Invitation to Nonlinear Algebra

Nonlinear algebra is the study of the algebraic structures that appear once one leaves the linear world: polynomial equations, their solution sets, and the interplay between the algebra of ideals and the geometry of varieties. The book grew out of courses taught in Leipzig and Berkeley, and is aimed at graduate students with a first course in abstract algebra behind them.

Topics include polynomial rings and Gröbner bases, varieties and their dimension, elimination, toric varieties and lattice polytopes, tensors and their ranks, tropical algebra, semidefinite programming and the algebra behind maximum likelihood estimation.

AMS published edition Preprint version (PDF, 6.9 MB)

The PDF is the pre-publication manuscript; the AMS edition is the version of record.