The term `sequence' is so familiar from daily life that it is easy to dismiss the need for a precise mathematical definition. In this lecture we start by looking at finite sequences, of a particularly pleasant kind, namely sequences of natural numbers. The distinction between the specification of such a sequence and a description of it is emphasized. We must also maintain some respect for sequences that get large---ultimately they can have qualitatively quite different properties. We also mention N. Sloane's On-line Encyclopedia of Integer Sequences, a valuable resource for mathematically minded people.
Does mathematics make logical sense? No, it does not. Foundational issues have been finessed by modern mathematicians, and this series aims to turn things around. And it will have interesting things to say also about mathematics education---especially at the primary and high school level. The plan is to start right from the beginning, and to define all the really important concepts of basic mathematics without any waffling or appeals to authority. Roughly we discuss first arithmetic, then geometry, then algebra, then analysis, then set theory. This course is aimed for a general audience, interested in mathematics, or willing to learn.