An introduction to the ideas of algebraic geometry in the motivated context of system theory.
Thus the author describes his textbook that has been specifically written to serve the needs of
students of systems and control. Without sacrificing mathematical care the author makes the
basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis
is on constructive methods and clarity rather than abstraction. The student will find here a
clear presentation with an applied flavor of the core ideas in the algebra-geometric treatment
of scalar linear system theory. The author introduces the four representations of a scalar
linear system and establishes the major results of a similar theory for multivariable systems
appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective
Algebraic Geometry). Prerequisites are the basics of linear algebra some simple notions from
topology and the elementary properties of groups rings and fields and a basic course in
linear systems. Exercises are an integral part of the treatment and are used where relevant in
the main body of the text. The present softcover reprint is designed to make this classic
textbook available to a wider audience. This book is a concise development of affine algebraic
geometry together with very explicit links to the applications...[and] should address a wide
community of readers among pure and applied mathematicians. -Monatshefte für Mathematik
