Archive for November, 2011  What is algebra?  We hear a lot
about the importance that all children master algebra before
they graduate from high school. But what exactly is algebra, and
is it really as important as everyone claims? And why do so many
people find it hard to learn?  Answering these questions turns
out to be a lot easier than, well, answering a typical school
algebra question, yet surprisingly, few people can give good
answers.  First of all, algebra is not “arithmetic with
letters.” At the most fundamental level, arithmetic and algebra
are two different forms of thinking about numerical issues. (I
should stress that in this article I’m focusing on school
arithmetic and school algebra. Professional mathematicians use
both terms to mean something far more general.)  Let’s start
with arithmetic. This is essentially the use of the four
numerical operations addition, subtraction, multiplication, and
division to calculate numerical values of various things. It is
the oldest part of mathematics, havin