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Full-Text Articles in Other Mathematics
Introduction To Computational Topology Using Simplicial Persistent Homology, Jason Turner, Brenda Johnson, Ellen Gasparovic
Introduction To Computational Topology Using Simplicial Persistent Homology, Jason Turner, Brenda Johnson, Ellen Gasparovic
Honors Theses
The human mind has a natural talent for finding patterns and shapes in nature where there are none, such as constellations among the stars. Persistent homology serves as a mathematical tool for accomplishing the same task in a more formal setting, taking in a cloud of individual points and assembling them into a coherent continuous image. We present an introduction to computational topology as well as persistent homology, and use them to analyze configurations of BuckyBalls®, small magnetic balls commonly used as desk toys.
On Spectral Theorem, Muyuan Zhang
On Spectral Theorem, Muyuan Zhang
Honors Theses
There are many instances where the theory of eigenvalues and eigenvectors has its applications. However, Matrix theory, which usually deals with vector spaces with finite dimensions, also has its constraints. Spectral theory, on the other hand, generalizes the ideas of eigenvalues and eigenvectors and applies them to vector spaces with arbitrary dimensions. In the following chapters, we will learn the basics of spectral theory and in particular, we will focus on one of the most important theorems in spectral theory, namely the spectral theorem. There are many different formulations of the spectral theorem and they convey the "same" idea. In …