### 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)