Difference Between Math and Arithmetic

Date: 11/06/2001 at 21:57:04
From: Vicki Kehoe
Subject: Difference between math and arithmetic

My students haven't heard the word arithmetic. No one seems to be able 
to tell the difference, if there is one, between arithmetic and 
mathematics. Is there a difference, and what is it?  

Date: 11/07/2001 at 08:53:42
From: Doctor Peterson
Subject: Re: Difference between math and arithmetic

Hi, Vicki.

Arithmetic is just one branch of mathematics, namely that involving 
basic techniques of calculation with numbers. When you add, subtract, 
multiply, divide, take square roots, and so on, you are doing 
arithmetic. When you solve an equation you are doing algebra. When you 
determine relations between shapes or find their area, you are doing 
geometry (though the latter calculation will be done by applying 
arithmetic to the geometric formulas). Most of what young children 
learn in math is arithmetic.

Here are some definitions of mathematics from the Dr. Math archives, 
to show how much bigger it is than arithmetic:

   What is Mathematics?
   http://mathforum.org/dr.math/problems/erum.09.22.00.html   

   What is Math?
   http://mathforum.org/dr.math/problems/rob.09.14.01.html   

Also, did you try a dictionary? Although lexicographers do not 
always get the details of mathematical terms right, they are experts 
at identifying nuances of meaning. According to Merriam-Webster 
(m-w.com), arithmetic is

    a branch of mathematics that deals usually with the nonnegative
    real numbers including sometimes the transfinite cardinals and
    with the application of the operations of addition, subtraction,
    multiplication, and division to them 

while mathematics is

    the science of numbers and their operations, interrelations,
    combinations, generalizations, and abstractions and of space
    configurations and their structure, measurement, transformations,
    and generalizations

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/