Concrete Mathematics: A Foundation for Computer Science

This book is an introduction to the mathematics that underpins programming and algorithm analysis. The main goal of its renowned authors — to lay a theoretical mathematical foundation and help acquire practical skills necessary for solving complex problems, computing sums of daunting appearance, discovering subtle patterns in data, and much more. This book is not only for specialists in the field of computer science — as its authors are — but also for anyone who seriously uses mathematics regardless of the field of knowledge in which they work. The title «concrete mathematics» comes from two terms: «CONtinuous mathematics» and «DIScrete mathematics». It can be understood literally: teaching general methods is conducted through numerous concrete examples and exercises of varying degrees of difficulty. The book contains over 500 exercises, divided into six categories of difficulty. Complete answers are provided for all exercises (except research problems), making the book especially valuable for self-study. The book can be viewed as an extended version of «Mathematical Introduction» from The Art of Computer Programming by D. Knuth, but with a more detailed and thorough presentation of the material and a deeper dive into specific topics. A number of new topics have been added, and the development of the most important ideas is traced back to their historical roots.