Abstract
Big data play an indispensable role not only in the cognitive mechanisms of human sensation, quantification, qualification, estimation, memory, and reasoning, but also in a wide range of engineering applications. A basic study on the theoretical foundations of big data science is presented with a coherent set of general principles and analytic methodologies for big data systems. Cognitive foundations of big data are explored in order to formally explain the origination and nature of big data. A set of mathematical models of big data are created that rigorously elicit the general essences and patterns of big data across pervasive domains in sciences, engineering, and societies. A significant finding towards big data science is that big data systems in nature are a recursive [Formula: see text]-dimensional-typed hyperstructure (RNTHS) rather than pure numbers. The fundamental topological property of big data reveals a set of denotational mathematical solutions for dealing with inherited complexities and unprecedented challenges in big data engineering.
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