Basic researches of big data science have triggered the emergence of mathematical theories of big data systems. This paper presents a rigorous analytic methodology for big data science and engineering known as Big Data Algebra (BDA). The mathematical models of big data science in BDA are formally elicited from common patterns and essences of a wide variety of big data systems. BDA reveals that any big data system is a Recursively Typed Hyperstructure (RTHS) beyond the traditional domain of pure numbers. It leads to a set of algebraic operators for big data modeling, analysis, and synthesis towards the denotational mathematical structure of BDA. The formal principles and properties of big data and their mathematical manipulations provide a theoretical framework of big data science as the basis for applications in big data engineering.
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