Schaum's Outline of Discrete Mathematics (Schaum's)

Discrete mathematics, or the study of finite systems, has become increasingly important for students of computer science, and this book is a good foundational text on the subject. This Schaum's outline is much more complete than the average Schaum's, and it is also very clear and instructive. It is not just a good text for discrete mathematics. It also covers the basics of abstract algebra and the basics of the theory of computation.The first 3 chapters cover sets, relations, functions, and algorithms, including a very good section on the complexity of algorithms. Chapter 4 is on logic and propositional calculus, which is the foundation of artificial intelligence and digital logic. The next three chapters cover the basics of vectors, matrices, counting (permutations and combinations), and probability theory. This material is important in the design and analysis of operating systems. Next are chapters on graph theory, directed graphs, and binary trees, all of which should be covered in any good course on the analysis of algorithms. These chapters include discussions of planarity, traversibility, minimal paths, and Warshall's and Huffman's algorithms. There is a chapter on languages and machines that includes material on regular expressions, automata, Turing machines, and computable functions. There is also a chapter dedicated to the very basics of abstract algebra, and another chapter on boolean algebra. This text is therefore a superset of what you will probably find in an upper level undergraduate class in discrete mathematics, and is definitely a book you want to keep around especially if you are a computer science student and need additional study material for your core courses of artificial intelligence, analysis of algorithms, operating systems, and theory of computation. Highly recommended.