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Assessing student teachers' skills in posing mathematical reasoning problems within their experiences in teacher education is essential due to the increasing challenges for them to prepare for 21st-century learning. This study aims at investigating the quality of mathematical reasoning problems posed by student teachers. As many as 34 student teachers who attended an assessment lecture posed mathematical problems, where the three aspects; suitability of indicators with problems posed, the plausibility of the solution, the correctness of the solution, and language readability were used to assess the problems posed. Results indicate that more than 70% of the student-teacher participants were successful in posing reasoning problems - either objective or subjective questions - indicated by those which are in accordance with the established criteria although most of the posed problems are categorized as \"analyze\" problem, instead of \"evaluate\" or \"create\" problem. (DIPF/Orig.)

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology* New perspectives on classic problems* Representative surveys of research groups from all around the world

Mathematical Miniatures is a problem collection of arresting mathematical insight and ingenuity. The authors brought together materials from mathematical competitions, books, research papers, discussions, and their own work. Such mathematical substance went far beyond the purposes of a traditional problem-solving book. The most attractive results refused to fit into the schemes of an instruction manual meant to exemplify typical problem solving techniques. A broader interpretation of these problems had to be identified, and this book is the fruit of that effort.

Almost everyone is acquainted with plane Euclidean geometry as it is usually taught in high school. This book introduces the reader to a completely different way of looking at familiar geometrical facts. It is concerned with transformations of the plane that do not alter the shapes and sizes of geometric figures. Such transformations play a fundamental role in the group theoretic approach to geometry. The treatment is direct and simple. The reader is introduced to new ideas and then is urged to solve problems using these ideas. The problems form an essential part of this book and the solutions are given in detail in the second half of the book.

If you have ever wondered how the laws of nature were worked out mathematically, this is the book for you. Above all, it captures some of Pólya's excitement and vision.

This study proposes a bald eagle search (BES) algorithm, which is a novel, nature-inspired meta-heuristic optimisation algorithm that mimics the hunting strategy or intelligent social behaviour of bald eagles as they search for fish. Hunting by BES is divided into three stages. In the first stage (selecting space), an eagle selects the space with the most number of prey. In the second stage (searching in space), the eagle moves inside the selected space to search for prey. In the third stage (swooping), the eagle swings from the best position identified in the second stage and determines the best point to hunt. Swooping starts from the best point and all other movements are directed towards this point. BES is tested by adopting a three-part evaluation methodology that (1) describes the benchmarking of the optimisation problem to evaluate the algorithm performance, (2) compares the algorithm performance with that of other intelligent computation techniques and parameter settings and (3) evaluates the algorithm based on mean, standard deviation, best point and Wilcoxon signed-rank test statistic of the function values. Optimisation results and discussion confirm that the BES algorithm competes well with advanced meta-heuristic algorithms and conventional methods.

In the era of healthcare, and its related research fields, the dimensionality problem of high dimensional data is a massive challenge as it contains a huge number of variables forming complex data matrices. The demand for dimension reduction of complex data is growing immensely to improvise data prediction, analysis and visualization. In general, dimension reduction techniques are defined as a compression of dataset from higher dimensional matrix to lower dimensional matrix. Several computational techniques have been implemented for data dimension reduction, which is further segregated into two categories such as feature extraction and feature selection. In this review, a detailed investigation of various feature extraction and feature selection methods has been carried out with a systematic comparison of several dimension reduction techniques for the analysis of high dimensional data and to overcome the problem of data loss. Then, some case studies are also cited to verify the better approach for data dimension reduction by considering few advances described in the technical literature. This review paper may guide researchers to choose the most effective method for satisfactory analysis of high dimensional data.

Facility layout problem (FLP) is defined as the placement of facilities in a plant area, with the aim of determining the most effective arrangement in accordance with some criteria or objectives under certain constraints, such as shape, size, orientation, and pick-up/drop-off point of the facilities. It has been over six decades since Koopmans and Beckmann published their seminal paper on modeling the FLP. Since then, there have been improvements to these researchers’ original quadratic assignment problem. However, research on many aspects of the FLP is still in its initial stage; hence, the issue is an interesting field to work on. Here, a review of literature is made by referring to numerous papers about FLPs. The study is mainly motivated by the current and prospective trends of research on such points as layout evolution, workshop characteristics, problem formulation, and solution methodologies. It points to gaps in the literature and suggests promising directions for future research on FLP.

Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first passage time, is an active area of research relevant to many disciplines. Exact results for the mean first passage time for diffusion on simple geometries, such as lines, discs and spheres, are well-known. In contrast, computational methods are often used to study the first passage time for diffusion on more realistic geometries where closed-form solutions of the governing elliptic boundary value problem are not available. Here, we develop a perturbation solution to calculate the mean first passage time on irregular domains formed by perturbing the boundary of a disc or an ellipse. Classical perturbation expansion solutions are then constructed using the exact solutions available on a disc and an ellipse. We apply the perturbation solutions to compute the mean first exit time on two naturally-occurring irregular domains: a map of Tasmania, an island state of Australia, and a map of Taiwan. Comparing the perturbation solutions with numerical solutions of the elliptic boundary value problem on these irregular domains confirms that we obtain a very accurate solution with a few terms in the series only. MATLAB software to implement all calculations is available at https://github.com/ProfMJSimpson/Exit_time .