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Algebra

  • Răzvan GelcaEmail author
  • Titu Andreescu
Chapter

Abstract

The treatment of algebra is split into four subchapters. The first two are more elementary: identities and inequalities, presenting inequalities such as Cauchy-Schwarz, triangle, and AM-GM, but also Sturm’s method, and polynomials, with particular focus on quadratic polynomials, Viète’s relations, the location of roots, irreducibility, and Chebyshev’s polynomials. Next, a chapter on linear algebra discusses matrices, determinants, with applications to linear systems of equations and vector spaces, including the Cayley-Hamilton and Perron-Frobenius theorems, followed by a subchapter on abstract algebra, which covers groups and rings.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.MathematicsUniversity of Texas at DallasRichardsonUSA

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