Outline of algebra

Updated on Dec 09, 2024

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The following outline is provided as an overview of and topical guide to algebra:

Algebra is one of the main branches of mathematics. In which we study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers symbols, variables, and set elements. Addition and multiplication are general operations, but their precise definitions lead to structures such as groups, rings, and fields.

Branches

Algebraic equations

An algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.

Linear equation – algebraic equation of degree one.

Polynomial equation – equation in which a polynomial is set equal to another polynomial.

Transcendental equation – equation involving a transcendental function of one of its variables.

Functional equation – equation in which the unknowns are functions rather than simple quantities.

Differential equation – equation involving derivatives.

Integral equation – equation involving integrals.

Diophantine equation – equation where the unknowns are required to be integers.

Polynomials

Variables

History

History of algebra

General algebra concepts

Algebra –

Cubic equation –

Fundamental theorem of algebra – states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.

Linear equation –

Quadratic equation –

Quartic equation –

Quintic equation –

Polynomial –

References

Outline of algebra Wikipedia

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Contents

Branches

Algebraic equations

History

General algebra concepts

References