FOUNDATIONS

A sampling of current systems engineering foundational topics supporting systems engineering as taught in some academic programs includes decision theory, operations research, risk analysis, information theory, probability theory, control theory, complexity theory, systems theory, network theory, and the rapidly maturing field of uncertainty quantification and systems thinking.(1)

Practicing systems engineers use a variety of analytical tools that are based on math and science. This requires competencies in the foundational math and science that is needed to analyze the systems of interest, and the enabling systems used to manufacture and support the systems. The systems engineer also must understand how to use probability and statistics to understand risk and uncertainty, and understand principles such as coupling and cohesion to manage systems complexity. For cyber-physical systems, a systems engineer of today must also have a basic understanding of control theory and communications. 

 (1.) https://en.wikipedia.org/wiki/Uncertainty_quantification

In addition to its math and science analytical foundations, systems engineering has evolved processes and procedures learned over decades of experience with large scale systems. These include systems engineering practices and heuristics captured in standards, handbooks, and guidelines. These knowledge repositories and standards have added to the foundations of systems engineering practice in recent years.

Given the breadth of mathematics, and the physical and social sciences needed to support systems engineering, there is an effort underway to describe how these different foundations can be abstracted and integrated into the theoretical foundations for systems engineering. These foundations can be more uniformly taught as part of a common systems engineering curriculum.