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Discrete Structure,
Logic, and Computability introduces the beginning computer science student to
some of the fundamental ideas and techniques used by computer scientists today.
The emphasis is on the computational aspects, so that the reader can see how the concepts are actually
used. Because of logic's fundamental importance to computer science, the topic
is examined extensively in three phases, which cover: informal logic; the technique
of inductive proof; and formal logic and its applications to computer science.
The choice of topics-and the depth and breadth of coverage-reflects the desire
to provide students with the foundations needed to successfully complete courses
at the upper division level in undergraduate computer science programs. The book
is the outgrowth of a computer science course at Portland State University that
has evolved over twenty years from a one-term course in discrete mathematics for
upper-division students into a one-year course in discrete structures, logic,
and computability for sophomores.
The book is organized more along the lines of technique than on a subject-by-subject
basis. The focus throughout the book is on the computation and construction of
objects. Therefore many traditional topics are dispersed throughout the text to
places where they fit naturally with the techniques under discussion. For example,
to read about properties of-and techniques for processing-natural numbers, lists,
strings, graphs, or trees, it's necessary to look in the index or scan the table
of contents to find the several places where they are found.
This book differs in several ways from current books about discrete mathematics
or foundations of computing. It presents an elementary and unified introduction
to a collection of topics that have not been available in a single source. A major
feature of the book is the unification of the material so that it doesn't fragment
into a vast collection of seemingly unrelated ideas.
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