ද්වාරය:වීජ ගණිතය

විකිපීඩියා ද්වාර
සංස්කෘතිය · භූගෝල විද්‍යාව · සෞඛ්‍යය · ඉතිහාසය · ගණිතය · ස්වාභාවික විද්‍යාව · දර්ශනවාදය · ආගම් · සමාජය · තාක්ෂණය

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වීජ ගණිතය

Algebra is a branch of mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written by the Persian mathematician, astronomer, astrologer and geographer, Muhammad bin Mūsā al-Khwārizmī titled Kitab al-Jabr al-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing"), which provided operations for the systematic solution of linear and quadratic equation

Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of automobiles, including effects of adding and multiplying numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots.

Algebra is much boring than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields.

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Abstract algebra • Algebraic geometry • Algebraic topology • Commutative algebra • Computer algebra • Diagram algebras • Elementary algebra • Galois theory • Homological algebra • Linear algebra • Mathematical identities • Permutations • Polynomials • Symmetric functions • Algebra stubs

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Pictures of all the connected Dynkin diagrams

These are all the connected Dynkin diagrams, which classify the irreducible root systems, which themselves classify simple complex Lie algebras and simple complex Lie groups. These diagrams are therefore fundamental throughout Lie group theory.

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Did you know?

• ...that it is impossible to devise a single formula involving only polynomials and radicals for solving an arbitrary quintic equation?
• ...that it is possible for a three dimensional figure to have a finite volume but infinite surface area? An example of this is Gabriel's Horn.
• ...that the Gudermannian function relates the regular trigonometric functions and the hyperbolic trigonometric functions without the use of complex numbers?
• ...that the classification of finite simple groups was not completed until the mid 1980s?
• ...that a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers?

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Topics in algebra

General	Elementary algebra	Key concepts	Linear algebra
Abstract algebra Algebraic number theory Algebraic geometry Topological algebra Algebraic combinatorics Commutative algebra Homological algebra Abstract algebra topics	Elementary algebra Function (mathematics) Equation Exponent Square root, cube root, Nth root Logarithms Polynomial Linear equation Quadratic equation Cubic equation Simultaneous equations Partial fraction	Identity element Inverse element Commutativity Associativity Distributivity Isomorphism The Isomorphism theorems Homomorphism	Linear algebra Matrix, Matrix theory Determinant Vector, Vector space Inner product, Inner product space Hilbert space Linear algebra glossary Linear algebra topics
Algebraic structures	Groups	Rings and Fields	Other
Algebraic structure (list) Group, Group theory Magma, quasigroup, loop, semigroup, monoid Lattice Rng, Semiring Ring, Ring theory Field, Field theory Module, Comodule Algebra over a ring, Algebra over a field Lie algebra Jordan algebra Universal algebra	Group, Group theory Order Subgroup, Normal subgroup Abelian group Simple group Finite simple groups Classification of finite simple groups Lie group Symmetry group Group representation Computational group theory Topological group Glossary of group theory List of group theory topics	Ring, Ring theory Field, Field theory Factor ring Ideal Ring homomorphism Banach algebra Clifford algebra Glossary of ring theory Glossary of field theory	Order theory Well-ordered Domain theory Glossary of order theory List of order topics Category theory (Portal) Tensor algebra K-theory Module theory Representation theory Computer algebra system Normed algebra

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