abstract algebra oor Indonesies
abstract algebra
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(mathematics) The branch of mathematics concerned with algebraic structures, such as groups, rings, and fields.
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aljabar abstrak
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math
Aljabar abstrak
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branch of mathematics
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Here are listed fundamental concepts in abstract algebra.
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Abstract algebra, in which algebraic structures such as groups, rings and fields are axiomatically defined and investigated.
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Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts.
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Vector spaces may be generalized in several ways, leading to more advanced notions in geometry and abstract algebra.
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Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.
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This level of abstraction revealed connections between geometry and abstract algebra.
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The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra.
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Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.
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Some areas of mathematics that fall under the classification abstract algebra have the word algebra in their name; linear algebra is one example.
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Derivatives and their generalizations appear in many fields of mathematics, such as complex analysis, functional analysis, differential geometry, measure theory, and abstract algebra.
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Amalie Emmy Noether (German: ; 23 March 1882 – 14 April 1935) was a German mathematician who made important contributions to abstract algebra and theoretical physics.
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In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
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A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology.
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Abstract algebra was developed in the 19th century, deriving from the interest in solving equations, initially focusing on what is now called Galois theory, and on constructibility issues.
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Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory, computational complexity, statistics, combinatorics, abstract algebra, number theory, and finite mathematics generally.
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The structural properties of these non-numerical objects were then abstracted into algebraic structures such as groups, rings, and fields.
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The study of numbers, called algebra at the beginning undergraduate level, extends to abstract algebra at a more advanced level; and the study of functions, called calculus at the college freshman level becomes mathematical analysis and functional analysis at a more advanced level.
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The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and real or complex numbers, often now called elementary algebra.
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With a qualifier, there is the same distinction: Without an article, it means a part of algebra, such as linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).
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Boolean algebra, a branch of algebra abstracting the computation with the truth values false and true.
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With an article, it means an instance of some abstract structure, like a Lie algebra, an associative algebra, or a vertex operator algebra.
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Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.
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Several major types of more abstract mathematics (including invariant theory, the Italian school of algebraic geometry, and Felix Klein's Erlangen programme resulting in the study of the classical groups) were based on projective geometry.
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