Related papers: Mathematical analysis without gaps
Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some theorems. These are slightly enhanced preparation notes for a talk given at the joint AMS meeting of January 16, 2014 in…
The aim of this book is to give a rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of the Stochastic Calculus of Variations of…
The analytical description of charts is an exciting and important research area with many applications in academia and industry. Yet, this challenging task has received limited attention from the computational linguistics research…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
Static analysis by abstract interpretation is generally designed to be "sound", that is, it should not claim to establish properties that do not hold-in other words, not provide "false negatives" about possible bugs. A rarer requirement is…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…
This is a survey on the geometry of warped products, without, or essentially with only soft, calculation. Somewhere in the paper, the goal was to give a synthetic account since existing approaches are rather analytic. Somewhere else, we…
The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
Here I introduce basic methods of qualitative analysis of differential equations used in mathematical biology for people with minimal mathematical background.
We propose a method for filling arbitrarily wide gaps in deterministic time series. Crucial to the method is the ability to apply Takens' theorem in order to reconstruct the dynamics underlying the time series. We introduce a functional to…
A very simple interpretation of matrix completion problem is introduced based on statistical models. Combined with the well-known results from missing data analysis, such interpretation indicates that matrix completion is still a valid and…
A high-quality content analysis is essential for retrieval functionalities but the manual extraction of key phrases and classification is expensive. Natural language processing provides a framework to automatize the process. Here, a…
Systematic Literature Reviews aim at investigating current approaches to conclude a research gap or determine a futuristic approach. They represent a significant part of a research activity, from which new concepts stem. However, with the…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
This Paper summarises the operation of software developed for the analysis of workbook structure. This comprises: the identification of layout in terms of filled areas formed into "Stripes", the identification of all the Formula…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
Marketing analytics is a diverse field, with both academic researchers and practitioners coming from a range of backgrounds including marketing, expert systems, statistics, and operations research. This paper provides an integrative review…