METHODOLOGY OF THE TEACHING OF FINITE MATHEMATICS AT THE PEDAGOGICAL UNIVERSITIES DUE TO THE NEW TRENDS IN THE EVOLUTION OF THE MATHEMATICAL SCIENCES

2021 ◽  
pp. 92-100
Author(s):  
D. GADJIEV
Keyword(s):  
Instructional Strategies ◽  
Numerical Solutions ◽  
Binomial Coefficients ◽  
Binomial Theorem ◽  
Binomial Expansion ◽  
Finite Mathematics ◽  
Engineering Sciences ◽  
Pedagogical Orientation ◽  
Mathematical Sciences ◽  
And Mathematics

There were introduced new methods of the teaching and instruction of the following parts of the Pre-calculus: (1) Binomial Series; (2) Trigonometry; (3) Partial Fractions. The problems introduced in the article for the Pre-Calculus Course in Finite Mathematics was developed by the author. These unabridged problems are developed within the new trends in the evolutions of the novelty of the syllabi in Mathematics due to the development of the Mathematics Sciences / Theory and Applications. These new trends in the Theory and Application of Mathematics Sciences have been added new demands to the newly revised textbooks and corresponding syllabi for the Mathematics Courses taught at the Junior two years Colleges and Pedagogical Universities.These newly developed problems are reflection of the Development of Mathematical and Engineering Sciences to offer great amount of learning conclusion/sequel to those who pursue a bachelor’s degree at the universities of the pedagogical orientation. The problems presented in the article here are developed and restructured in terms of the newly developed techniques to solve the problem in Finite Mathematics and Engineering sciences. Moreover, the techniques offered in the article here are more likely to get utilized in Advanced Engineering Sciences, too, within the content of the problems, which require to obtain finite numerical solutions to the Real Phenomena Natural Problems in Engineering Sciences and Applied Problems in Mathematical Physics.The aim of this present publication is to offer new advanced techniques and instructional strategies to discuss methodology and instructional strategies of the mathematical training of the students at the Pedagogical Universities. Moreover, these new teaching techniques and strategies introduced may be extended to the engineering sciences at the technical universities, too.The results and scientific novelty of the introduced methodology and learning conclusions and sequel of the new knowledge the students at the Pedagogical universities may be benefited from are in the following list of the learning conclusions, presented in the article here. The students of the pedagogical orientation may attain the mastery skills in the following sections of the combinatorics in Finite Mathematics subject:- The n! Combination of n different terms.- Evaluate the expressions with factorials.- Identify that there are -!!( )!nrnr various of combinations of r identical terms in n variations.- Identify and evaluate the combinatorial coefficients from the Binomial Theorem.- Identify and able to build the Pascal’s triangle of the binomial coefficients.- Utilize the Binomial Theorem to expand the binomial formula for any natural powers.- Utilize the Binomial Theorem to obtain the general formula for the n-th term of binomial expansion.- Utilize the Sigma Symbols in the Binomial Theorem for the n-th terms of the binomial expansion. 19- Generate the expansion for the power of the ex, where e is the base of natural logarithmic function y = f(x) = x.Practical significance: the methods of teaching and new teaching strategies offered here in the article alongside with the application of the new trends in the development of mathematical and mathematics education sciences can be useful for prospective and currently practicing teachers of mathematics. Moreover, the materials presented here in this article can be useful for the educational professionals in their professional development plans to improve the quality in education

scholarly journals Learning progressions: framing and designing coherent sequences for STEM education

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Richard A. Duschl
Keyword(s):  
Instructional Strategies ◽  
Stem Education ◽  
Future Research ◽  
Learning Progressions ◽  
Scientific Practices ◽  
Discourse Practices ◽  
And Mathematics ◽  
Conclusion Section ◽  
Early Childhood Learning ◽  
Teaching Experiments

AbstractThe coupled influences of scholarship in the fields of Psychology, Philosophy, and Pedagogy beginning in the 1950s, set in motion the emergence of new images, methodological perspectives, theories, and design principles about learners and learning. Advances in cognitive and sociocultural psychology, shifting images of the nature of science, recognition of the importance of disciplinary discourse practices in learning, the scaffolding of learning by tools and technologies, along with the adoption of ‘assessment for learning’ instructional strategies are among the factors that have led researchers and practitioners to advance positions that learning ought to be coordinated and sequenced along conceptual trajectories, developmental corridors, and learning progressions (LP). Following opening Introduction and LP Research Framework sections that provide an overview of the runup to LP research and development, I then turn to future research discussions and implications targeting five LP domains: Using Knowledge with Scientific Practices; Instructional Pathways – Early Childhood Learning; Teaching Experiments – Science and Mathematics; Upper/Lower Anchors for Measuring Progress; and Concepts & Practices. The Conclusion section points to overarching challenges for researchers, planners, and teachers in STEM education. There is much to learn for all!

scholarly journals A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 923 ◽  
Author(s):  
Omar Abu Arqub ◽  
Mohamed S. Osman ◽  
Abdel-Haleem Abdel-Aty ◽  
Abdel-Baset A. Mohamed ◽  
Shaher Momani
Keyword(s):  
Convergence Analysis ◽  
Fractional Order ◽  
Numerical Algorithm ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Discretization Method ◽  
Fractional Models ◽  
Discretization Technique ◽  
And Mathematics

This paper deals with the numerical solutions and convergence analysis for general singular Lane–Emden type models of fractional order, with appropriate constraint initial conditions. A modified reproducing kernel discretization technique is used for dealing with the fractional Atangana–Baleanu–Caputo operator. In this tendency, novel operational algorithms are built and discussed for covering such singular models in spite of the operator optimality used. Several numerical applications using the well-known fractional Lane–Emden type models are examined, to expound the feasibility and suitability of the approach. From a numerical viewpoint, the obtained results indicate that the method is intelligent and has several features stability for dealing with many fractional models emerging in physics and mathematics, using the new presented derivative.

scholarly journals Preface

1994 ◽  
Vol 347 (1684) ◽  
pp. 449-449 ◽  
Keyword(s):  
Stock Prices ◽  
Large Scale ◽  
18Th Century ◽  
Telecommunication Networks ◽  
Financial Industry ◽  
Interacting Systems ◽  
Mathematical Sciences ◽  
And Mathematics ◽  
The City ◽  
Made In

There is money to be made in the financial industry. Academics, under pressure to exhibit relevance, are happy to point to their consultancies in the City as evidence of their value in the market, and the industry has shown a notable ability to recruit the brightest and best from our Universities. These observations should not obscure the profound scientific challenges posed by the area of finance. The area has both stimulated and benefited from advances in a range of mathematical sciences, most obviously probability, differential equations, optimization, statistics and numerical analysis. One thinks, for example, of Bernoulli’s resolution, in the 18th century, of the St Petersburg Problem through his introduction of a logarithmic utility, of Bachelier’s description, at the turn of this century, of the stochastic process we now call brownian motion, of Kendall’s investigation, forty years ago, of the statistical unpredictability of stock prices, and of the current enormously fertile interaction between economics and mathematics centred around martingale representations. Looking to the future, some of the mathematical ideas originally motivated by statistical mechanics, and since used to model the large-scale telecommunication networks upon which the financial industry relies, may also provide insight into the very difficult problems that arise in economics concerning interacting systems of rational agents.

scholarly journals Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 215 ◽  
Author(s):  
Alessandra Jannelli
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Fractional Differential Equations ◽  
Numerical Solutions ◽  
Diffusion Reaction ◽  
Unconditionally Stable ◽  
Advection Diffusion ◽  
Engineering Sciences ◽  
Hydrodynamic Processes ◽  
Fractional Differential

This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF–ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF–ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems.

scholarly journals An integrated model for interdisciplinary graduate education: Computation and mathematics for biological networks

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257872
Author(s):  
Kelsey E. McKee ◽  
Daniel Serrano ◽  
Michelle Girvan ◽  
Gili Marbach-Ad
Keyword(s):  
Biological Networks ◽  
Network Science ◽  
Graduate Program ◽  
Interdisciplinary Training ◽  
Faculty Advisors ◽  
Social Events ◽  
Engineering Sciences ◽  
Domain 3 ◽  
And Mathematics ◽  
Program Components

The current challenges at the forefront of data-enabled science and engineering require interdisciplinary solutions. Yet most traditional doctoral programs are not structured to support successful interdisciplinary research. Here we describe the design of and students’ experiences in the COMBINE (Computation and Mathematics for Biological Networks) interdisciplinary graduate program at the University of Maryland. COMBINE focuses on the development and application of network science methods to biological systems for students from three primary domains: life sciences, computational/engineering sciences, and mathematical/physical sciences. The program integrates three established models (T-shaped, pi-shaped and shield-shaped) for interdisciplinary training. The program components largely fall into three categories: (1) core coursework that provides content expertise, communication, and technical skills, (2) discipline-bridging elective courses in the two COMBINE domains that complement the student’s home domain, (3) broadening activities such as workshops, symposiums, and formal peer-mentoring groups. Beyond these components, the program builds community through both formal and informal networking and social events. In addition to the interactions with other program participants, students engage with faculty in several ways beyond the conventional adviser framework, such as the requirement to select a second out-of-field advisor, listening to guest speakers, and networking with faculty through workshops. We collected data through post-program surveys, interviews and focus groups with students, alumni and faculty advisors. Overall, COMBINE students and alumni reported feeling that the program components supported their growth in the three program objectives of Network Science & Interdisciplinarity, Communication, and Career Preparation, but also recommended ways to improve the program. The value of the program can be seen not only through the student reports, but also through the students’ research products in network science which include multiple publications and presentations. We believe that COMBINE offers an effective model for integrated interdisciplinary training that can be readily applied in other fields.

scholarly journals WITH SYMMETRY IN LIFE AND MATHEMATICS To the 75th anniversary of Corresponding Member of NAS of Ukraine A.G. Nikitin

2020 ◽  
pp. 87-92
Author(s):  
Vyacheslav M. Boyko ◽  
◽  
Olena O. Vaneeva ◽  
Alexander Yu. Zhalij ◽  
Roman O. Popovych ◽  
...  
Keyword(s):  
Science And Technology ◽  
Mathematical Physics ◽  
The State ◽  
State Prize ◽  
75Th Anniversary ◽  
Mathematical Sciences ◽  
And Mathematics

December 25 marks the 75th anniversary of the famous Ukrainian specialist in mathematical physics, winner of the State Prize of Ukraine in Science and Technology (2001) and the M.M. Krylov Prize of the NAS of Ukraine (2010), Head of the Department of Mathematical Physics of the Institute of Mathematics of the NAS of Ukraine, Doctor of Physical and Mathematical Sciences (1987), Professor (2001), Corresponding Member of the NAS of Ukraine (2009) Anatoly G. Nikitin.

scholarly journals Series Representation of Power Function

2018 ◽  
Author(s):  
Petro Kolosov
Keyword(s):  
Numerical Methods ◽  
Power Function ◽  
Exponential Function ◽  
Finite Differences ◽  
Series Representation ◽  
Discrete Case ◽  
Natural Numbers ◽  
Binomial Theorem ◽  
Binomial Expansion

In this paper described numerical expansion of natural-valued power function xn, in point x = x0 where n, x0 - natural numbers. Apply- ing numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. Received results were compared with solutions according to Newton’s Binomial theorem and MacMillan Double Bi- nomial sum. Additionally, in section 4 exponential function’s ex representation is shown.

scholarly journals Decolonizing the training of engineers and scientists: The case of the Faculty of Physical Sciences and Mathematics at Universidad de Chile

2021 ◽  
Vol 5 (1) ◽  
pp. 87
Author(s):  
Claudia Rodríguez-Seeger ◽  
Doris Sáez-Hueichapan ◽  
Alexandra Fuenzalida-Artigas ◽  
Ignacio Ñancupil-Quirilao ◽  
María Elena Lienqueo ◽  
...  
Keyword(s):  
Higher Education ◽  
Teaching And Learning ◽  
Indigenous Communities ◽  
Intercultural Training ◽  
Physical Sciences ◽  
Scientific Performance ◽  
Creative Commons ◽  
The World ◽  
Mathematical Sciences ◽  
And Mathematics

Given current global crises, there is a need to move beyond the anthropocentric, reductionist and short-term vision of the world, imposed through the hegemony of Western culture. Are we still in time to change the prevailing hegemonic vision of the world and better address global crises and their local impacts? What is the role of intercultural higher education in this challenging task? We conceive this type of education for the training of future decision-makers, as well as scientists and technicians who must respond to current and future challenges in society. Therefore, we evaluate the contribution of the Indigenous Peoples Program (PPI) of the Faculty of Physical and Mathematical Sciences (FCFM) at Universidad de Chile (UCH). We conclude that the PPI opens up possibilities for intercultural training in the FCFM, which can contribute to changing the professional and scientific performance of its graduates, opening their minds to other cultures, worldviews, values and paradigms. Keywords: Indigenous, Higher education, Interculturality, Indigenous communities, Discrimination How to ite this article: Rodríguez-Seeger, C., Sáez-Hueichapan, D., Fuenzalida-Artigas, A., Ñancupil-Quirilao, I., Lienqueo, M.E., Contreras-Painemal, C. & Díaz-Alvarado, F. 2021. Decolonizing the training of engineers and scientists: the case of the Faculty of Physical Sciences and Mathematics at Universidad de Chile. Scholarship of Teaching and Learning in the South. 5(1): 87-106. DOI: 10.36615/sotls.v5i1.154. This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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