Paul Erdos 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 Erdos, along with his brilliant ways of working toward their answers. It includes young Erdos's proof of Bertrand's postulate, the Erdos-Szekeres Happy End Theorem, De Bruijn-Erdos theorem, Erdos-Rado delta-systems, Erdos-Ko-Rado theorem, Erdos-Stone theorem, the Erdos-Renyi-Sos Friendship Theorem, Erdos-Renyi random graphs, the Chvatal-Erdos theorem on Hamilton cycles, and other results of Erdos, 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 Erdos, this book offers a behind-the-scenes look at interactions with the legendary collaborator.

Paul Erdos 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 Erdos, along with his brilliant ways of working toward their answers. It includes young Erdos's proof of Bertrand's postulate, the Erdos-Szekeres Happy End Theorem, De Bruijn-Erdos theorem, Erdos-Rado delta-systems, Erdos-Ko-Rado theorem, Erdos-Stone theorem, the Erdos-Renyi-Sos Friendship Theorem, Erdos-Renyi random graphs, the Chvatal-Erdos theorem on Hamilton cycles, and other results of Erdos, 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 Erdos, this book offers a behind-the-scenes look at interactions with the legendary collaborator.

This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience.

The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us.