Ebook: Algebraic Foundations for Applied Topology and Data Analysis

How to reveal, characterize, and exploit the structure in data? Meeting this central
challenge of modern data science requires the development of new mathematical approaches to data analysis, going beyond traditional statistical methods.
Fruitful mathematical methods can originate in geometry, topology, algebra, analysis, stochastics, combinatorics, or indeed virtually any field of mathematics.
Confronting the challenge of structure in data is already leading to productive
new interactions among mathematics, statistics, and computer science, notably in
machine learning. We invite novel contributions (research monographs, advanced
textbooks, and lecture notes) presenting substantial mathematics that is relevant
for data science. Since the methods required to understand data depend on the
source and type of the data, we very much welcome contributions comprising
significant discussions of the problems presented by particular applications. We
also encourage the use of online resources for exercises, software and data sets.
Contributions from all mathematical communities that analyze structures in data
are welcome. Examples of potential topics include optimization, topological data
analysis, compressed sensing, algebraic statistics, information geometry, manifold
learning, tensor decomposition, support vector machines, neural networks, and
many more.