BASIC ARITHMETIC
What is arithmetic?
Arithmetic is a branch of mathematics that deals with numerical computation; specifi-
cally, it includes computation using integers, rational numbers, real numbers, or
complex numbers. The word “arithmetic” has its roots in the Greek word for “to
count” (arithmeein;also arithmos,or “number”).
Arithmetic contains all the rules for combining two or more numbers. In most cases,
when mathematicians talk about elementary arithmetic, they are speaking of those sub-
jects most of us learned in grade school: addition, subtraction, multiplication, and divi-
sion being the most common; and fractions, geometry and measurements, ratios and
proportion, simple probabilities, and algebra examined in more advanced levels. For even
more advanced students, such arithmetic lessons as congruence calculation, root extrac-
tion, power computations, and advanced factorizations are often presented.
Are there more advanced conceptsin arithmetic?
Yes, arithmetic can even be more advanced than the ideas mentioned above. For exam-
ple, higher arithmetic is the archaic term for number theory,which is the study of the
properties of integers, or whole numbers (0, ± 1, ± 2 ...). It can include anything from
simpler arithmetic concepts to the more complex, such as diophantine equations (for
more information about these equations, see “Algebra”), prime numbers (see below),
and functions such as the Riemann hypothesis (for more about Friedrich Bernhard Rie-
mann, see “History of Mathematics” and “Geometry and Trigonometry”).
There are other more advanced ideas in arithmetic, too. For example, modular
arithmeticis known as the arithmetic of congruences (see below). The model theory 67
MATH BASICS