Mathematics for computer scientists. An introduction to this topic using practical examples from the computer world (Q2756966)

This book is intended for introductory courses of mathematics in advanced technical colleges. It ist distinguished from other similar books by the much broader scope. Besides the classical themes calculus, linear algebra, logic and perhaps probability theory (which is not dealt with here) it contains chapters on elementary number theory, set theory, combinatorics, difference equations, algebra and graph theory, these fill nearly half of the volume. Every chapters begins with a short motivation explaining why computer scientists should know the following. Consequently many applications are exhibited: information retrieval in the case of logic, cryptography for number theory, data bases for set theory, complexity of algorithms for combinatorics and finding shortest paths and matchings for graph theory. This is of course true also for the classical themes, so there are sections on splines, numerical integration and vector-space-based information retrieval. NEWLINENEWLINENEWLINEThe scope and depth of the material can best be shown by some examples: in the section on difference equations difference operators are defined and discrete antiderivaties are introduced. But there is no formal result on the existence of solutions, instead several examples are solved ``by hand'', so that the reader can grasp the idea. In the chapter on algebra groups, rings, fields etc. are defined and it is stated that polynomial rings over fields are euclidean, but the term euclidean is not mentioned. The correspondence of roots of polynomials with linear factors is proven, but the fundamental theorem of algebra is not stated as such. However the fundamental theorem of number theory is proven very explicitly. The section on cryptography ends with the principles of the RSA-method, which are excellently motivated. NEWLINENEWLINENEWLINEThe exposition is always elementary and with as little formal ballast as possible, many themes are only touched on, but the reader always gets the central ideas and important applications. Many well chosen exercises are given, their solutions are available from the author's website.