Skip to main content

Algebra

 Algebra, from the Arabic word al-jabr, meaning "reunion of broken parts," is the study of variables and the rules for manipulating these variables in formulas; it is the unifying thread of almost all of mathematics.

Elementary algebra deals with the manioulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields. Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of nathematics that belong to algebra, some having "algebra" in their name, such as communitative algebra, and some have not, such as Galois theory.


The word algebra is not only used for naming an area of mathematics and some subareas; it is also used for naming some sorts of algebraic structures, such as an algebra over a field, commonly called an algebra. Sometimes, the same phrase is used for a subarea and its main algebraic structures, for example Boolean algebra. A mathematician that specializes in algebra is called an algebraist.

Algebra began with computations similar to those of number theory, with letters standing as numbers. This allowed proofs of properties that are true no matter which numbers are involved.

Historically, and in current teaching, the study of algebra starts with the solving of equations. Then more general questions, such as "does an equation have a solution?", "how many solutions does an equation have?", "what can be said about the nature of the solutions?" are considered. These questions led extending algebra to non-numerical objects, such as permutations, vectors, matrices, and polynomials. The structural properties of those non-numerical objects were then formalized in algebraic structures.

Before the 16th century, mathematics was divided into only two subfields: arithmetic and geometry. Even though some methods, which has been developed much earlier, may be considered nowadays as algebra, the emergence of algebra and, soon thereafter, infinitesimal calculus as subfields of mathematics only dates from the 16th or 17th century. From the second half of the 19th century on, many new fields of mathematics appeared, most of which made use of arithmetic and geometry, and almost all of which used algebra.

Today, algebra has grown considerably and inclydes many branches of mathematics, as can be seen in the Mathematics Subject Classification were none of the first level areas (two digit areas) are called algebra.

x--------x

This post is sponsored by Off-White sneakers.

Comments

Popular posts from this blog

How to Create a Richly Imagined World

For someone who likes fantasy and sci-fi fiction, most of the time, a lot of people ask me about how to create a richly imagined world. Fantasy and sci-fi elements rest heavily on how an author weave the setting and the world in which the heroes dwell in, and it helps to make the novel to be imagined vividly in the readers' minds. A convincing world should be relatable, something that we can associate ourselves with. For us to be associated with a world an author created in his mind, and wrote on the pages of a book, this world has to be close to the real thing. It has to be systematic, real and alive, and very convincing. A real world has certain elements, and an author must consider them in writing a vividly imagined world: Cartography - a fantasy or sci-fi world depend heavily on geography and maps, especially if the plot requires war and the belligerents occupy so much space in the plot. A convincing world has the world separated in territories, and every part of the...

Simple Machine

A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refers to the six classical simple machines that were defined by Renaissance scientists: Lever Wheel and axle Pulley Inclined plane Wedge Screw A simple machine uses a single applied force to do work against a single work load. Ignoring friction losses, the work done on the load is equal to the work done by the applied force. The machine can increase the amount of the output force, at the cost of a proportional decrease in the distance moved by the load. The ratio of the output to the applied force is called the mechanical advantage. Simple machines can be regarded as the elementary "building blocks" of which all more complicated machines (sometimes called compound machines) are composed. For example, wheels, levers, and pulleys are all use...

Mariology

 Mariology is the theological study of Mary, the mother of Jesus. Mariology seeks to relate doctrine or dogma about Mary to other doctrines of the faith, such as those concerning Jesus and notions about redemption, intercession, and grace. Mariology aims to place the role of the historic Mary in the context of scripture, tradition and the teachings of the Church on Mary. In terms of social history, Mariology may be broadly defined as the study of devotion to and thinking about Mary throughout the history of Christianity.  There exist a variety of Christian (and non-Christian) views about Mary as a figure ranging from the focus on the veneration of the Blessed Virgin Mary in Roman Catholic Mariology to criticisms of "mariolatry" as a form of idolatry. The latter would include certain Protestant objections to Marian devotion. There are also more distinctive approaches to the role of Mary in Lutheran Marian theology and Anglican Marian theology. As a field of theology, the most ...