Handbook Of Mathematics Research Articles

Developing Digital Pocketbook Interactive Based on HTML-5 to Improve Mathematics Learning Outcomes

Interactive learning media have an essential role in realizing interesting and interactive mathematics learning, so they have the potential to optimize student learning outcomes. This research aims to develop and evaluate an Interactive Mathematics pocketbook in HTML5 format that can be used to improve student learning outcomes. This research and development uses a 4D model. This research found that elementary school students need and like mathematics pocketbooks that look attractive and have interactive features as a learning tool. The product validation test results obtained a final score from material and language experts of 86.47%, which means that the product reached the very feasible category regarding content quality, graphics, and language. Media experts gave a final score of 88.3%, which means that the product is very worthy in terms of content structure, appearance, ease of use, and ease of learning. The results of field trials also show that the media developed can improve student learning outcomes in the medium category with an n-gain score of 0.56. These findings indicate that the development of an Interactive Mathematics Handbook in HTML5 format with a 4D model can produce a valid and effective product used to support the learning process of elementary school students.

VOLUME 52 (2022)

VOLUME 52 (2022)

“Palpable to thinking”: Othello and Gross Conceits

Beginning with Iago’s insults against Cassio as both “arithmetician” (1.1.18) and “counter-caster” (1.1.30), this essay explores the deep epistemological divides that the two terms suggested in the period. The essay turns to another mathematical conceit in the play, the word “gross.” Although suggesting stupidity, stolidity, and other terms of weight, the paper locates the associations of “gross” within debates on mathematical representation in the period. The essay focuses on the term gross in the period’s mathematical handbooks, particularly in John Dee’s preface to Euclid’s The Elements (1570). It shows how Dee is juggling complex epistemic issues in positing a third category between the material and the immaterial. This third category, mathematics, relies upon metaphors of the gross and ideas of movement in order to gain a foothold in Dee’s cosmic system for all forms of thought. The essay thus shows how Shakespeare’s tragedy picks up on the mathematical and representational difficulties of the term “gross” to both point to and play with the productive limitations of language. In Othello’s persistent use of “gross” to describe the inability of representation to fully reach its auditors, the essay uncovers a similar concern with the gaps between language and mental apprehension. Both mathematics and Othello, that is, traffic in the concerns over what is gross, what can never be gross, and characters’ need to imagine objects and ideas as gross in order to theorize computations. [K.W.]

Developing a Handbook on Multimedia Integration in Mathematics Teaching for Indonesian Primary School Students

This study has developed a digital mathematics handbook that helps students to strengthen their mathematical skills at the elementary level of education. A survey of mathematics teachers collected data. In developing an integration manual on technology based on a survey of the state of technological integration in schools, it employed a research and development (RD) approach. A number of 24 teachers participated in the material creation. The multimedia materials produced during the trial were developed and used. Participants consisted of primary learning children. Results have shown that the trainers' preferred theory is undergraduate, and most of them have a poor capacity to integrate creativity into a research analysis. In the presentation of the under-graduates in mathematics the material produced was extremely good.

Study of Theory and Technology of Exponential Function in Senior High School based on Practseology Organization

The purpose of this study was to determine the change in exponential function material in the KBK 2004 curriculum textbooks up to the 2013 revised 2017 curriculum in Indonesia in a study of theory and technology and based on reference to the epistemological model of exponent functions containing pre-psychological organisation. The data source was taken from the mathematics handbook of class XII IPA for KBK 2004 curriculum and KTSP 2006 curriculum, the BSE math class XII book for 2013 curriculum until the 2013 revised 2016 curriculum and the mathematics module specialization book for class X for the 2013 revised curriculum 2017. Data analysis techniques used by researchers were divided into 4, namely coding, categorizing, comparison, discussion. The results of research that has been done, researchers have found the presentation of exponential function theory with 5 core categories of understanding. In theoretical studies, the 2013 revised 2016 curriculum mathematics textbook has a more complex theory and is in accordance with the reference epistemological models. While technology studies have math books, there are more complex technologies, namely the 2013 revised 2014 curriculum mathematics textbooks, there is the first form of technology and in the 2013 revised 2017 curriculum mathematics textbooks and the 2016 revised 2013 curriculum mathematics textbooks, there is a third form of technology textbooks and the curriculum mathematics textbooks 2006 (KTSP 2006) there is a third form of technology.

Financial econometrics, mathematics, statistics, and financial technology: an overall view

Based upon my experience in research, teaching, writing textbooks, and editing handbooks and journals, this review paper discusses how financial econometrics, mathematics, statistics, and financial technology can be used in research and teaching for students majoring in quantitative finance. A major portion of this paper discusses essential content of Lee and Lee (Handbook of financial econometrics, mathematics, statistics, and machine learning, World Scientific, Singapore, 2020). Then Lee (From east to west: memoirs of a finance professor on academia, practice, and policy, World Scientific, Singapore, 2017), Lee et al. (Financial econometrics, mathematics and statistics, Springer, New York, 2019a; Machine learning for predicting default of credit card holders and success of kickstarters. Working paper, 2019b), and Lee and Lee (Handbook of financial econometrics and statistics, Springer, New York, 2015) are used to enhance the content of this paper. In addition, important and relevant papers, which have been published in different journals are also used to support the issues discussed in this paper. I have found the applications of financial econometrics, mathematics, statistics, and technology have improved drastically over the last five decades. Therefore, both practitioners and academicians need to update their skills in this area to compete in both financial market and academic research.

DEVELOPMENT OF TEACHER HANDBOOKS AND REALISTIC MATHEMATICS STUDENTS BASIC SCHOOLS

The research aims to develop teacher and student handbooks for realistic mathematics lessons for elementary schools. The development of this handbook is based on the reality in the field where the handbook of teachers and students especially the subjects using the 2013 curriculum still do not exist, and in daily learning activities teachers and students still use books that use themes. This research uses development research (Developmental Research). The subjects of this study were grade V students of SD Negeri 163085, H.A Bilal Tebingtinggi City and SD Negeri 106162, Medan Estate District, Deliserdang Regency. In the initial stage, observations were made during the learning process at the two schools and continued with interviews with students and teachers. From the results of these observations and interviews a primary school realistic mathematics teacher and student handbook was prepared. Furthermore, the realistic elementary school mathematics teacher and student handbook is validated by a team that aims to see and assess the quality of the realistic elementary school teacher and student mathematics handbook in order to arrange an effective handbook that will be used by teachers and students in learning. The validation results show that realistic mathematics teacher and student handbooks are developed in both categories and can be used in teaching and learning. The media book test was conducted on grade V students of SD Negeri 163085 Tebingtinggi city and SD Negeri 106162 Medan Estate Deliserdang Regency. The trial results show that the elementary school teacher and student mathematics handbook is effective and can help facilitate understanding of mathematical concepts at the elementary school level. This can be seen from the number of students who can reach the KKM from the two schools is increasing. For SD Negeri 163085 HA Bilal, Tebingtinggi City, if at the time of the pre-test only 1 student (3%) was able to reach the KKM, then after being given the learning process using a teacher and student handbook developed the number of students who could reach the KKM increased to 24 students (82.7%) while those under the KKM were only (17.3%) or 5 students. The same thing was seen in SD Negeri 106162, Medanestate Subdistrict, Deliserdang Regency. If at the time of the Pre-test only 2 students (6.6%) had scored above the KKM, after the post-test there was an increase in students who achieved the KKM score of 25 students (83.3%). An increase of 76.7% when compared to the pre test. Keywords: Handbook, teacher, student, PMR

Reframing teacher knowledge: a research and development agenda

This article undertakes a reframing of the concept of teacher knowledge. It argues that in order to help teachers create more powerful learning environments, a much more general framing is required—one that incorporates a teacher’s perceptions, inclinations and orientations as well as their understandings and related proficiencies. A main point of departure is the Teaching for Robust Understanding (TRU) framework, which focuses on essential dimensions of classroom practice. Questions of teacher knowledge are reframed as: “How can we reconceptualize teacher knowledge (perhaps better, teacher proficiency) so that it encompasses the broad range of perceptions, orientations, understandings and proficiencies that support teachers in crafting learning environments from which students emerge as knowledgeable, flexible, and resourceful thinkers and problem solvers? How can it be organized so that it can be worked on productively? This paper explores these issues. It employs the TRU framework as the initial mechanism for reframing, while drawing on Schoenfeld’s (How we think. Routledge, New York, 2010) work on teachers’ decision making and Schoenfeld and Kilpatrick’s (International handbook of mathematics teacher education, volume 2: tools and processes in mathematics teacher education. Sense Publishers, Rotterdam, pp 321–354, 2008) work on teacher proficiency to suggest what should be included in an expanded framing of teacher knowledge.

IMPLEMENTASI MODEL PEMBELAJARAN MATEMATIKA PENDIDIKAN SEKOLAH DASAR BERBASIS KEUNGGULAN LOKAL DI KABUPATEN ACEH TENGAH

Purpose of this study is to: to find out the objective conditions of local superiority in mathematics learning in elementary schools in Central Aceh Regency, to design mathematical learning models based on local superiority of class I students, and to find out student responses to local excellence based mathematics learning models in Central Aceh Regency. The subjects of this study were all 4th grade students of elementary school in Bebesen Central Aceh District. And the samples are SD 1 Bebesen, SDN 2 Bebesen, SDN 5 Bebesen, SDN 8 Bebesen, SDN 9 Bebesen, SD 10 Bebesen, SDN 10 Bebesen, SDN 11 Bebesen, SDN 12 Bebesen, SDN 14 Bebesen, SDN 16 Bebesen, SDN 16 Bebesen, SDN 17 Bebesen, SDN 17 Bebesen, SD IT Scholar. The research results were obtained that: (1) the objective conditions of mathematics learning of elementary students in Central Aceh Regency as follows. a) In the learning process the teacher has not linked mathematics with the local character and potential of the area. b) The mathematics handbook used today has not linked students' personal character. (2) During the learning process of mathematics based on local excellence and the potential character of antusius elementary school students to learn mathematics, the steps of the local superiority-based learning model are (a) the teacher conditions the class, starts with prayer by preparing facilities and infrastructure, doing Apperception of the local potential of central Aceh district b) Presenting contextual problems, Explicitly negotiating, Cooperative intervention, guiding students in groups to discuss contextual issues contained in the LAS. Give students the opportunity to present their model findings through class discussions. c) Guiding students to formulate the results of the discussion while making a summary of the material discussed, Providing material evaluations through giving quizzes or home assignments. The design of elementary school mathematics learning based on locally designed excellence received a good response from all students. 83.74% of students gave a positive response to the local excellence-based learning model. From these results it is expected that the mathematics learning model in the class must be tailored to the needs of students so that the objectives of the learning process can be achieved maximally.

Expert mathematics teacher educators’ purposes and practices for providing prospective teachers with opportunities to develop pedagogical content knowledge in content courses

Enhancing teachers’ pedagogical content knowledge (PCK) is essential to improving the teaching and learning of mathematics. Mathematics teacher educators (MTEs) need to help prospective teachers enhance PCK (Marks in J Teach Educ 41(3):3–11, 1990. doi: 10.1177/002248719004100302 ; Mason 2008). However, we know very little about the practices of MTEs, especially in mathematics content courses, as these practices are not widely researched or disseminated (e.g., Bergsten and Grevholm, in: Jaworski, Wood (eds) The international handbook of mathematics teacher education, vol 4, Sense Publishers, Rotterdam, pp 223–246, 2008; Floden and Philipp, in: Lester, Ferrini-Mundy (eds) Proceedings of the NCTM research catalyst conference, National Council of Teachers of Mathematics, Reston, pp 171–176, 2003). This phenomenographical study offers empirical findings on commonly identified purposes across ten expert MTEs who provided K-8 prospective teachers with opportunities to develop PCK in their mathematics content courses. Furthermore, our emergent findings indicated that expert MTEs also provided opportunities for prospective teachers to develop orientations toward teaching the subject, which prompted framework adaptations and articulations of “orientations” as a construct discussed in the broader literature outside of mathematics teacher education research (Magnusson et al., in: Gess-Newsome, Lederman (eds) Examining pedagogical content knowledge, Kluwer, Dordrecht, pp 95–132, 1999). Research and practitioner implications from this study provide specific PCK-related learning opportunities of prospective teachers through the lenses of expert MTEs’ (personal and professional) purposes and reflections on teaching, as a foundation on which the field can continue building future research and MTEs can continue building their practice in mathematics content courses.

Sustaining and scaling up the impact of professional development programmes

This paper deals with a crucial topic: which factors influence the sustainability and scale-up of a professional development programme’s impact? Theoretical models and empirical findings from impact research (e.g. Zehetmeier and Krainer, ZDM Int J Math 43(6/7):875–887, 2011) and innovation research (e.g. Cobb and Smith, International handbook of mathematics teacher education, vol 3, pp 231–254, Sense Publishers, Rotterdam, 2008; Rogers, Diffusion of innovations, Free Press, New York, 2003) are combined in order to be used as a theoretical framework for a qualitative impact analysis of a mathematics teacher professional development programme in Austria. The paper provides data from document analyses and interview series to describe as well as explain this programme’s various impacts on different levels within a case study setting. In particular, this study focuses on factors (e.g. networks, shared vision or mutual accountability) which are influencing the scale-up and sustainability of a professional development programme’s impact (e.g. on teachers’ knowledge, beliefs or practice). Finally, implications for upcoming professional development programmes are discussed.

A concise handbook of mathematics, physics, and engineering sciences

MATHEMATICS Arithmetic and Elementary Algebra Elementary Functions Elementary Geometry Analytic Geometry Algebra Limits and Derivatives Integrals Series Functions of Complex Variables Integral Transforms Ordinary Differential Equations Partial Differential Equations Special Functions and Their Properties Probability Theory PHYSICS Physical Foundations of Mechanics Molecular Physics and Thermodynamics Electrodynamics Oscillations and Waves Optics Quantum Mechanics. Atomic Physics Quantum Theory of Crystals Elements of Nuclear Physics ELEMENTS OF APPLIED AND ENGINEERING SCIENCES Dimensions and Similarity Mechanics of Point Particles and Rigid Bodies Elements of Strength of Materials Hydrodynamics Mass and Heat Transfer Electrical Engineering Empirical and Engineering Formulas and Criteria for Their Applicability SUPPLEMENTS Integrals Integral Transforms Orthogonal Curvilinear Systems of Coordinates Ordinary Differential Equations Some Useful Electronic Mathematical Resources Index References appear at the end of each chapter.

A Generalization of Some Huang–Johnson Semifields

In [H. Huang, N.L. Johnson: Semifield planes of order $8^2$, Discrete Math., 80 (1990)], the authors exhibited seven sporadic semifields of order $2^6$, with left nucleus ${\mathbb F}_{2^3}$ and center ${\mathbb F}_2$. Following the notation of that paper, these examples are referred as the Huang–Johnson semifields of type $II$, $III$, $IV$, $V$, $VI$, $VII$ and $VIII$. In [N. L. Johnson, V. Jha, M. Biliotti: Handbook of Finite Translation Planes, Pure and Applied Mathematics, Taylor Books, 2007], the question whether these semifields are contained in larger families, rather then sporadic, is posed. In this paper, we first prove that the Huang–Johnson semifield of type $VI$ is isotopic to a cyclic semifield, whereas those of types $VII$ and $VIII$ belong to infinite families recently constructed in [N.L. Johnson, G. Marino, O. Polverino, R. Trombetti: Semifields of order $q^6$ with left nucleus ${\mathbb F}_{q^3}$ and center ${\mathbb F}_q$, Finite Fields Appl., 14 (2008)] and [G.L. Ebert, G. Marino, O. Polverino, R. Trombetti: Infinite families of new semifields, Combinatorica, 6 (2009)]. Then, Huang–Johnson semifields of type $II$ and $III$ are extended to new infinite families of semifields of order $q^6$, existing for every prime power $q$.

A class of $${\Sigma _{3}^{0}}$$ modular lattices embeddable as principal filters in $${\mathcal{L}^{\ast }(V_{\infty })}$$

Let I 0 be a a computable basis of the fully effective vector space V ∞ over the computable field F. Let I be a quasimaximal subset of I 0 that is the intersection of n maximal subsets of the same 1-degree up to *. We prove that the principal filter $${\mathcal{L}^{\ast}(V,\uparrow )}$$ of V = cl(I) is isomorphic to the lattice $${\mathcal{L}(n, \overline{F})}$$ of subspaces of an n-dimensional space over $${\overline{F}}$$ , a $${\Sigma _{3}^{0}}$$ extension of F. As a corollary of this and the main result of Dimitrov (Math Log 43:415–424, 2004) we prove that any finite product of the lattices $${(\mathcal{L}(n_{i}, \overline{F }_{i}))_{i=1}^{k}}$$ is isomorphic to a principal filter of $${\mathcal{ L}^{\ast}(V_{\infty})}$$ . We thus answer Question 5.3 “What are the principal filters of $${\mathcal{L}^{\ast}(V_{\infty}) ?}$$ ” posed by Downey and Remmel (Computable algebras and closure systems: coding properties, handbook of recursive mathematics, vol 2, pp 977–1039, Stud Log Found Math, vol 139, North-Holland, Amsterdam, 1998) for spaces that are closures of quasimaximal sets.

Handbook of mathematics for engineers and scientists

Authors Foreword Main Notation DEFINITIONS, FORMULAS, METHODS, AND THEOREMS Arithmetic and Elementary Algebra Elementary Functions Elementary Geometry Analytic Geometry Algebra Limits and Derivatives Integrals Series Differential Geometry Functions of Complex Variable Integral Transforms Ordinary Differential Equations First-Order Partial Differential Equations Linear Partial Differential Equations Nonlinear Partial Differential Equations Integral Equations Difference Equations and Other Functional Equations Special Functions and Their Properties Calculus of Variations and Optimization Probability Theory Mathematical Statistics MATHEMATICAL TABLES Finite Sums and Infinite Series Integrals Integral Transforms Ordinary Differential Equations Systems of Ordinary Differential Equations First-Order Partial Differential Equations Linear Equations and Problems of Mathematical Physics Nonlinear Mathematical Physics Equations Systems of Partial Differential Equations Integral Equations Functional Equations Supplement: Some Useful Electronic Mathematical Resources Index

Impedance Calculations for Elements of Sonar Arrays by Neural-Network-Based Integration

In this paper, a technique of neural network based integration is proposed to calculate the self-and mutual-impedances within arrays of sonar transducers. The multi-dimensional integrals appearing in self-and mutual-impedance formulations are transformed into neural-network-based integration and the final results can be found from look-up tables in mathematical handbooks. Initially, the integrand is modeled by a trained neural network. Integration on the integrand then becomes integration on the linear combination of weights and basis functions within the neural network. The results will become the linear combination of error functions which can be looked up in mathematical handbooks. Numerical simulation shows that the results calculated by the proposed method are consistent with those given in other existing studies. The proposed technique requires neither numerical nor artificial integration procedure. Due to the inherent learning and predicting property of neural network, only a small number of sampling points for the integrand are required in the proposed integration technique.

Mathematical Handbook for Electrical Engineers [Book Review

This book consists of three parts. Part I contains the most widely used fundamental mathematical definitions, laws, and rules that are used to solve the majority of electrical engineering problems. Part II contains solved examples in four different areas of electrical engineering: circuits and devices; antennas and propagation; waveforms and signal processing; and stochastic radio engineering. The majority of the problems fall in the later category. Part III contains reference data on all sorts of mathematical expressions. Engineers, especially electrical engineers who work with mathematical problems either on a regular basis or infrequently, would find this book to be a useful resource for setting up and solving problems.

Environmental engineer's mathematics handbook

Environmental engineer's mathematics handbook

Mathematics in the Supply Chain

Mathematical models and methods have been established in various fields of applications in recent years. These include transport and traffic (see for instance the Oberwolfach workshop on “Traffic and Transport Optimization” in 1999), production planning (see Handbooks in Operations Research and Management Science, the volume on “Logistics of Production and Inventory” Graves, Rinnooy Kan and Zipkin (eds.), North-Holland, 1993), communication networks (see “Handbook of Discrete and Combinatorial Mathematics” Rosen (ed.), or “Handbook in Operations Research and Management Science” the volume on “Network Models” Ball, Magnanti, Monma and Nemhauser (eds.)) and financial engineering (“Options, Futures, and Other Derivatives” by J. Hull). The success of mathematical methods does not only rely on progress in computer technology, but in a fundamental way it relies on the improvement of the underlying mathematical models, methods and associated algorithmic developments. In recent years new challenges from industry and business have arisen. Modern problems contain more and more structures whose origins lie in various disciplines of mathematics, including graphs and networks, optimization, control and stochastic processes. A prominent field in which such problems arise is supply chain management. Supply chain management is typically defined as: A set of approaches utilized to efficiently integrate suppliers, manufacturers, warehouses, and stores so that merchandise is produced and distributed in the right quantities, to the right locations, and at the right time, in order to minimize systemwide costs while satisfying service level requirements. The idea of the workshop was to bring people from mathematics who have successfully applied mathematical methods for the solution of practical problems together with people who are in touch with the real-world problems that constitute supply chain management. To motivate and initiate interactions between the two groups, the mathematicians presented their applied methods and explained the situations in which they are effective as well as the underlying theory. These methods and concepts cover a wide spectrum, ranging from integer programming and dynamic programming methods through approximation algorithms to stochastic optimization methods. Similarly, supply chain management experts explained their problems, pointed out where current methods will help and where further developments are necessary. The scope of these problems is quite impressive. It includes distribution problems that integrate warehousing and transportation, inventory management models, the integration of procurement and manufacturing activities with demand planning processes and pricing and auction models that are used to improve business-to-consumer and business-to-business interactions. In this way we hope that the workshop provided a forum for open discussions about interesting new mathematical problems that are of central importance to supply chain management. The workshop itself was organized as follows. We had a series of plenary talks from world leading experts in mathematics and in supply chain management about the current state-of-the-art in these fields. We completed the program by having a series of shorter talks where people reported on their chosen models and solution methods for these models. In particular we invited and encouraged young people to participate in the workshop. They used the chance to gain as well as to present insights into new developments in applied mathematics and supply chain management. The interconnection of the two disciplines showed to provide a great source for new, interesting research projects in the future. The Oberwolfach workshop on “Mathematics in the Supply Chain” turned out to be of great interest for both experts in mathematics and experts in supply chain management. The meeting offered a platform for mathematicians to become acquainted with an important future-oriented field of applications. Vice versa, it offered a platform for supply chain management people to learn more about current mathematical models and methods potentially useful in solving further problems. We are very happy that we had the opportunity to organize such an interdisciplinary workshop at Oberwolfach.

Model of m-level low-frequency current fluctuations in metal thermionic cathodes

A new model of low-frequency fluctuations, based on the thermionic current model [Mathematical Handbook for Scientists and Engineers, New York, 1961; Introduction to Statistical Radio-Physic. Part 1: Random Processes, Moscow, 1976 (in Russian)], has been designed. The proposed model provides calculation of realization, auto-correlation function (ACF) and power spectral density (PSD) of an m-level quantum signal. This model has allowed to explain the reason of very small magnitude of low-frequency (LF) boundary (10 −4 to 10 −2 Hz) on experimental spectra of LF current fluctuations in a metal thermionic cathodes.