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Encyclopedia > Theory of equations

In mathematics, the theory of equations comprises a major part of traditional algebra. Topics include polynomials, algebraic equations, separation of roots including Sturm's theorem, approximation of roots, and the application of matrices and determinants to the solving of equations. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... Algebra is a branch of mathematics which studies structure and quantity. ... In mathematics, AMIT RAJs functions, or polynomials, are an important class of simple and smooth functions. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In mathematics, Sturms theorem is a symbolic procedure to determine the number of unique real roots of a polynomial. ... For the square matrix section, see square matrix. ... In linear algebra, the determinant is a function that associates a scalar det(A) to every square matrix A. The fundamental geometric meaning of the determinant is as the scale factor for volume when A is regarded as a linear transformation. ...


From the point of view of abstract algebra, the material is divided between symmetric function theory, field theory, Galois theory, and computational considerations including numerical analysis. Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... In mathematics, the theory of symmetric functions is part of the theory of polynomial equations, and also a substantial chapter of combinatorics. ... Field theory is a branch of mathematics which studies the properties of fields. ... In mathematics, Galois theory is a branch of abstract algebra. ... Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). ...


See also


  Results from FactBites:
 
Theory of Equations - MSN Encarta (1019 words)
Theory of Equations, branch of mathematics concerned with the nature of the roots of polynomial equations and with the methods of finding the roots and related problems.
Prior to the 17th century, the theory of equations was handicapped by the failure of mathematicians to recognize negative or complex numbers (see Number) as roots of equations.
In 1635 French philosopher and mathematician René Descartes published a text on the theory of equations, including his rule of signs for the number of positive and negative roots of an equation.
NationMaster - Encyclopedia: Theory of equations (529 words)
Topics include polynomials, algebraic equations, separation of roots including Sturm's theorem, approximation of roots, and the application of matrices and determinants to the solving of equations.
In mathematics, the theory of symmetric functions is part of the theory of polynomial equations, and also a substantial chapter of combinatorics.
In mathematics, Galois theory is a branch of abstract algebra.
  More results at FactBites »


 

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