Scheme Theory
In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It has no generally ..., a scheme is a mathematical structure In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ... that enlarges the notion of algebraic variety Algebraic varieties are the central objects of study in algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zero of a function, zeros of multivariate polynomials. Modern algebraic geometry is based on the us ... in several ways, such as taking account of multiplicities In mathematics, the multiplicity of a member of a multiset is the number of time ... [...More Info...] [...Related Items...] 

Mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no general consensus about its exact scope or . Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of . These objects are either s from nature (such as s or "a "), or (in modern mathematics) abstract entities that are defined by their basic properties, called s. A consists of a succession of applications of some to already known results, including previously proved s, axioms and (in case of abstraction from nature) some basic properties that are considered as true starting points of the theory under consideration. The result of a proof is called a ''theorem''. Contrary to s, the validity of a theorem (its truth) does not rely on any but on the correctness of its reasoning (though experimentation is often useful for ... [...More Info...] [...Related Items...] 