A captivating introduction to key results of discrete mathematics through the work of Paul Erdős, blended with first-hand reminiscences.

Paul Erdős published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdős, along with his brilliant ways of working toward their answers. It includes young Erdős's proof of Bertrand's postulate, the Erdős-Szekeres Happy End Theorem, De Bruijn-Erdős theorem, Erdős-Rado delta-systems, Erdős-Ko-Rado theorem, Erdős-Stone theorem, the Erdős-Rényi-Sós Friendship Theorem, Erdős-Rényi random graphs, the Chvátal-Erdős theorem on Hamilton cycles, and other results of Erdős, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erdős, this book offers a behind-the-scenes look at interactions with the legendary collaborator.

This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.

This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.

This book provides a thorough and up-to-date discussion of arc routing by world-renowned researchers. Organized by problem type, the book offers a rigorous treatment of complexity issues, models, algorithms, and applications. Arc Routing: Problems, Methods, and Applications opens with a historical perspective of the field and is followed by three sections that cover complexity and the Chinese Postman and the Rural Postman problems; the Capacitated Arc Routing Problem and routing problems with min-max and profit maximization objectives; and important applications, including meter reading, snow removal, and waste collection.

Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.

Everyone talks about style, but no one explains it. The authors of this book do; and in doing so, they provoke the reader to consider style, not as an elegant accessory of effective prose, but as its very heart. At a time when writing skills have virtually disappeared, what can be done? If only people learned the principles of verbal correctness, the essential rules, wouldn't good prose simply fall into place? Thomas and Turner say no. Attending to rules of grammar, sense, and sentence structure will no more lead to effective prose than knowing the mechanics of a golf swing will lead to a hole-in-one. Furthermore, ten-step programs to better writing exacerbate the problem by failing to recognize, as Thomas and Turner point out, that there are many styles with different standards. In the first half of Clear and Simple, the authors introduce a range of styles--reflexive, practical, plain, contemplative, romantic, prophetic, and others--contrasting them to classic style. Its principles are simple: The writer adopts the pose that the motive is truth, the purpose is presentation, the reader is an intellectual equal, and the occasion is informal. Classic style is at home in everything from business memos to personal letters, from magazine articles to university writing. The second half of the book is a tour of examples--the exquisite and the execrable--showing what has worked and what hasn't. Classic prose is found everywhere: from Thomas Jefferson to Junichirō Tanizaki, from Mark Twain to the observations of an undergraduate. Here are many fine performances in classic style, each clear and simple as the truth. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.