A Trusted Guide to Discrete Mathematics with ProofNow in a Newly Revised Edition
Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field
of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding
of this important topic, exposing readers to a wide range of modern and technological applications.
The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent
chapters explore additional related topics including counting, finite probability theory, recursion, formal models
in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the
Second Edition include:
* An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof
by contradiction, and combinatorial proofs
* New sections on applications of elementary number theory, multidimensional induction, counting tulips, and
the binomial distribution
* Important examples from the field of computer science presented as applications including the Halting problem,
Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases
* Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance
algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus
problem, and the five-color theorem
* Extensive appendices that outlinesupplemental material on analyzing claims and writing mathematics, along
with solutions to selected chapter exercises
Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material
by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block
designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct
representatives. A related Web site features animations and visualizations of combinatorial proofs that assist
readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout
the book to motivate ideas and illustrate the proofs and conclusions of theorems.
Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book
for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals
in various technical fields who would like an introduction to discrete mathematics.