Introduction to Some Methods of Algebraic $K$-Theory (CBMS Regional Conference Series in Mathematics)

Part I. Introduction: Elementary matrices Stability $K_1(A[t])$ and unipotents Grothendieck and Whitehead groups of categories with exact sequences A Grothendieck style definition of $K_1(A)$ Homology, mapping cones, and Euler characteristics Resolution theorems Projective resolutions and regular rings Hilbert's syzygy theorem Appendix 1 Part II. Localisation, divissage and applications: The localisation sequence Categories of nilpotent endomorphisms $K_1(A[t,t^-1])$ Devissage Some calculations with the localisation sequence and $K_1$-Laurent theorem Computations with the Mayer-Vietoris sequence References