Mathematics is everywhere, and with the rise of big data it becomes a useful tool when extracting information and analysing large datasets. We begin by explaining how maths underpins many of the tools that are used to manage and analyse big data. We show how very different applied problems can have common mathematical aims, and therefore can be addressed using similar mathematical tools. We then introduce three such tools, based on a linear algebra framework: eigenvalues and eigenvectors for ranking graph Laplacian for clustering and singular value decomposition for data compression.

Introduction to key mathematical concepts in big data analytics: eigenvalues and eigenvectors, principal component analysis (PCA), the graph Laplacian, and singular value decomposition (SVD)
Application of eigenvalues and eigenvectors to investigate prototypical problems of ranking big data
Application of the graph Laplacian to investigate prototypical problems of clustering big data
Application of PCA and SVD to investigate prototypical problems of big data compression