The Mathematical Foundations of Science and Engineering

Abstract

The mathematics of scalar quantities in science and engineering has traditionally relied on the real and complex number systems. One theme of this chapter is that, in themselves, those number systems are not powerful enough to represent the algebraic structure that we need when we operate with physically dimensioned quantities. The main points are very simple, and the central proposals are not new in any essential way. I am simply trying to make explicit what many practitioners are already doing. The goal is to elucidate the unstated formal system that lies behind the use of dimensioned scalars. These initial arguments are necessary in order to have an agreed-upon foundation on which to build to more advanced issues of vectors and matrices in the following chapters.

The axiomatic method has many advantages over honest work. —Bertrand Russell