Difference between revisions of "Algebra"
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By using unknowns, algebra can go beyond individual number facts and express general relationships between ''sets'' of numbers. Thus, the equation above represents ''every pair'' of numbers that add up to 11: | By using unknowns, algebra can go beyond individual number facts and express general relationships between ''sets'' of numbers. Thus, the equation above represents ''every pair'' of numbers that add up to 11: | ||
| − | *x could be 4 and y could be 7 | + | *x could be 4 and y could be 7, |
| − | *x could be 5 and y could be 6 | + | *x could be 5 and y could be 6, |
*x could be 10 and y could be 1. | *x could be 10 and y could be 1. | ||
| − | There are 12 such pairs of | + | There are 12 such pairs of non-negative integers, but an infinite number of solutions to this equation. |
==Notes and references== | ==Notes and references== | ||
Revision as of 01:11, December 25, 2009
Algebra is a major branch of mathematics that analyzes the relationships between quantities or items. In higher math the principal fields of algebra are linear algebra, which focuses on matrices, and group theory.[1]
Basic Algebra
Algebra is a generalization of arithmetic in which letters stand for numbers in order to accomplish this purpose. Ordinary arithmetic deals with specific numbers, treated individually: 4 + 7 = 11.
Algebra generalizes these operations by using variables or letters instead of specific numbers. These letters are called unknowns. For example,
- x + y = 11
By using unknowns, algebra can go beyond individual number facts and express general relationships between sets of numbers. Thus, the equation above represents every pair of numbers that add up to 11:
- x could be 4 and y could be 7,
- x could be 5 and y could be 6,
- x could be 10 and y could be 1.
There are 12 such pairs of non-negative integers, but an infinite number of solutions to this equation.
Notes and references
- ↑ The name algebra comes from the Arabic word al jebr, which means reduction or "reunion of broken parts" Algebra as mentioned in a book Hisab al-jabr w'al-muqabala translated as Science of the Reunion and the Opposition. This text was written in in about 830 AD by Mohammad ibn-Musa al-Khwarizmi of Baghdad. See the Biography of Al-Khwarizmi
