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Graph and Network Theory - An Applied Approach using Mathematica (R) (Hardcover, 1st ed. 2022)
Loot Price: R3,533
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Graph and Network Theory - An Applied Approach using Mathematica (R) (Hardcover, 1st ed. 2022)
Series: Springer Optimization and Its Applications, 193
Expected to ship within 10 - 15 working days
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This textbook covers a diversity of topics in graph and network
theory, both from a theoretical standpoint, and from an applied
modelling point of view. Mathematica (R) is used to demonstrate
much of the modelling aspects. Graph theory and model building
tools are developed in tandem with effective techniques for solving
practical problems via computer implementation. The book is
designed with three primary readerships in mind. Individual syllabi
or suggested sequences for study are provided for each of three
student audiences: mathematics, applied mathematics/operations
research, and computer science. In addition to the visual appeal of
each page, the text contains an abundance of gems. Most chapters
open with real-life problem descriptions which serve as motivation
for the theoretical development of the subject matter. Each chapter
concludes with three different sets of exercises. The first set of
exercises are standard and geared toward the more mathematically
inclined reader. Many of these are routine exercises, designed to
test understanding of the material in the text, but some are more
challenging. The second set of exercises is earmarked for the
computer technologically savvy reader and offer computer exercises
using Mathematica. The final set consists of larger projects aimed
at equipping those readers with backgrounds in the applied sciences
to apply the necessary skills learned in the chapter in the context
of real-world problem solving. Additionally, each chapter offers
biographical notes as well as pictures of graph theorists and
mathematicians who have contributed significantly to the
development of the results documented in the chapter. These notes
are meant to bring the topics covered to life, allowing the reader
to associate faces with some of the important discoveries and
results presented. In total, approximately 100 biographical notes
are presented throughout the book. The material in this book has
been organized into three distinct parts, each with a different
focus. The first part is devoted to topics in network optimization,
with a focus on basic notions in algorithmic complexity and the
computation of optimal paths, shortest spanning trees, maximum
flows and minimum-cost flows in networks, as well as the solution
of network location problems. The second part is devoted to a
variety of classical problems in graph theory, including problems
related to matchings, edge and vertex traversal, connectivity,
planarity, edge and vertex coloring, and orientations of graphs.
Finally, the focus in the third part is on modern areas of study in
graph theory, covering graph domination, Ramsey theory, extremal
graph theory, graph enumeration, and application of the
probabilistic method.
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