Search results for: engineering mathematics
1146 Eccentric Connectivity Index, First and Second Zagreb Indices of Corona Graph
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 divisionrelated corona graphs.
Keywords: Corona graph, Degree, Eccentricity, Eccentric Connectivity Index, First Zagreb index, Second Zagreb index and Subdivision graphs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26481145 Constructive Proof of Tychonoff’s Fixed Point Theorem for Sequentially Locally Non-Constant Functions
Authors: Yasuhito Tanaka
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We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.
Keywords: sequentially locally non-constant functions, Tychonoff’s fixed point theorem, constructive mathematics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14931144 Investigations on Some Operations of Soft Sets
Authors: Xun Ge, Songlin Yang
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Soft set theory was initiated by Molodtsov in 1999. In the past years, this theory had been applied to many branches of mathematics, information science and computer science. In 2003, Maji et al. introduced some operations of soft sets and gave some operational rules. Recently, some of these operational rules are pointed out to be not true. Furthermore, Ali et al., in their paper, introduced and discussed some new operations of soft sets. In this paper, we further investigate these operational rules given by Maji et al. and Ali et al.. We obtain some sufficient-necessary conditions such that corresponding operational rules hold and give correct forms for some operational rules. These results will be help for us to use rightly operational rules of soft sets in research and application of soft set theory.
Keywords: Soft sets, union, intersection, complement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17031143 Study of a BVAR(p) Process Applied to U.S. Commodity Market Data
Authors: Jan Sindelar
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The paper presents an applied study of a multivariate AR(p) process fitted to daily data from U.S. commodity futures markets with the use of Bayesian statistics. In the first part a detailed description of the methods used is given. In the second part two BVAR models are chosen one with assumption of lognormal, the second with normal distribution of prices conditioned on the parameters. For a comparison two simple benchmark models are chosen that are commonly used in todays Financial Mathematics. The article compares the quality of predictions of all the models, tries to find an adequate rate of forgetting of information and questions the validity of Efficient Market Hypothesis in the semi-strong form.
Keywords: Vector auto-regression, forecasting, financial, Bayesian, efficient markets.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11871142 A Intelligent Inference Model about Complex Systems- Stability: Inspiration from Nature
Authors: Naiqin Feng, Yuhui Qiu, Yingshan Zhang, Fang Wang
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A logic model for analyzing complex systems- stability is very useful to many areas of sciences. In the real world, we are enlightened from some natural phenomena such as “biosphere", “food chain", “ecological balance" etc. By research and practice, and taking advantage of the orthogonality and symmetry defined by the theory of multilateral matrices, we put forward a logic analysis model of stability of complex systems with three relations, and prove it by means of mathematics. This logic model is usually successful in analyzing stability of a complex system. The structure of the logic model is not only clear and simple, but also can be easily used to research and solve many stability problems of complex systems. As an application, some examples are given.Keywords: Complex system, logic model, relation, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13161141 Modeling and Simulation of Robotic Arm Movement using Soft Computing
Authors: V. K. Banga, Jasjit Kaur, R. Kumar, Y. Singh
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In this research paper we have presented control architecture for robotic arm movement and trajectory planning using Fuzzy Logic (FL) and Genetic Algorithms (GAs). This architecture is used to compensate the uncertainties like; movement, friction and settling time in robotic arm movement. The genetic algorithms and fuzzy logic is used to meet the objective of optimal control movement of robotic arm. This proposed technique represents a general model for redundant structures and may extend to other structures. Results show optimal angular movement of joints as result of evolutionary process. This technique has edge over the other techniques as minimum mathematics complexity used.Keywords: Kinematics, Genetic algorithms (GAs), Fuzzy logic(FL), Optimal control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29911140 Elimination of Redundant Links in Web Pages– Mathematical Approach
Authors: G. Poonkuzhali, K.Thiagarajan, K.Sarukesi
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With the enormous growth on the web, users get easily lost in the rich hyper structure. Thus developing user friendly and automated tools for providing relevant information without any redundant links to the users to cater to their needs is the primary task for the website owners. Most of the existing web mining algorithms have concentrated on finding frequent patterns while neglecting the less frequent one that are likely to contain the outlying data such as noise, irrelevant and redundant data. This paper proposes new algorithm for mining the web content by detecting the redundant links from the web documents using set theoretical(classical mathematics) such as subset, union, intersection etc,. Then the redundant links is removed from the original web content to get the required information by the user..Keywords: Web documents, Web content mining, redundantlink, outliers, set theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19991139 Design Method for Knowledge Base Systems in Education Using COKB-ONT
Authors: Nhon Do, Tuyen Trong Tran, Phan Hoai Truong
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Nowadays e-Learning is more popular, in Vietnam especially. In e-learning, materials for studying are very important. It is necessary to design the knowledge base systems and expert systems which support for searching, querying, solving of problems. The ontology, which was called Computational Object Knowledge Base Ontology (COB-ONT), is a useful tool for designing knowledge base systems in practice. In this paper, a design method for knowledge base systems in education using COKB-ONT will be presented. We also present the design of a knowledge base system that supports studying knowledge and solving problems in higher mathematics.Keywords: artificial intelligence, knowledge base systems, ontology, educational software.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20311138 Movies and Dynamic Mathematical Objects on Trigonometry for Mobile Phones
Authors: Kazuhisa Takagi
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This paper is about movies and dynamic objects for mobile phones. Dynamic objects are the software programmed by JavaScript. They consist of geometric figures and work on HTML5-compliant browsers. Mobile phones are very popular among teenagers. They like watching movies and playing games on them. So, mathematics movies and dynamic objects would enhance teaching and learning processes. In the movies, manga characters speak with artificially synchronized voices. They teach trigonometry together with dynamic mathematical objects. Many movies are created. They are Windows Media files or MP4 movies. These movies and dynamic objects are not only used in the classroom but also distributed to students. By watching movies, students can study trigonometry before or after class.
Keywords: Dynamic mathematical object, JavaScript, Google drive, transfer jet.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10001137 Neural Network Learning Based on Chaos
Authors: Truong Quang Dang Khoa, Masahiro Nakagawa
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Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.
Keywords: learning and evolutionary computing, Chaos Optimization Algorithm, Artificial Neural Networks, nonlinear optimization, intelligent computational technologies.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17701136 Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI
Authors: Elham Amini Boroujeni, Hamid Reza Momeni
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Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28671135 Implementation of Student-Centered Learning Approach in Building Surveying Course
Authors: Amal A. Abdel-Sattar
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The curriculum of architecture department in Prince Sultan University includes ‘Building Surveying’ course which is usually a part of civil engineering courses. As a fundamental requirement of the course, it requires a strong background in mathematics and physics, which are not usually preferred subjects to the architecture students and many of them are not giving the required and necessary attention to these courses during their preparation year before commencing their architectural study. This paper introduces the concept and the methodology of the student-centered learning approach in the course of building surveying for architects. One of the major outcomes is the improvement in the students’ involvement in the course and how this will cover and strength their analytical weak points and improve their mathematical skills. The study is conducted through three semesters with a total number of 99 students. The effectiveness of the student-centered learning approach is studied using the student survey at the end of each semester and teacher observations. This survey showed great acceptance of the students for these methods. Also, the teachers observed a great improvement in the students’ mathematical abilities and how keener they became in attending the classes which were clearly reflected on the low absence record.
Keywords: Architecture, building surveying, student-centered learning, teaching, and learning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12701134 Problems and Possible Solutions with the Development of a Computer Model of Quantum Theory
Authors: Hans H. Diel
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A computer model of Quantum Theory (QT) has been developed by the author. Major goal of the computer model was support and demonstration of an as large as possible scope of QT. This includes simulations for the major QT (Gedanken-) experiments such as, for example, the famous double-slit experiment. Besides the anticipated difficulties with (1) transforming exacting mathematics into a computer program, two further types of problems showed up, namely (2) areas where QT provides a complete mathematical formalism, but when it comes to concrete applications the equations are not solvable at all, or only with extremely high effort; (3) QT rules which are formulated in natural language and which do not seem to be translatable to precise mathematical expressions, nor to a computer program. The paper lists problems in all three categories and describes also the possible solutions or circumventions developed for the computer model.Keywords: Computability, Foundation of Quantum Mechanics, Measurement Process, Modeling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16881133 Unconventional Calculus Spreadsheet Functions
Authors: Chahid K. Ghaddar
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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.Keywords: Calculus functions, nonlinear systems, differential algebraic equations, solvers, spreadsheet.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24431132 A Numerical Study on Rear-spoiler of Passenger Vehicle
Authors: Xu-xia Hu, Eric T. T. Wong
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The simulation of external aerodynamics is one of the most challenging and important automotive CFD applications. With the rapid developments of digital computers, CFD is used as a practical tool in modern fluid dynamics research. It integrates fluid mechanics disciplines, mathematics and computer science. In this study, two different types of simulations were made, one for the flow around a simplified high speed passenger car with a rear-spoiler and the other for the flow without a rear-spoiler. The standard k-ε model is selected to numerically simulate the external flow field of the simplified Camry model with or without a rear-spoiler. Through an analysis of the simulation results, a new rear spoiler is designed and it shows a mild reduction of the vehicle aerodynamics drag. This leads to less vehicle fuel consumption on the road.
Keywords: CFD, vehicle rear-spoiler design.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 48871131 Modified Fast and Exact Algorithm for Fast Haar Transform
Authors: Phang Chang, Phang Piau
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Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.Keywords: Fast Haar Transform, Haar transform, Wavelet analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 31261130 A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces
Authors: Jyh-Yang Wu, Sheng-Gwo Chen
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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14961129 Effect of Personalization on Students' Achievement and Gender Factor in Mathematics Education
Authors: Nurettin Simsek, Özlem Cakır
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The aim of this study is to point out whether personalization of mathematical word problems could affect student achievement or not. The research was applied on two-grades students at spring semester 2008-2009. Before the treatment, students personal data were taken and given to the computer. During the treatment, paper-based personalized problems and paper-based non personalized problems were prepared by computer as the same problems and then these problems were given to students. At the end of the treatment, students- opinion was taken. As a result of this research, it was found out that there were no significant differences between learners through personalized or non-personalized materials, and also there were no significant differences between gender through personalized and non-personalized problems. However, opinion of students was highly positive through the personalized problems.
Keywords: Personalization, word problem, computer aided personalization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19191128 Adomian Decomposition Method Associated with Boole-s Integration Rule for Goursat Problem
Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran
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The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18441127 How are Equalities Defined, Strong or Weak on a Multiple Algebra?
Authors: Mona Taheri
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For the purpose of finding the quotient structure of multiple algebras such as groups, Abelian groups and rings, we will state concepts of ( strong or weak ) equalities on multiple algebras, which will lead us to research on how ( strong or weak) are equalities defined on a multiple algebra over the quotients obtained from it. In order to find a quotient structure of multiple algebras such as groups, Abelian groups and loops, a part of this article has been allocated to the concepts of equalities (strong and weak) of the defined multiple functions on multiple algebras. This leads us to do research on how defined equalities (strong and weak) are made in the multiple algebra on its resulted quotient.
Keywords: Multiple algebra, mathematics, universal algebra.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12351126 Experimental teaching, Perceived usefulness, Ease of use, Learning Interest and Science Achievement of Taiwan 8th Graders in TIMSS 2007 Database
Authors: Pei Wen Liao, Tsung Hau Jen
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the data of Taiwanese 8th grader in the 4th cycle of Trends in International Mathematics and Science Study (TIMSS) are analyzed to examine the influence of the science teachers- preference in experimental teaching on the relationships between the affective variables ( the perceived usefulness of science, ease of using science and science learning interest) and the academic achievement in science. After dealing with the missing data, 3711 students and 145 science teacher-s data were analyzed through a Hierarchical Linear Modeling technique. The major objective of this study was to determine the role of the experimental teaching moderates the relationship between perceived usefulness and achievement.Keywords: TIMSS database, Science achievement, Experimental teaching, Perceived Usefulness, Perceived Ease of Use
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16381125 Evaluating the Understanding of the University Students (Basic Sciences and Engineering) about the Numerical Representation of the Average Rate of Change
Authors: Saeid Haghjoo, Ebrahim Reyhani, Fahimeh Kolahdouz
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The present study aimed to evaluate the understanding of the students in Tehran universities (Iran) about the numerical representation of the average rate of change based on the Structure of Observed Learning Outcomes (SOLO). In the present descriptive-survey research, the statistical population included undergraduate students (basic sciences and engineering) in the universities of Tehran. The samples were 604 students selected by random multi-stage clustering. The measurement tool was a task whose face and content validity was confirmed by math and mathematics education professors. Using Cronbach's Alpha criterion, the reliability coefficient of the task was obtained 0.95, which verified its reliability. The collected data were analyzed by descriptive statistics and inferential statistics (chi-squared and independent t-tests) under SPSS-24 software. According to the SOLO model in the prestructural, unistructural, and multistructural levels, basic science students had a higher percentage of understanding than that of engineering students, although the outcome was inverse at the relational level. However, there was no significant difference in the average understanding of both groups. The results indicated that students failed to have a proper understanding of the numerical representation of the average rate of change, in addition to missconceptions when using physics formulas in solving the problem. In addition, multiple solutions were derived along with their dominant methods during the qualitative analysis. The current research proposed to focus on the context problems with approximate calculations and numerical representation, using software and connection common relations between math and physics in the teaching process of teachers and professors.
Keywords: Average rate of change, context problems, derivative, numerical representation, SOLO taxonomy.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7401124 On One Application of Hybrid Methods For Solving Volterra Integral Equations
Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova
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As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13861123 A Validity and Reliability Study of Grasha- Riechmann Student Learning Style Scale
Authors: Yaşar Baykul, Musa Gürsel, Hacı Sulak, Erhan Ertekin, Ersen Yazıcı, Osman Dülger, Yasin Aslan, Kağan Büyükkarcı
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The reliability of the tools developed to learn the learning styles is essential to find out students- learning styles trustworthily. For this purpose, the psychometric features of Grasha- Riechman Student Learning Style Inventory developed by Grasha was studied to contribute to this field. The study was carried out on 6th, 7th, and 8th graders of 10 primary education schools in Konya. The inventory was applied twice with an interval of one month, and according to the data of this application, the reliability coefficient numbers of the 6 sub-dimensions pointed in the theory of the inventory was found to be medium. Besides, it was found that the inventory does not have a structure with 6 factors for both Mathematics and English courses as represented in the theory.Keywords: Learning styles, Grasha-Riechmann, reliability, validity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 65451122 A Case Study of Mobile Game Based Learning Design for Gender Responsive STEM Education
Authors: Raluca Ionela Maxim
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Designing a gender responsive Science, Technology, Engineering and Mathematics (STEM) mobile game based learning solution (mGBL) is a challenge in terms of content, gamification level and equal engagement of girls and boys. The goal of this case study was to research and create a high-fidelity prototype design of a mobile game that contains role-models as avatars that guide and expose girls and boys to STEM learning content. For this research purpose it was applied the methodology of design sprint with five-phase process that combines design thinking principles. The technique of this methodology comprises smart interviews with STEM experts, mind-map creation, sketching, prototyping and usability testing of the interactive prototype of the gender responsive STEM mGBL. The results have shown that the effect of the avatar/role model had a positive impact. Therefore, by exposing students (boys and girls) to STEM role models in an mGBL tool is helpful for the decreasing of the gender inequalities in STEM fields.
Keywords: Design thinking, design sprint, gender-responsive STEM education, mobile game based learning, role-models.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13471121 Factoring a Polynomial with Multiple-Roots
Authors: Feng Cheng Chang
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A given polynomial, possibly with multiple roots, is factored into several lower-degree distinct-root polynomials with natural-order-integer powers. All the roots, including multiplicities, of the original polynomial may be obtained by solving these lowerdegree distinct-root polynomials, instead of the original high-degree multiple-root polynomial directly. The approach requires polynomial Greatest Common Divisor (GCD) computation. The very simple and effective process, “Monic polynomial subtractions" converted trickily from “Longhand polynomial divisions" of Euclidean algorithm is employed. It requires only simple elementary arithmetic operations without any advanced mathematics. Amazingly, the derived routine gives the expected results for the test polynomials of very high degree, such as p( x) =(x+1)1000.Keywords: Polynomial roots, greatest common divisor, Longhand polynomial division, Euclidean GCD Algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15671120 Modeling Exponential Growth Activity Using Technology: A Research with Bachelor of Business Administration Students
Authors: V. Vargas-Alejo, L. E. Montero-Moguel
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Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.Keywords: Covariation reasoning, exponential function, modeling, representations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4851119 Alternative Convergence Analysis for a Kind of Singularly Perturbed Boundary Value Problems
Authors: Jiming Yang
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A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.
Keywords: Convergence analysis, green's function, singularly perturbed, equi-distribution, moving mesh.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16861118 Complementing Assessment Processes with Standardized Tests: A Work in Progress
Authors: Amparo Camacho
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ABET accredited programs must assess the development of student learning outcomes (SOs) in engineering programs. Different institutions implement different strategies for this assessment, and they are usually designed “in house.” This paper presents a proposal for including standardized tests to complement the ABET assessment model in an engineering college made up of six distinct engineering programs. The engineering college formulated a model of quality assurance in education to be implemented throughout the six engineering programs to regularly assess and evaluate the achievement of SOs in each program offered. The model uses diverse techniques and sources of data to assess student performance and to implement actions of improvement based on the results of this assessment. The model is called “Assessment Process Model” and it includes SOs A through K, as defined by ABET. SOs can be divided into two categories: “hard skills” and “professional skills” (soft skills). The first includes abilities, such as: applying knowledge of mathematics, science, and engineering and designing and conducting experiments, as well as analyzing and interpreting data. The second category, “professional skills”, includes communicating effectively, and understanding professional and ethnical responsibility. Within the Assessment Process Model, various tools were used to assess SOs, related to both “hard” as well as “soft” skills. The assessment tools designed included: rubrics, surveys, questionnaires, and portfolios. In addition to these instruments, the Engineering College decided to use tools that systematically gather consistent quantitative data. For this reason, an in-house exam was designed and implemented, based on the curriculum of each program. Even though this exam was administered during various academic periods, it is not currently considered standardized. In 2017, the Engineering College included three standardized tests: one to assess mathematical and scientific reasoning and two more to assess reading and writing abilities. With these exams, the college hopes to obtain complementary information that can help better measure the development of both hard and soft skills of students in the different engineering programs. In the first semester of 2017, the three exams were given to three sample groups of students from the six different engineering programs. Students in the sample groups were either from the first, fifth, and tenth semester cohorts. At the time of submission of this paper, the engineering college has descriptive statistical data and is working with various statisticians to have a more in-depth and detailed analysis of the sample group of students’ achievement on the three exams. The overall objective of including standardized exams in the assessment model is to identify more precisely the least developed SOs in order to define and implement educational strategies necessary for students to achieve them in each engineering program.
Keywords: Assessment, hard skills, soft skills, standardized tests.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7941117 A Virtual Learning Environment for Deaf Children: Design and Evaluation
Authors: Nicoletta Adamo-Villani
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The object of this research is the design and evaluation of an immersive Virtual Learning Environment (VLE) for deaf children. Recently we have developed a prototype immersive VR game to teach sign language mathematics to deaf students age K- 4 [1] [2]. In this paper we describe a significant extension of the prototype application. The extension includes: (1) user-centered design and implementation of two additional interactive environments (a clock store and a bakery), and (2) user-centered evaluation including development of user tasks, expert panel-based evaluation, and formative evaluation. This paper is one of the few to focus on the importance of user-centered, iterative design in VR application development, and to describe a structured evaluation method.Keywords: 3D Animation, Virtual Reality, Virtual Learning Environments, User-Centered Design, User-centered Evaluation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2186