Reader Reflections: May 2005

2005 ◽  
Vol 98 (9) ◽  
pp. 580-581
Keyword(s):  
Mathematics Teacher ◽  
Arbitrary Number ◽  
Pythagorean Triple

In his letter to “Reader Reflections” (“Get More from Pythagorean Ideas,” Mathematics Teacher, September 2004, p. 68), Ken Sullins gives a way of generating a particular type of Pythagorean triple. While no proof is given, it is easy to see why his method works. I show how this leads to methods for generating other types of triples. Sullins extends his method to quartets and pentads. I show how other types of quartets can be generated. Finally, I show how Sullins's method can be extended to an arbitrary number of terms.

MATHEMATICS TEACHER EDUCATION AND THE FLEXIBLE USE OF TECHNOLOGIES IN DIGITAL AGE

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Hans-Georg Weigand
Keyword(s):  
Teacher Education ◽  
Mathematics Teacher ◽  
Industrial Revolution ◽  
Empirical Studies ◽  
Mathematics Teacher Education ◽  
Digital Technologies ◽  
Digital Age ◽  
Competence Model ◽  
Advantages And Disadvantages ◽  
Concept Representations

Advantages and disadvantages of the use of digital technologies (DT) in mathematics lessons are worldwidedissussed controversially. Many empirical studies show the benefitof the use of DT in classrooms. However, despite of inspiringresults, classroom suggestions, lesson plans and research reports,the use of DT has not succeeded, as many had expected during thelast decades. One reason is or might be that we have not been ableto convince teachers and lecturers at universities of the benefit ofDT in the classrooms in a sufficient way. However, to show thisbenefit has to be a crucial goal in teacher education because it willbe a condition for preparing teachers for industrial revolution 4.0.In the following we suggest a competence model, which classifies– for a special content (like function, equation or derivative) –the relation between levels of understanding (of the concept),representations of DT and different kind of classroom activities.The flesxible use of digital technologies will be seen in relationto this competence model, results of empirical investigations willbe intergrated and examples of the use of technologies in the upcoming digital age will be given.

THE SYSTEM OF INFORMATICS COMPETENCIES FOR THE MATHEMATICS TEACHER

2020 ◽  
pp. 57-72
Author(s):  
Nadiia Ponomareva
Keyword(s):  
Information Technology ◽  
Secondary Education ◽  
Mathematics Teachers ◽  
Mathematics Teacher ◽  
Systems Analysis ◽  
Web Technologies ◽  
Key Competencies ◽  
Teachers Training ◽  
Technology Specialists ◽  
Further Development

As a result of the analysis of domestic and foreign standards of key competencies, basic and complete secondary education, teachers’ training (in particular, mathematics teachers’ training) and information technology specialists training, the system of informatics competencies of a mathematics teacher, developed by Yu. S. Ramskyi, was updated in terms of the structure, content and indicators of competencies formation. It has been found out that the formation of the informatics competencies of a mathematics teacher begins with basic informatics competencies, the further development of which occurs primarily in the competencies in system administration, web technologies, programming and systems analysis.

Kinematic analysis and deformation of a planar lattice with an arbitrary number of panels

2020 ◽  
pp. 15-19
Author(s):  
M.N. Kirsanov
Keyword(s):  
Exact Solution ◽  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Design Parameters ◽  
Lattice Deformation ◽  
Planar Lattice ◽  
Force Loading

Formulae are obtained for calculating the deformations of a statically determinate lattice under the action of two types of loads in its plane, depending on the number of panels located along one side of the lattice. Two options for fixing the lattice are analyzed. Cases of kinematic variability of the structure are found. The distribution of forces in the rods of the lattice is shown. The dependences of the force loading of some rods on the design parameters are obtained. Keywords: truss, lattice, deformation, exact solution, deflection, induction, Maple system. [email protected]

Pengembangan E-modul Berbasis Smartphone Pada Materi Integral Tak Tentu Berorientasi Keterampilan Abad Ke-21

2020 ◽  
Vol 3 (2) ◽  
pp. 222-233
Author(s):  
Veronika Fany Monica Yuniarti ◽  
Nurul Anriani ◽  
Cecep Anwar H. F. Santosa
Keyword(s):  
Research And Development ◽  
21St Century ◽  
Mathematics Teacher ◽  
21St Century Skills ◽  
Research Method ◽  
Effective Medium ◽  
Developmental Research ◽  
High Category ◽  
Research Show

Abstrak: Penelitian ini bertujuan untuk menghasilkan aplikasi e-modul berbasis smartphone pada materi integral tak tentu berorientasi keterampilan abad ke-21 yang valid, praktis, dan efektif. Penelitian menggunakan metode Research and Development (R&D) dari Borg dan Gall yang dimodifikasi menjadi enam langkah. Hasil penelitian menyatakan bahwa hasil skor validasi ahli materi sebesar 4.2 termasuk kategori valid, ahli media diperoleh 3.8 termasuk kategori valid dan guru matematika diperoleh 3.7 termasuk kategori valid. Sedangkan hasil efektivitas diperoleh dari persentase ketuntasan 70% dengan kategori tinggi, dan n-gain sebesar 0,7682 termasuk kategori interpretasi tinggi. Lebih jauh, hasil praktis diperoleh 44.55 jumlah rata-rata skor pernyataan yang termasuk kategori sangat praktis dan 39.80 jumlah rata-rata skor pernyataan yang termasuk kategori praktis. Berdasarkan hasil tersebut maka dapat disimpulkan bahwa pengembangan aplikasi e-modul berbasis smartphone merupakan media yang valid, praktis, dan efektif. Abstract: The research aims to produce a valid, practical, and effective smartphone-based e-module applications 21st-century skills-oriented integral material. The Research method was developmental research (R&D) according to Borg and Gall which was modified into six steps. The results of the research show that the validity of material experts score is 4.2 (valid category), media experts obtained is 3.8 (valid category) and the mathematics teacher score is 3.7 (valid category). While the effectiveness results obtained from the percentage of completeness of 70% with a high category and n-gain of 0.7682 including the high interpretation category. As well as the practical results obtained 44.55 the average number of statements in the very practical category and 39.80 the average number of statements in the practical category. Based on these results it can be concluded that the development of smartphone-based e-module applications is a valid, practical, and effective medium.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Alessandro Torrielli
Keyword(s):  
Spectral Problem ◽  
Transfer Matrix ◽  
Arbitrary Number ◽  
Free Fermion ◽  
Nearest Neighbour ◽  
Bogoliubov Transformation ◽  
Free Fermions ◽  
New Models ◽  
Lower Dimensional

Abstract In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 [36] satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS3, mixed-flux relativistic AdS3 and massless AdS2. We also attack the class of models akin to AdS5 with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.

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