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. Negative numbers are not allowed in algebra because they do not represent countable quantities. For example, suppose the unknowns represent the number of sheep on two different fields. It does not make sense for one field to have 13 sheep and the other to have -2 sheep, because there is no such thing as a negative sheep.
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