Pearls of Discrete Mathematics (Discrete Mathematics and Its Applications) 1st Edition by Martin Erickson (PDF)

Description

Methods Used to Solve Discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this areaPearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics.Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon’s theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix.With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book has very good things and very bad things about it !Good is the variety of topics covered – from combinatorics , to probability, to information theory. Rook path problems, number of ways of providing change for 1 million dollars – All fascinating choices. Well done Sir!Bad is the writing style. I find the proofs cursory and hurried. Sometimes they are downright suspicious. I find myself having to look up topics on the Internet at almost every chapter to get a clear understanding of the proofs.Worse, the author has the annoying habit of writing down, without warning , a complicated formula. People like me will stop at the formula, stare at it incomprehensibly for an hour, give up, resort to Stack Exchange,, and return to the book, and then realise that the author gives (some) explanation of the formula after it was written down. This non-linear, back-to-front style of writing is a real struggle for me. Examples of this includes the calculation of the derangement number for the bridge hand example 10.10 on page 72, the generating function to count the number of pays of giving change for 1m dollars on p42 etc. I’m afraid forward-references are no-nos for me, when reading a mathematical text.I am happy to have this book and do recommend purchasing it, however it comes with a warning that the writing style may make its reading unsettling, and make absorbing the material slower than it should be.I purchased this book to prepare for technical interviews. A similar book (perhaps) is Peter Winkler”s ‘mathematical mind benders’, although ‘Pearls of Discrete mathemarics’ is slightly less recreational in feel.

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