve as guide not only for the outreach projects of tertiary institutions, but also to service providers in general so that the process of addressing educators needs become coordinated, organised and delivered in a systemic manner. This paper describes one area of a broader needs assessment exercise to collect data regarding the needs of educators in a district of 45 secondary schools in the Western Cape Province of South Africa. This research focuses on the needs and challenges faced by science educators at these schools as articulated by the relevant stakeholders. The objectives of this investigation are two-fold: (1) to create a data base that will capture the needs and challenges identified by science educators of the selected secondary schools; and (2) to develop a needs profile for each of the participating secondary schools that will serve as a strategic asset to be shared with the various service providers as part of a community of practice whose core business is to support science educators and science education at large. The data was collected by a means of a needs assessment questionnaire (NAQ) which was developed in both actual and preferred versions. An open-ended questionnaire was also administered which allowed teachers to express their views. The categories of the questionnaire were predetermined by participating researchers, educators and education department officials. Group interviews were also held with the science teachers at each of the schools. An analysis of the data revealed important trends in terms of science educator needs and identified schools that can be clustered around priority needs, logistic reasoning and educator profiles. The needs database also provides opportunity for the community of practice to strategise and coordinate their interventions.

Keywords: needs assessment, science and mathematics education, evaluation, teaching and learning, South Africa

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Authors: M. Azarbarmas, J. M. Cabrera, J. Calvo, M. Aghaie-Khafri

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The modeling of hot deformation behavior for unseen conditions is important in metal-forming. In this study, the hot deformation of IN718 has been characterized in the temperature range 950-1100 and strain rate range 0.001-0.1 s-1 using hot compression tests. All stress-strain curves showed the occurrence of dynamic recrystallization. These curves were implemented quantitatively in mathematics, and then constitutive equation indicating the relationship between the flow stress and hot deformation parameters was obtained successfully.

Keywords: compression test, constitutive equation, dynamic recrystallization, hot working

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Authors: Mpofu Vongai, Vhurumuku Elaosi

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Many African countries, such as Zimbabwe and South Africa, have curricula reform agendas that include incorporation of Indigenous Knowledge and Nature of Science (NOS) into school Science, Technology, Engineering and Mathematics (STEM) education. It is argued that at high school level, STEM learning, which incorporates understandings of indigenization science and NOS, has the potential to provide a strong foundation for a culturally embedded scientific knowledge essential for their advancement in Science and Technology. Globally, investment in STEM education is recognized as essential for economic development. For this reason, developing countries such as Zimbabwe and South Africa have been investing into training specialized teachers in natural sciences and technology. However, in many cases this training has been detached from the cultural realities and contexts of indigenous learners. For this reason, the STEM curricula reform has provided implementation challenges to teachers. An issue of major concern is the teachers’ pedagogical content knowledge (PCK), which is essential for effective implementation of these STEM curricula. Well-developed Teacher PCK include an understanding of both the nature of indigenous knowledge (NOIK) and of NOS. This paper reports the results of a study that investigated the development of 3 South African and 3 Zimbabwean in-service teachers’ abilities to integrate NOS and NOIK as part of their PCK. A participatory action research design was utilized. The main focus was on capturing, determining and developing teachers STEM knowledge for integrating NOIK and NOS in science classrooms. Their use of indigenous games was used to determine how their subject knowledge for STEM and pedagogical abilities could be developed. Qualitative data were gathered through the use dialogues between the researchers and the in-service teachers, as well as interviewing the participating teachers. Analysis of the data provides a methodological window through which in-service teachers’ PCK can be STEMITIZED and their abilities to integrate NOS and NOIK developed. Implications are raised for developing teachers’ STEM education in universities and teacher training colleges.

Keywords: indigenous knowledge, nature of science, pedagogical content knowledge, STEM education

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Authors: A. Pascual Ramsay

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Accounts of the management of the economic and euro crisis in Spain have been dominated by an emphasis on external constraints. However, this approach leaves unanswered important questions about the role of domestic political factors. Using systematic qualitative primary research and employing elite interviewing and process tracing, this paper aims to fill this gap for the period of the Partido Socialista Obrero Español (PSOE) administration. The paper shows that domestic politics played a crucial role in the management of the crisis, most importantly by determining the shape of the measures undertaken. In its three distinct stages – downplaying/inaction, reaction/stimulus, and austerity/reform – the PSOE's response was certainly constrained by external factors, most notably EMU membership and the actions of sovereign-bond investors, the ECB and Germany. Yet while these external constraints forced the government to act, domestic political factors fundamentally shaped the content of key measures: the fiscal stimulus, the labour, financial and pension reforms, the refusal to accept a bailout or the reform of the Constitution. Seven factors were particularly influential: i) electoral and political cost, ii) party and partisanship, iii) organised interests, iv) domestic institutions, v) ideological preferences, vi) ineffective decision-making, and vii) judgement and personal characteristics of decision-makers. In conclusion, domestic politics played an important role in the management of the crisis, a role that has been underestimated by dominant approaches focusing on external constraints and weak domestic policy autonomy. The findings provide empirical evidence to support research agendas that identify significant state discretion in the face of international economic integration and an important role for domestic political factors such as institutions, material interests, partisanship and ideology in shaping economic outcomes.

Keywords: economic crisis, Euro, PSOE, Spain

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Authors: Syed Muhammad Wajih ul Hassan

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This research looks at the perception of first-time voters in Pakistan on the political dynamics of the country. This paper shall review the researches that were conducted by Gallup Pakistan and compare it with our findings regarding the voter behavior and factors that affect the priorities of the voters. A country where democracy has just completed its 2 consecutive tenures for the first time, one would always want to know about the voting trends among youth where young population makes 60% of the population in the country. In that case, it is not only a big task to find out voter patterns and trends voters might adhere to while a general election is approaching. Also, the paper discovers the psychology of young Pakistani voters on the upcoming election of 2018 but also the factors that influence the voting decisions of a voter. This research tries to study the relations among voters and how they view each other in general. The paper also explores the views of voters on the factors that impact decision making of a voter while casting his/her vote in Pakistan. The paper thoroughly studies the expectations of the voters from the current system that prevails in the country. The reason this research was conducted is that this kind of positive approach towards finding out the voter perception is heavily untouched in Pakistani academia. This study can benefit a lot of institutions and professions in the future too. The constraints and obstacles that came while this research was being conducted are also identified in the paper. The mode of research is primary research as it was impossible to find out the perceptions of first-time voters without going on the field and carrying out the research. The research was conducted in one of the most reputable and liberal educational institutions of Pakistan. This research is based on a survey that was conducted through questionnaires where responses were collected through a mix process of random and convenient sampling. The major findings of the study show that young voters have a realistic perspective about the electoral process in the country. The research also articulates the factors that affect the priorities of young voters, and also how young voters view other voters that belong from other sections of the society. To conclude, we can say that this research will give us a perspective that can define and identify the voter priorities of the future in Pakistan.

Keywords: first time voters, general election 2018, Pakistan, young

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Authors: Dimiter M. Dimitrov, Abdullah Sadaawi

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The National Assessment for Schools (NAFS) in Saudi Arabia consists of standardized tests in Mathematics, Reading, and Science for school grade levels 3, 6, and 9. One main goal is to classify students into four categories of NAFS performance (minimal, basic, proficient, and advanced) by schools and the entire national sample. The NAFS scoring and equating is performed on a bounded scale (D-scale: ranging from 0 to 1) in the framework of the recently developed “D-scoring method of measurement.” The specificity of the NAFS measurement framework and data complexity presented both challenges and opportunities to (a) the estimation of score reliability for schools, (b) setting cut-scores for the classification of students into categories of performance, and (c) generating plausible values for distributions of student performance on the D-scale. The estimation of score reliability at the school level was performed in the framework of generalizability theory (GT), with students “nested” within schools and test items “nested” within test forms. The GT design was executed via a multilevel modeling syntax code in R. Cut-scores (on the D-scale) for the classification of students into performance categories was derived via a recently developed method of standard setting, referred to as “Response Vector for Mastery” (RVM) method. For each school, the classification of students into categories of NAFS performance was based on distributions of plausible values for the students’ scores on NAFS tests by grade level (3, 6, and 9) and subject (Mathematics, Reading, and Science). Plausible values (on the D-scale) for each individual student were generated via random selection from a statistical logit-normal distribution with parameters derived from the student’s D-score and its conditional standard error, SE(D). All procedures related to D-scoring, equating, generating plausible values, and classification of students into performance levels were executed via a computer program in R developed for the purpose of NAFS data analysis.

Keywords: large-scale assessment, reliability, generalizability theory, plausible values

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Authors: Hassan Al Salman

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We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.

Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis

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Authors: Kourosh Modarresi

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The Netflix problem has brought the topic of “Recommendation Systems” into the mainstream of computer science, mathematics, and statistics. Though much progress has been made, the available algorithms do not obtain satisfactory results. The success of these algorithms is rarely above 5%. This work is based on the belief that the main challenge is to come up with “scalable personalization” models. This paper uses an adaptive regularization of inverse singular value decomposition (SVD) that applies adaptive penalization on the singular vectors. The results show far better matching for recommender systems when compared to the ones from the state of the art models in the industry.

Keywords: convex optimization, LASSO, regression, recommender systems, singular value decomposition, low rank approximation

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Authors: Kamariah Abu Bakar, Jennifer Way

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This study investigated how young children (six years old) constructed and used representations in mathematics classroom; particularly in problem solving. The purpose of this study is to explore the ways children used representations in solving addition problems and to determine whether their representations can play a supportive role in understanding the problem situation and solving them correctly. Data collection includes observations, children’s artifact, photographs and conversation with children during task completion. The results revealed that children were able to construct and use various representations in solving problems. However, they have certain preferences in generating representations to support their problem solving.

Keywords: young children, representations, addition, problem solving

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Authors: Sarolta Lipóczi, Ildikó Szabó

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The use of ICT in European Schools has increased over the last decade but there is still room for improvement. Also interactive technology is often used below its technical and pedagogical potentials. The pedagogical potential of interactive technology in classrooms has not yet reached classrooms in different countries and in a substantial way. To develop these materials cooperation between educational researchers and teachers from different backgrounds is necessary. INTACT project brings together experts from science education, mathematics education, social science education and foreign language education – with a focus on bilingual education – and teachers in secondary and primary schools to develop a variety of pedagogically qualitative interactive teaching and learning resources. Because of the backgrounds of the consortium members INTACT project focuses on the areas of science, mathematics and social sciences. To combine these two features (science/math and foreign language) the project focuses on bilingual education. A big issue supported by ‘interactiveness’ is social and collaborative learning. The easy way to communicate and collaborate offered by web 2.0 tools, mobile devices connected to the learning material allows students to work and learn together. There will be a wide range of possibilities for school co-operations at regional, national and also international level that allows students to communicate and cooperate with other students beyond the classroom boarders while using these interactive teaching materials. Opening up the learning scenario enhance the social, civic and cultural competences of the students by advocating their social skills and improving their cultural appreciation for other nations in Europe. To enable teachers to use the materials in indented ways descriptions of successful learning scenarios (i.e. using design patterns) will be provided as well. These materials and description will be made available to teachers by teacher trainings, teacher journals, booklets and online materials. The resources can also be used in different settings including the use of a projector and a touchpad or other technical interactive devices for the input i.e. mobile phones. Kecskemét College as a partner of INTACT project has developed two teaching and learning resources in the area of foreign language teaching. This article introduces these resources as well.

Keywords: bilingual educational settings, international cooperation, interactive teaching and learning resources, work across culture

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Authors: Shaloom Mbambu Kabeya, Léonard Kabeya Mukeba

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Churches, cathedrals and castles beaten from antiquity to modern times were relevant from that time to the present day, and preserved as cultural heritage. Our predecessors as François 1er1, Michelangelo2, and Giotto3 left us traces. Gustave Eiffel4, Hector Guimard5 did not decrease their time to show modernization (evolution) in architecture. Plagiarism is a brake on architectural development, construction works of spirits is necessary architecture. This work explains the relationship between ancient and modern architecture. It also shows the power of mathematics in modern architecture.

Keywords: architectural modernization, heritage, mathematical architecture, materials

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: M. Isabel Santos, Ana Breda, Ana Margarida Almeida

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Research on academic abilities of individuals with autism spectrum disorder (ASD) underlines the importance of mathematics interventions. Yet the proposal of digital applications for children and youth with ASD continues to attract little attention, namely, regarding the development of mathematical reasoning, being the use of the digital technologies an area of great interest for individuals with this disorder and its use is certainly a facilitative strategy in the development of their mathematical abilities. The use of digital technologies can be an effective way to create innovative learning opportunities to these students and to develop creative, personalized and constructive environments, where they can develop differentiated abilities. The children with ASD often respond well to learning activities involving information presented visually. In this context, we present the digital Learning Environment on Mathematics for Autistic children (LEMA) that was a research project conducive to a PhD in Multimedia in Education and was developed by the Thematic Line Geometrix, located in the Department of Mathematics, in a collaboration effort with DigiMedia Research Center, of the Department of Communication and Art (University of Aveiro, Portugal). LEMA is a digital mathematical learning environment which activities are dynamically adapted to the user’s profile, towards the development of mathematical abilities of children aged 6–12 years diagnosed with ASD. LEMA has already been evaluated with end-users (both students and teacher’s experts) and based on the analysis of the collected data readjustments were made, enabling the continuous improvement of the prototype, namely considering the integration of universal design for learning (UDL) approaches, which are of most importance in ASD, due to its heterogeneity. The learning strategies incorporated in LEMA are: (i) provide options to custom choice of math activities, according to user’s profile; (ii) integrates simple interfaces with few elements, presenting only the features and content needed for the ongoing task; (iii) uses a simple visual and textual language; (iv) uses of different types of feedbacks (auditory, visual, positive/negative reinforcement, hints with helpful instructions including math concept definitions, solved math activities using split and easier tasks and, finally, the use of videos/animations that show a solution to the proposed activity); (v) provides information in multiple representation, such as text, video, audio and image for better content and vocabulary understanding in order to stimulate, motivate and engage users to mathematical learning, also helping users to focus on content; (vi) avoids using elements that distract or interfere with focus and attention; (vii) provides clear instructions and orientation about tasks to ease the user understanding of the content and the content language, in order to stimulate, motivate and engage the user; and (viii) uses buttons, familiarly icons and contrast between font and background. Since these children may experience little sensory tolerance and may have an impaired motor skill, besides the user to have the possibility to interact with LEMA through the mouse (point and click with a single button), the user has the possibility to interact with LEMA through Kinect device (using simple gesture moves).

Keywords: autism spectrum disorder, digital technologies, inclusion, mathematical abilities, mathematical learning activities

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Authors: Lulu Sun

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In Addition is an after-school mathematics program in which students and their parents build mathematical confidence and competence by solving problems they curious about. It is a program consists of mix-grade from 4th to 6th grade of 10 to 20 students, including math problem solving and other activities. This partnership will focus on the relationship between the In-Addition and the parents’ engagement; in this kind of partnership, it has the In-Addition program teaching and the family engagement. This partnership is purpose to building cooperation between the program and parents, strengthening the links between the program and families.

Keywords: program-family, family engagement, positive bias, partnership

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Authors: John Ibanga

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Since May 1999, when Nigeria returned to uninterrupted democratic rule, there have been various attempts by successive governments at committing themselves to democratic ideals. Such efforts include a revision of communication policies after repeated calls by civil society organisations, development partners, researchers, and academics to allow not only the commencement of campus radio broadcasting but also the takeoff of community radio broadcasting. Thus, in 2015, operating licenses were granted to several communities spread across the six geopolitical zones in the country for the establishment of community radio stations culminating in the establishment of the first community radio in Nigeria on July 17, 2015. And, since citizens’ involvement in policy matters and governance is one of the tenets of participatory democracy, it becomes imperative to investigate how the emerging community radio sector in Nigeria is facilitating participatory democracy among Nigerians, even in the face of attempts by the present government to silence all dissenting voices. This study, therefore, examines how residents in Ondo State, Southwest Nigeria, are utilising programmes on Ejule Nen and Kakaaki community radio stations in Ondo State, Nigeria, to deepen participatory democracy. Much of the existing studies on the role of community radio in participatory democracy and citizens' engagement efforts miss out on Nigeria because of the delayed implementation of community radio policy in Nigeria being Africa’s most populous nation as well as a major player in the affairs of the African continent. While the participatory communication and communication infrastructure theories were used as framework, data were collected from in-depth interviews with staff of the community radio station and community leaders, focus group discussions with the community residents, and qualitative content analysis of programmes on the station. The residents used the community radio stations as platforms for demanding accountability from government, mobilising resources for the execution of a number of community projects, promoting credible electoral practices, and influencing the implementation of free education policy in their communities. Hence the community radio stations became the reliable and authoritative voices of residents for participating in the public sphere and, generally, the democratic process.

Keywords: community, community radio, democracy, participatory democracy

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Authors: C. Suphioglu , V. Simbag, J. Markham, C. Coady, S. Belward, G. Di Trapani, P. Chunduri, J. Chuck, Y. Hodgson, L. Lluka, L. Poladian, D. Watters

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Advances in science have made quantitative skills (QS) an essential graduate outcome for undergraduate science programs in Australia and other parts of the world. However, many students entering into degrees in Australian universities either lack these skills or have little confidence in their ability to apply them in their biological science units. It has been previously reported that integration of quantitative skills into life science programs appears to have a positive effect on student attitudes towards the importance of mathematics and statistics in biological sciences. It has also been noted that there is deficiency in QS resources available and applicable to undergraduate science students in Australia. MathBench (http://mathbench.umd.edu) is a series of online modules involving quantitative biology scenarios developed by the University of Maryland. Through collaboration with Australian universities, a project was funded by the Australian government through its Office for Learning and Teaching (OLT) to develop customized MathBench biology modules to promote the quantitative skills of undergraduate biology students in Australia. This presentation will focus on the assessment of changes in performance, perception and attitude of students in a third year Cellular Physiology unit after use of interactive online cellular diffusion modules modified for the Australian context. The modules have been designed to integrate QS into the biological science curriculum using familiar scenarios and informal language and providing students with the opportunity to review solutions to diffusion QS-related problems with interactive graphics. This paper will discuss results of pre and post MathBench quizzes composed of general and module specific questions that assessed change in student QS after MathBench; and pre and post surveys, administered before and after using MathBench modules to evaluate the students’ change in perception towards the influence of the modules, their attitude towards QS and on the development of their confidence in completing the inquiry-based activity as well as changes to their appreciation of the relevance of mathematics to cellular processes. Results will be compared to changes reported by Thompson et al., (2010) at the University of Maryland and implications for further integration of interactive online activities in the curriculum will be explored and discussed.

Keywords: quantitative skills, MathBench, maths in biology

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Authors: H. S. Kang

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Coupled electrical and optical model for conversion of electrical energy into coherent optical energy for transmitter-receiver link by solid state device is presented. Probability distribution for travelling laser beam switching time intervals and the number of switchings in the time interval is obtained. Selector function mapping is employed to regulate optical data transmission speed. It is established that regulated laser transmission from PhotoActive Laser transmitter follows principal of invariance. This considerably simplifies design of PhotoActive Laser Transmission networks.

Keywords: computational mathematics, finite difference Markov chain methods, sequence spaces, singularly perturbed differential equations

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Authors: S. R. Santhanam

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A gifted child is one who gives evidence of creativity, good memory, rapid learning. In mathematics, a teacher often comes across some gifted children and they exhibit the following characteristics: unusual alertness, enjoying solving problems, getting bored on repetitions, self-taught, going beyond what teacher taught, ask probing questions, connecting unconnected concepts, vivid imagination, readiness for research work, perseverance of a topic. There are two main areas of research carried out on them: 1)identifying gifted children, 2) interacting and channelizing them. A lack of appropriate recognition will lead the gifted child demotivated. One of the main findings is if proper attention and nourishment are not given then it leads a gifted child to become depressed, underachieving, fail to reach their full potential and sometimes develop negative attitude towards school and study. After identifying them, a mathematics teacher has to develop them into a fall fledged achiever. The responsibility of the teacher is enormous. The teacher has to be resourceful and patient. But interacting with them one finds a lot of surprises and awesomeness. The elementary algebraic identities like (a+b)(a-b)=a²-b², expansion of like (a+b)²(a-b)² and others are taught to students, of age group 13-15 in India. An average child will be satisfied with a single proof and immediate application of these identities. But a gifted child expects more from the teacher and at one stage after a little training will surpass the teacher also. In this short paper, the author shares his experience regarding teaching algebraic identities to gifted children. The following problem was given to a set of 10 gifted children of the specified age group: If a natural number ‘n’ to expressed as the sum of the two squares, will 2n also be expressed as the sum of two squares? An investigation has been done on what multiples of n satisfying the criterion. The attempts of the gifted children were consolidated and conclusion was drawn. A second problem was given to them as: can two natural numbers be found such that the difference of their square is 3? After a successful solution, more situations were analysed. As a third question, the finding of the sign of an algebraic expression in three variables was analysed. As an example: if a,b,c are real and unequal what will be sign of a²+4b²+9c²-4ab-12bc-6ca? Apart from an expression as a perfect square what other methods can be employed to prove an algebraic expression as positive negative or non negative has been analysed. Expressions like 4x²+2y²+13y²-2xy-4yz-6zx were given, and the children were asked to find the sign of the expression for all real values of x,y and z. In all investigations, only basic algebraic identities were used. As a next probe, a divisibility problem was initiated. When a,b,c are natural numbers such that a+b+c is at least 6, and if a+b+c is divisible by 6 then will 6 divide a³+b³+c³. The gifted children solved it in two different ways.

Keywords: algebraic identities, gifted children, Indian scenario, research

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Authors: A. Kulandai Therese

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The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics.In this paper, we present the explicit eccentric connectivity index, first and second Zagreb indices for a Corona graph and sub division-related corona graphs.

Keywords: corona graph, degree, eccentricity, eccentric connectivity index, first zagreb index, second zagreb index, subdivision graphs

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Authors: Valencia P. L. Rodrigo, Morita A. Adelina, Vargas V. Martin

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This proposal consists of an analysis of macro concepts involved within an organization growth using educational technologies, which will relate each concept, in a mathematical way with a vision of harmonic work. Working collaboratively, competitively and cooperatively so that this growth is harmonious and homogenous, coining a new term, Harmonic Work. The Harmonic Work ensures that the organization grows in all business directions, allowing managers to project a much more accurate growth, making clear the contribution of each department, resulting in an algorithm that analyzes each of the variables both endogenous and exogenous, establishing different performance indicators in its process of growth.

Keywords: business projection, collaboration, competitiveness, educational technology, harmonious growth

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Authors: Yuhei Kunihiro, Sorin V. Sabau, Kazuhiro Shibuya

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We study the molecular evolution of insulin from the metric geometry point of view. In mathematics, and particularly in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from the geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

Keywords: metric geometry, evolution, insulin, C. elegans

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Authors: Karam Chand Gupta

Abstract:

When steel reinforcement is placed in mesh form in circular concrete slab at base or domes at top in case of over head service reservoir or any other structure, it is difficult to estimate/measure the total quantity of steel that would be needed or placed. For the purpose of calculating the total length of the steel bars, at present, the practice is – the length of each bar is measured and then added up. This is tiresome and time consuming process. I have derived a mathematics formula with the help of which we can calculate in one line the quantity of total steel that will be needed. This will not only make it easy and time saving but also avoids any error in making entries and calculations.

Keywords: dome, mesh, slab, steel

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Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

Abstract:

In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Paloma Mendes Saldanha

Abstract:

Access to information is a prerequisite for democracy while also guiding the material construction of fundamental rights. The exercise of citizenship requires knowing, understanding, questioning, advocating for, and securing rights and responsibilities. In other words, it goes beyond mere active electoral participation and materializes through awareness and the struggle for rights and responsibilities in the various spaces occupied by the population in their daily lives. In times of hyper-cultural connectivity, active citizenship is shaped through ethical trust processes, most often established between humans and algorithms. Automated decisions, so prevalent in various everyday situations, such as purchase preference predictions, virtual voice assistants, reduction of accidents in autonomous vehicles, content removal, resume selection, etc., have already found their place as a normalized discourse that sometimes does not reveal or make clear what violations of fundamental rights may occur when algorithmic explainability is lacking. In other words, technological and market development promotes a normalization for the use of automated decisions while silencing possible restrictions and/or breaches of rights through a culturally modeled, unethical, and unexplained trust process, which hinders the possibility of the right to a healthy, transparent, and complete exercise of citizenship. In this context, the article aims to identify the violations caused by the absence of algorithmic explainability in the exercise of citizenship through the construction of an unethical and silent trust process between humans and algorithms in automated decisions. As a result, it is expected to find violations of constitutionally protected rights such as privacy, data protection, and transparency, as well as the stipulation of algorithmic explainability as a fundamental right in the exercise of Brazilian citizenship in the era of virtualization, facing a threefold foundation called trust: culture, rules, and systems. To do so, the author will use a bibliographic review in the legal and information technology fields, as well as the analysis of legal and official documents, including national documents such as the Brazilian Federal Constitution, as well as international guidelines and resolutions that address the topic in a specific and necessary manner for appropriate regulation based on a sustainable trust process for a hyperconnected world.

Keywords: artificial intelligence, ethics, citizenship, trust

Procedia PDF Downloads 56