[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588671-105":59,"doc-detail-588671-en":129},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":122,"head_meta":124,"extra_data":126,"updated_unix":128},105,"en","the-math-open-source-application-for-easier-learning-of-numerical-mathematics-abstract","THE MATH - OPEN SOURCE APPLICATION FOR EASIER LEARNING OF NUMERICAL MATHEMATICS - Abstract","","The article presents THE MATH, an open-source software application designed to support learning of Applied Mathematics with a focus on Numerical Mathematics. It provides an easy-to-use graphical user interface and integrated plotting for visual representation of numerical results. THE MATH supports step-by-step solutions to help students understand methods, and it enables speed and precision comparison. 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The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt library and other 3rd party libraries. The MATH is a convenient tool for use in education process, thanks to its capability of showing step-by-step solutions for better understanding of the whole process for both undergraduate and graduate students. It enables also speed and precision comparison for various similar methods. The main goal of this application was to support student learning process and after all, speed up the learning curve.  \nKey words: Numerical Methods, Step-by-Step Solutions, Qt, LMS Approximation, Error Estimation  \n1. Introduction  \nNumerical analysis is a subject of extreme interest to mathematicians, computer scientists and engineers who could profit from the mentioned application. In the process of learning the mathematics and especially in the case of undergraduates, understanding the basics of numerical mathematics plays the key role. In order to be able to choose the best suited numerical method, one has to be aware of how those various numerical methods work, their advantages and disadvantages in a form of a calculation speed, precision and complexity.  \nThere are several open source and web-based application with similar capabilities (that the author are aware of), but they are usually not designed for understanding the very basics of various numerical methods, which are very important and so not very well suited for education process.  \n2. Motivation  \nFor engineers and scientists, there is often a question which method will work the best, is the most accurate, the fastest, etc. To be able to correctly decide, there is important to know the basis and the core of all those methods that are available to use. As the application is designed mainly for educational purposes, to achieve this goal, the application was designed to show not only results, but also partial results and solutions. This step-by-step approach is important for understanding how these methods work and realize all important steps. The MATH connects the ability to solve numerical problems and visualize it with a few simple steps.  \nTo summarize, the MATH application is designed to achieve several goals:  \n􀀐 Provide all calculation steps for each numerical method with easy to use graphical interface.  \n􀀐 Enable graphical visualization of calculated data as well as the option of exporting acquired data and graphs in suitable formats.  \n3. The Software architecture and design  \nThe MATH application covers all methods needed by students for their further specialized studies. It provides so far these numerical methods for calculation and comparison [9][10] [11][12][13]:  \n1) Nonlinear equation  \n􀀐 Bisection method  \n􀀐 Regula Falsi method  \n􀀐 Secant method  \n􀀐 Newton method  \n􀀐 Iteration method  \n2) Definite integration  \n􀀐 Rectangular method  \n􀀐 Trapezoid method  \n􀀐 Simpson’s method  \n􀀐 Monte Carlo Hit of Miss method  \n􀀐 Monte Carlo Average method  \n3) Double definite integration (Monte Carlo method)  \n4) Numerical differentiation (up to 4. degree of differentiation)  \n5) System of linear equations  \n􀀐 Jacobi Iteration method  \n6) Matrix calculation (basic numerical operations, transpose, inverse, etc.)  \n7) The least mean square approximation (LMS)  \nThe MATH application can be extended by additional Numerical methods since it is open source. The MATH is used as an education tool on several faculties of Technical University of Kosice. There are still many numerical methods and graphical capabilities to be implemented in the close future.  \nThe MATH is designed in ","cbCaieM9DGcoyERy","https://ap.wps.com/l/cbCaieM9DGcoyERy","pdf",606293,"English","# Introduction\n# Motivation\n# The Software architecture and design\n## Nonlinear equation\n## Definite integration\n## Double definite integration\n## Numerical differentiation\n## System of linear equations\n## Matrix calculation\n## The least mean square approximation (LMS)","[{\"question\":\"What is THE MATH and what learning goal does it serve?\",\"answer\":\"THE MATH is an open-source application supporting education in Applied Mathematics with a focus on Numerical Mathematics. Its goal is to improve understanding and speed up the learning process through guided numerical method solutions.\"},{\"question\":\"How does THE MATH help users understand numerical methods?\",\"answer\":\"THE MATH provides step-by-step solutions and shows partial results, which clarifies how different numerical methods work. It also supports visualization to connect solving with graphical interpretation.\"},{\"question\":\"Which types of numerical methods are included in THE MATH?\",\"answer\":\"The application includes methods such as bisection, regula falsi, secant, and Newton for nonlinear equations; rectangular, trapezoid, Simpson’s, and Monte Carlo variants for integration; numerical differentiation; systems of linear equations; matrix operations; and LMS approximation.\"}]","THE MATH - OPEN SOURCE APPLICATION FOR EASIER LEARNING OF NUMERICAL MATHEMATICS - Abstract | PDF",15]