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An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.
A multivector that is the exterior product of linearly independent vectors is called a blade, and is said to be of grade . [f] A multivector that is the sum of blades of grade is called a (homogeneous) multivector of grade . From the axioms, with closure, every multivector of the geometric algebra is a sum of blades.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
Normally, expressions and formulas do not appear alone, but are included in sentences of the current language, where expressions play the role of noun phrases and formulas play the role of clauses. Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and ...
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
It is often contrasted with arithmetic: arithmetic deals with specified numbers, [3] whilst algebra introduces variables (quantities without fixed values). [4] This use of variables entails use of algebraic notation and an understanding of the general rules of the operations introduced in arithmetic: addition, subtraction, multiplication ...
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