algebra summary

Understand the purpose and structure of algebra

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Below is the article summary. For the full article, see algebra.

mathematicians of the Greco-Roman world
This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).

algebra, Generalized version of arithmetic that uses variables to stand for unspecified numbers. Its purpose is to solve algebraic equations or systems of equations. Examples of such solutions are the quadratic formula (for solving a quadratic equation) and Gaussian elimination (for solving a system of equations in matrix form). In higher mathematics, an “algebra” is a structure consisting of a class of objects and a set of rules (analogous to addition and multiplication) for combining them. Basic and higher algebraic structures share two essential characteristics: (1) calculations involve a finite number of steps and (2) calculations involve abstract symbols (usually letters) representing more general objects (usually numbers). Higher algebra (also known as modern or abstract algebra) includes all of elementary algebra, as well as group theory, theory of rings, field theory, manifolds, and vector spaces.

Omar Khayyam Summary

Omar Khayyam was a Persian mathematician, astronomer, and poet, renowned in his own country and time for his scientific achievements but chiefly known to English-speaking readers through the translation of a collection of his robāʿīyāt (“quatrains”) in The Rubáiyát of Omar Khayyám (1859), by the

Euclid Summary

Euclid was the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements. Of Euclid’s life nothing is known except what the Greek philosopher Proclus (c. 410–485 ce) reports in his “summary” of famous Greek mathematicians. According to him, Euclid

vector parallelogram for addition and subtraction

linear algebra Summary

Linear algebra, mathematical discipline that deals with vectors and matrices and, more generally, with vector spaces and linear transformations. Unlike other parts of mathematics that are frequently invigorated by new ideas and unsolved problems, linear algebra is very well understood. Its value

John von Neumann Summary

John von Neumann Hungarian-born American mathematician. As an adult, he appended von to his surname; the hereditary title had been granted his father in 1913. Von Neumann grew from child prodigy to one of the world’s foremost mathematicians by his mid-twenties. Important work in set theory