Difference between revisions of "Algebra"
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| − | '''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]].<ref>The name algebra comes from the [[Arabic]] word ''al jebr'', which means reduction or "reunion of broken parts" [http://dictionary.reference.com/browse/algebra 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 [[Muhammad ibn Mūsā al-Khwārizmī| Mohammad ibn-Musa al-Khwarizmi]] of [[Baghdad]]. See the [http://www.sjsu.edu/depts/Museum/alkhwa.html Biography of Al-Khwarizmi]</ref> | + | '''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]].<ref>The name algebra comes from the [[Arabic]] word ''al jebr'', which means reduction or "reunion of broken parts" [http://dictionary.reference.com/browse/algebra 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 [[Muhammad ibn Mūsā al-Khwārizmī| Mohammad ibn-Musa al-Khwarizmi]] of [[Baghdad]]. See the [http://www.sjsu.edu/depts/Museum/alkhwa.html Biography of Al-Khwarizmi]. For this reason, many prominent mathematicians have proposed that "algebra" be renamed "metarithmetic", since it is the abstraction of simple arithmetic. This would rightfully categorize this study as something that has seen the majority of development come from Christian mathematicians.</ref> |
== Basic Algebra == | == Basic Algebra == | ||
Revision as of 17:18, August 12, 2010
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 where both x and y are non-negative integers. If solutions are not restricted to non-negative integers then an infinite number of solutions to this equation exist.
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. For this reason, many prominent mathematicians have proposed that "algebra" be renamed "metarithmetic", since it is the abstraction of simple arithmetic. This would rightfully categorize this study as something that has seen the majority of development come from Christian mathematicians.