"Approximate Commutative Algebra": an ill-chosen name for an important discipline

Abstract

Classical algebra has always considered itself as a discipline in Discrete Mathematics, even when it dealt with objects over the real or complex numbers (R or C), where the inherent topology of the number fields would have invited the use of analytic tools. A first change occurred only when the models of applied mathematics required the treatment of larger and larger systems of linear equations and the emerging electronic computers permitted the implementation of algorithms with huge data sets. In the rapidly growing "Numerical Linear Algebra", norms and distances, contractive iterations etc. were used as standard tools: Classical linear algebra over R and C became embedded into Analysis. (As a consequence, in the 2000 Mathematics Subject Classification of the AMS, "Numerical Linear Algebra" is not listed as a subdiscipline of Algebra but of Numerical Analysis.)

Index Terms

• Mathematics of computing

  • Mathematical analysis

    • Numerical analysis

      • Computations on polynomials