Algebra is a more general form of arithmetic that uses symbols (often letters) in place of (some) numbers. The symbols can represent any number, so the results are more general. Here is an example of arithmetic generalised to algebra: 5 + 3 is the same as 3 + 5. Both equal eight. We can see that if we alternate the order of the numbers in additions like this, we will not change the answer. Algebra lets us say this general rule symbolically: (a + b) = (b + a) Which means that any number (a) added to any other number (b) will have the same sum as the other number (b) added to the original number (a). Algebra as detection Algebra is the detective department of mathematics. With algebra we use symbols to mark the parts of the situation we do not know and then see if we can find them out by treating things we do know as the clues. The symbol we use just means "something we do not know". So 2x = y means "two of something we do not know that we will call x equals one of another thing that we do not know that we will call y". Like detectives drawing the possibilities on a flipchart, we can make a diagram of the possible solutions in the form of a graph. We solve the problem when we find out what x or y is. If we find out one, it tells us the other. Thought forms like algebra Using symbols for unknown quantities is a very useful technique. For example, it is used in computing to find files or words or numbers where only part of the name is known. Here the parts we know are called literal characters and the ones we do not know are called wildcards or metacharacters. A combination of literals and wildcards is called a regular expression. An example of a wildcard is the asterisk (*). If you search for *.exe on a computer you will get a list of all the files with the extension exe, whatever the first part of the name. Analysis Analysis in mathematics can refer to
the (related) part of mathematics that includes functions and calculus, or to "x is a function of y" means you should be able to work out x if you know what y is (or y if you know what x is) and what the equation is that relates them "x is a function of y and z" means you should be able to work out x if you know what y and z are and what the equation is that relates them. "x = 2yz" is an equation relating x, y and z.
"insanity is a function of
two variables" (Charles Mercier 1890)
Calculus is a method of finding rates of change by adding up very small differences in changing variables. External Links: wikipedia Calculus: an introduction Calculus: Introduction to Differentiation Differential and Integral Calculus See Expression, Variable, Equation Equation In mathematics, an equation is a statement that two amounts or values are equal. Two very simple equations are:
y = 10
Expression An expression usually refers to an algebraic expression, which is a combination of symbols which stands for numbers and for operations with them. 2a + 3b is an algebraic expression. Because it has two terms (2a and 3b) it is called a binomial expression.
Variable  Something that changes
We use variables in
algebra,
in
statistics,
and in
experiments.
In algebra we also use general expressions, like a, b, x, where the symbol represents a number that varies. In algebra, a variable is a symbol used to represent any number. For example, in this equation: 2(x+y) = 2x + 2y
x and y are variables (general expressions) that represent any number,
whereas the definite number 2 is called a constant because it stays
the same.
Statistical variables are contrasted with
attributes, which are
qualitative (nonnumerical) descriptions like a person's gender or
class.
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