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Home > Algebra

Algebra (from the Arabic "al-jabr" meaning "reunion", "connection" or "completion") is a branch of mathematics which may be roughly characterized as a generalization and extension of arithmetic; it also refers to a particular kind of abstract algebra structure, the algebra over a field.

Algebra may be roughly divided into the following categories:

• elementary algebra, where the properties of operations on the real number system are recorded, symbols are used as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied,
• abstract algebra, where algebraic structures such as groups, rings and as fields are axiomFor the algebra software named Axiom, see Axiom (algebra software). For the 1970s Australian rock music group, see Axiom (band). In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built upatically defined and investigated.
• The specific properties of vector spaceThe fundamental concept in linear algebra is that of a vector space or linear space . This is a generalization of the set of all geometrical vectors and is used throughout modern mathematics. Formal definition A set V is a vector space over a field F (fors are studied in linear algebraLinear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is wi.
• universal algebraUniversal algebra is the field of mathematics that studies the ideas common to all algebraic structures. Basic idea From the point of view of universal algebra, an algebra is a set A together with a collection of operations on A. An n- ary operation on A, where those properties common to all algebraic structures are studied.
• computer algebra, where algorithmFlowcharts were often used to represent algorithms. An algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will result in a corresponding recognisable end-state (contrast with heuristic). Algors for the symbolic manipulation of mathematical objects are collected

1 Forms of algebra

There are many forms of algebraic equations. Some are listed below:

• Linear equations
• Quadratic equations
• Cubic equations
• Exponential equations

1.1 Linear equations

• Y is the answer to the equation.
• M is the co-efficient of the variable, and it represents the slope. The slope is the steepness of the line produced when the equation is graphed
• X is the variable in the equation. The variable is the part that can be changed. When X changes, so does y. When the equation is graphed, the line showes what y is for each value of x.
• B is the number added to the equation. In the expression 2X+3, b=3. B also represents the y intercept on a graph.

The y intercept is where the line crosses the y axis.

1.2 Quadratic equations

When a quadratic equation is graphed, it produces a curved line called a parabola.

• A is the co-efficient of the variable squared
• B is the co-efficient of the variable
• C is the extra added number. It is the same as the b in Linear equations

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Topics: Algebra Equations Variable Co-efficient Times Symbols Equation...

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Algebraically closed fieldAbstract algebra In mathematics, a field F is said to be algebraically closed if every polynomial of degree at least 1, with coefficients in F has a zero in F''. In that case, every such polynomial splits into linear factors. It can be shown that a field Algebraic numberAbstract algebra Algebra In mathematics, an algebraic number relative to a field F is any element x of a given field K containing F such that x is a solution of a polynomial equation of the form : a x n + a x n minus;1 + ··· + a x + a 0 where n is a posit AlgebraAlgebra Algebra (from the Arabic al-jabr meaning reunion connection or completion is a branch of mathematics which may be roughly characterized as a generalization and extension of arithmetic; it also refers to a particular kind of abstract algebra struct Algebraic geometryAlgebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of algebraic equations . When there is more than o Algebraic extensionAbstract algebra Algebra In abstract algebra, a field extension L ''K is called algebraic if every element of L is algebraic over K i. if every element of L is a root of some non-zero polynomial with coefficients in K''. Field extensions which are not alg Algebraic closureField theory In mathematics, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics. Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that Algebraic topology Algebraic chess notation Algebraic integer Algebraic structure Algebraic element Algebra over a field Algebraic enumeration Algebraic number field Algebraic group