This illuminating textbook provides a concise review of the core
concepts in mathematics essential to computer scientists. Emphasis
is placed on the practical computing applications enabled by
seemingly abstract mathematical ideas, presented within their
historical context. The text spans a broad selection of key topics,
ranging from the use of finite field theory to correct code and the
role of number theory in cryptography, to the value of graph theory
when modelling networks and the importance of formal methods for
safety critical systems. This fully updated new edition has been
expanded with a more comprehensive treatment of algorithms, logic,
automata theory, model checking, software reliability and
dependability, algebra, sequences and series, and mathematical
induction. Topics and features: includes numerous pedagogical
features, such as chapter-opening key topics, chapter introductions
and summaries, review questions, and a glossary; describes the
historical contributions of such prominent figures as Leibniz,
Babbage, Boole, and von Neumann; introduces the fundamental
mathematical concepts of sets, relations and functions, along with
the basics of number theory, algebra, algorithms, and matrices;
explores arithmetic and geometric sequences and series,
mathematical induction and recursion, graph theory, computability
and decidability, and automata theory; reviews the core issues of
coding theory, language theory, software engineering, and software
reliability, as well as formal methods and model checking; covers
key topics on logic, from ancient Greek contributions to modern
applications in AI, and discusses the nature of mathematical proof
and theorem proving; presents a short introduction to probability
and statistics, complex numbers and quaternions, and calculus. This
engaging and easy-to-understand book will appeal to students of
computer science wishing for an overview of the mathematics used in
computing, and to mathematicians curious about how their subject is
applied in the field of computer science. The book will also
capture the interest of the motivated general reader.
General
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