Classical K-Theory: Completion of Unimodular Rows

Abstract

In this thesis, we explore the problem of the completion of unimodular rows which has its historical importance in the solution of Serre's problem. We also study Classical Algebraic K-theory in the context of projective modules and unimodular rows. We end the thesis with the study of a recent theorem on the completion of unimodular row of length 3 and understand its constructive proof using the help of the software Macaulay2.