I think this paragraph in particular should be explained to all introductory students in any STEM-related field. It sets the stage for a basic yet profound unde

I think this paragraph in particular should be explained to all introductory students in any STEM-related field. It sets the stage for a basic yet profound understanding of what mathematics is all about: > "To discuss this subject we start in the middle. We suppose that we already know what integers are, what zero is, and what it means to increase a number by one unit. You may say, “That is not in the middle!” But it is the middle from a mathematical standpoint, because we could go even further back and describe the theory of sets in order to derive some of these properties of integers. But we are not going in that direction, the direction of mathematical philosophy and mathematical logic, but rather in the other direction, from the assumption that we know what integers are and we know how to count." Beyond that, an understanding of algebraic concepts in terms of how equations can be manipulated from one form to another (and of the rationale for why one can) might benefit from the addition of the concepts of distribution and commutation, which are not included in this lecture (although the important basic idea of a successor is).