College Math Resources - Topics in Precalculus

The Real Number System

Most of the mathematics studied in high school and college has to do with the Real Numbers. These were invented to give us a way of describing and calculating with physical measurements such as length, time, temperature, etc., and so they are essential for most practical applications of mathematics.

An important point is that the real numbers correspond to all possible measurements along a linear scale and so include not just whole number positions but also others in between (so they can be represented graphically on a "Number Line").

For calculus, you will need both a good facility with basic algebraic operations and also an understanding of how to deal with the concepts of ordering and distance in terms of inequalities and absolute value.

There are a number of other web sites that offer further explanation and practice with these basic concepts.

Most introductory calculus courses assume an intuitive understanding of the number system and do not go into a rigorous analysis or justification of its properties. But an important aspect of mathematics is the fact that its results are logically provable from more "elementary" assumptions. Where not adressed in first year calculus, these issues are often introduced in an Introductory Analysis course at the second year level. There are several other sites with on-line analysis course materials)