# Articles — Math

Articles tagged Math

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Building new topological spaces through canonical maps
Suppose we have some topological spaces lying around. How can we build new topological spaces using the old ones? There are four fundamental constructions: subspaces, disjoint unions, products, and quotients. Defining the topologies on each can be done in two ways. One way is through ad hoc definitions. These definitions make some intuitive sense, but look very different from one construction to the next. The other way uses canonical maps. Canonical maps provide a single framework in which all constructions obey the same unifying principle.
Sean Raleigh
FSU-MATH2300-Project3
This is a project to develop students' understanding of Newton's Method using the tools available in Geogebra. This project was adapted from a similar project developed by folks at Grand Valley State University. (If any of you see this and would like more specific attributions, please let me know.)
Sarah Wright
TALLER ALGEBRA LINEAL ISAAC RODRIGUEZ
Taller álgebra lineal
Isaac Rodriguez Escallon
Cp1 :2005
Primeiras questões respondidas do banco de Cálculo 1 da UFAL.
Antônio Marcos Barbosa
The domain of a composite function
A short look at how to compute the domain of a composite function.
Aidan Horn
An application of the Ncut algorithm, with an open-source implementation (in the R environment).
Although the analysis of data is a task that has gained the interest of the statistical community in recent years and whose familiarity with the statistical computing environment, they encourage the current statistical community (to students and teachers of the area) to complete statistical analysis reproducible by means of the tool R. However for years there has been a gap between the calculation of matrices on a large scale and the term "big data", in this work the Normalized Cut algorithm for images is applied. Despite the expected, the R environment to do image analysis is poorly, in comparison with other computing platforms such as the Python language or with specialized software such as OpenCV. Being well known the absence of such function, in this work we share an implementation of the Normalized Cut algorithm in the R environment with extensions to programs and processes performed in C ++, to provide the user with a friendly interface in R to segment images. The article concludes by evaluating the current implementation and looking for ways to generalize the implementation for a large scale context and reuse the developed code. Key words: Normaliced Cut, image segmentation, Lanczos algorithm, eigenvalues and eigenvectors, graphs, similarity matrix, R (the statistical computing environment), open source, large scale and big data.
José Antonio garcia