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A textbook suitable for undergraduate courses. The materials are
presented very explicitly so that students will find it very easy
to read. A wide range of examples, about 500 combinatorial problems
taken from various mathematical competitions and exercises are also
included.
This book is the essential companion to Counting (2nd Edition)
(World Scientific, 2013), an introduction to combinatorics for
secondary to undergraduate students. The book gives solutions to
the exercises in Counting (2nd Edition). There is often more than
one method to solve a particular problem and the authors have
included alternative solutions whenever they are of interest. The
rigorous and clear solutions will aid the reader in further
understanding the concepts and applications in Counting (2nd
Edition). An introductory section on problem solving as described
by George P lya will be useful in helping the lay person understand
how mathematicians think and solve problems.
This book in its Second Edition is a useful, attractive
introduction to basic counting techniques for upper secondary to
undergraduate students, as well as teachers. Younger students and
lay people who appreciate mathematics, not to mention avid puzzle
solvers, will also find the book interesting. The various problems
and applications here are good for building up proficiency in
counting. They are also useful for honing basic skills and
techniques in general problem solving. Many of the problems avoid
routine and the diligent reader will often discover more than one
way of solving a particular problem, which is indeed an important
awareness in problem solving. The book thus helps to give students
an early start to learning problem-solving heuristics and thinking
skills.New chapters originally from a supplementary book have been
added in this edition to substantially increase the coverage of
counting techniques. The new chapters include the Principle of
Inclusion and Exclusion, the Pigeonhole Principle, Recurrence
Relations, the Stirling Numbers and the Catalan Numbers. A number
of new problems have also been added to this edition.
"This book should be a must for all mathematicians who are involved
in the training of Mathematical Olympiad teams, but it will also be
a valuable source of problems for university courses." Mathematical
Reviews A textbook suitable for undergraduate courses. The
materials are presented very explicitly so that students will find
it very easy to read. A wide range of examples, about 500
combinatorial problems taken from various mathematical competitions
and exercises are also included.
This book is an expansion of our first book Introduction to Graph
Theory: H3 Mathematics. While the first book was intended for
capable high school students and university freshmen, this version
covers substantially more ground and is intended as a reference and
textbook for undergraduate studies in Graph Theory. In fact, the
topics cover a few modules in the Graph Theory taught at the
National University of Singapore. The reader will be challenged and
inspired by the material in the book, especially the variety and
quality of the problems, which are derived from the authors' years
of teaching and research experience.
This book is an expansion of our first book Introduction to Graph
Theory: H3 Mathematics. While the first book was intended for
capable high school students and university freshmen, this version
covers substantially more ground and is intended as a reference and
textbook for undergraduate studies in Graph Theory. In fact, the
topics cover a few modules in the Graph Theory taught at the
National University of Singapore. The reader will be challenged and
inspired by the material in the book, especially the variety and
quality of the problems, which are derived from the authors' years
of teaching and research experience.
This book in its Second Edition is a useful, attractive
introduction to basic counting techniques for upper secondary to
undergraduate students, as well as teachers. Younger students and
lay people who appreciate mathematics, not to mention avid puzzle
solvers, will also find the book interesting. The various problems
and applications here are good for building up proficiency in
counting. They are also useful for honing basic skills and
techniques in general problem solving. Many of the problems avoid
routine and the diligent reader will often discover more than one
way of solving a particular problem, which is indeed an important
awareness in problem solving. The book thus helps to give students
an early start to learning problem-solving heuristics and thinking
skills.New chapters originally from a supplementary book have been
added in this edition to substantially increase the coverage of
counting techniques. The new chapters include the Principle of
Inclusion and Exclusion, the Pigeonhole Principle, Recurrence
Relations, the Stirling Numbers and the Catalan Numbers. A number
of new problems have also been added to this edition.
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