Possibilities of Preparing Pupils for Proof Problems of Synthetic Plane Geometry Solvable by Deductive Methods

Proof problems, especially the ones of the synthetic plane geometry solvable by deductive methods, play a significant role in mathematical education and due to their demanding principle also in the above-standard education including mathematical competitions. Therefore, the issue of preparing pupils for solving the proof problems is very important. This study aimed to find out if the contemporary state of the system of pupils’ preparation for synthetic plane geometry proof problems is sufficient enough for the mentioned purpose. From the full set of schools of the Czech Republic, there were 14 schools identified as the successful ones based on the results of the national round of the Mathematical Olympiad. These schools were asked questions about literature used for pupils’ preparation and the publications named in the answers were then deeply inspected. The results showed a narrow range of the literature used by the schools and the didactic-methodical inspection of stated literature detected considerable space for improvements which led the author to the main theme of his dissertation.

Visualization In Mathematics Teaching

In recent years, there has been an increased use of information and communication technologies and mathematical software in mathematics teaching. Numerous studies of the effectiveness of mathematical learning have shown the justification and usefulness of the implementation of new teaching aids. They also showed that learning with educational software has a great impact on students' achievement in the overall acquisition of mathematical knowledge during the school year as well as in the final exam at the end of primary education. Teaching realized by using computers and software packages is interesting for students, increases their interest and active participation. It is indisputable that the use of computers and mathematical software has great benefits that have been proven and presented in their works by many researchers of effective learning. It is also indisputable that one of the main tasks of teaching mathematics is to develop constructive thinking of students. Visualization and representation of mathematical laws are of great importance in the realization of mathematics teaching. They should be applied everywhere and whenever possible.

New Iterative Method with Application

In this paper, we consider iterative methods to find a simple root of a nonlinear equation f(x) = 0, where f : D∈R→R for an open interval D is a scalar function.

Second Order Partial Derivatives

The rules for calculating partial derivatives and differentials are the same as for calculating the derivative of a function of one variable, except that when finding partial derivatives per one variable, the other variables are considered as constants

Results on a faster iterative scheme for a generalized monotone asymptotically

This article devoted to present results on convergence of Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically αn-nonexpansive mapping (shortly, ma αn-n mapping) in partial ordered Banach space (shortly, POB space). Which are auxiliary theorem for demi-close's proof of this type of mappings, weakly convergence of increasing FFH-scheme to a fixed point with aid monotony of a norm and Σn+=∞1 λn= +∞, λn =min{hn , (1-hn)} where hn ⸦ (0,1) where is associated with FH-scheme for an integer n>0 more than that, convergence amounts to be strong by using Kadec-Klee property and finally, prove that this scheme is weak-w2 stable up on suitable status.

New types of almost contact metric submersions

We introduce the concept of conjugaison in contact geometry. This concept allows to define new structures which are used as base space of a Riemannian submersion. With these new structures, we study new three types of almost contact metric submersions.

Metallic Ratios in Primitive Pythagorean Triples : Metallic Means embedded in Pythagorean Triangles and other Right Triangles

The Primitive Pythagorean Triples are found to be the purest expressions of various Metallic Ratios. Each Metallic Mean is epitomized by one particular Pythagorean Triangle. Also, the Right Angled Triangles are found to be more “Metallic” than the Pentagons, Octagons or any other (n2+4)gons. The Primitive Pythagorean Triples, not the regular polygons, are the prototypical forms of all Metallic Means.

A survey of topics related to Functional Analysis and Applied Sciences

This survey is the result of investigations suggested by recent publications on functional analysis and applied sciences. It contains short accounts of the above theories not usually combined in a single document and completes the work of D. Huet 2017. The main topics which are dealt with involve spectrum and pseudospectra of partial differential equations, Steklov eigenproblems, harmonic Bergman spaces, rotation number and homeomorphisms of the circle, spectral flow, homogenization. Applications to different types of natural sciences such as echosystems, biology, elasticity, electromagnetisme, quantum mechanics, are also presented. It aims to be a useful tool for advanced students in mathematics and applied sciences.

Heat Dissipation Performance of Micro-channel Heat Sink with Various Protrusion Designs

This research will focus on studying the effect of aperture size and shape of the micro-channel heat sink on heat dissipation performance for chip cooling. The micro-channel heat sink is considered to be a porous medium with fluid subject inter-facial convection. Derivation based on energy equation gives a set of governing partial differential equations describing the heat transfer through the micro-channels. Numerical simulation, including steady-state thermal analysis based on CFD software, is used to create a finite element solver to tackle the derived partial differential equations with properly defined boundary conditions related to temperature. After simulating three types of heat sinks with various protrusion designs including micro-channels fins, curly micro-channels fins, and Micro-pin fins, the result shows that the heat sink with the maximum contact area per unit volume will have the best heat dissipation performance, we will interpret the result by using the volume averaging theorem on the porous medium model of the heat sink.

PDE boundary conditions that eliminate quantum weirdness: a mathematical game inspired by Kurt Gödel and Alan Turing

Although boundary condition problems in quantum mathematics (QM) are well known, no one ever used boundary conditions technology to abolish quantum weirdness. We employ boundary conditions to build a mathematical game that is fun to learn, and by using it you will discover that quantum weirdness evaporates and vanishes. Our clever game is so designed that you can solve the boundary condition problems for a single point if-and-only-if you also solve the “weirdness” problem for all of quantum mathematics. Our approach differs radically from Dirichlet, Neumann, Robin, or Wolfram Alpha. We define domain Ω in one-dimension, on which a partial differential equation (PDE) is defined. Point α on ∂Ω is the location of a boundary condition game that involves an off-center bi-directional wave solution called Æ, an “elementary wave.” Study of this unusual, complex wave is called the Theory of Elementary Waves (TEW). We are inspired by Kurt Gödel and Alan Turing who built mathematical games that demonstrated that axiomatization of all mathematics was impossible. In our machine quantum weirdness vanishes if understood from the perspective of a single point α, because that pinpoint teaches us that nature is organized differently than we expect.