Bender E. Foundations of Combinatorics with App 2005 + Sol Man torrent

Textbook in PDF format

Combinatorics, the mathematics of the discrete, has blossomed in this generation. On the theoretical side, a variety of tools, concepts and insights have been developed that allow us to solve previously intractable problems, formulate new problems and connect previously unrelated topics. On the applied side, scientists from physicists to biologists have found combinatorics essential in their research. In all of this, the interaction between computer science and mathematics stands out as a major impetus for theoretical developments and for applications of combinatorics. This text provides an introduction to the mathematical foundations of this interaction and to some of its results.
This book does not assume any previous knowledge of combinatorics or discrete mathematics. Except for a few items which can easily be skipped over and some of the material on generating functions in Part IV, calculus is not required. What is required is a certain level of ability or sophistication in dealing with mathematical concepts. The level of mathematical sophistication that is needed is about the same as that required in a solid beginning calculus course.
You may have noticed similarities and differences in how you think about various fields of mathematics such as algebra and geometry. In fact, you may have found some areas more interesting or more difficult than others partially because of the different thought patterns required. The field of combinatorics will also require you to develop some new thought patterns. This can sometimes be a difficult and frustrating process. Here is where patience, mathematical sophistication and a willingness to ask stupid questions can all be helpful. Combinatorics differs as much from mathematics you are likely to have studied previously as algebra differs from geometry. Some people find this disorienting and others find it fascinating. The introductions to the parts and to the chapters can help you orient yourself as you learn about combinatorics. Don’t skip them.
Because of the newness of much of combinatorics, a significant portion of the material in this text was only discovered in this generation. Some of the material is closely related to current research. In contrast, the other mathematics courses you have had so far probably contained little if anything that was not known in the Nineteenth Century. Welcome to the frontiers!
Preface
Counting and Listing
Basic Counting
Functions
Decision Trees
Sieving Methods
Graphs
Basic Concepts in Graph Theory
A Sampler of Graph Topics
Recursion
Induction and Recursion
Sorting Theory
Rooted Plane Trees
Generating Functions
Ordinary Generating Functions
Generating Function Topics
A Induction
B Rates of Growth and Analysis of Algorithms
C Basic Probability
D Partial Fractions
Solutions to Odd Exercises and Most Appendix Exercises