Extend students’ mathematical maturity and ability to deal with abstraction   Strong emphasis on reading and writing proofs — Illustrates most proofs of theorems with annotated figures to provide additional explanation and insight into the proofs. EXPANDED! More than 100 new exercises have been added to the first three chapters: Sets and Logic, Proofs, and Functions, Sequences, and Relations. There are now more than 1,750 worked examples and exercises in these chapters. Problem Solving Corners, a hallmark feature that helps students attack and solve problems and show them how to do proofs. Extensive discussion of algorithms, recursive algorithms, and the analysis of algorithms — The algorithms are written in a flexible form of pseudocode, which resembles currently popular languages such as C, C++, and Java. Extensive applications with an emphasis on computer science. Approximately 150 computer exercises are included throughout the book. Emphasis on the interplay among the various topics — For example, mathematical induction is closely tied to recursive algorithms; the Fibonacci sequence is used in the analysis of the Euclidean algorithm; many exercises throughout the book require mathematical induction; demonstrations of how to characterise the components of a graph by defining an equivalence relation on the set of vertices; and more. Figures and tables — Illustrate concepts, show how algorithms work, elucidate proofs, and motivate the material. Figure captions provide additional explanation and insight into figures accompanying proofs. Summaries of the mathematical and algorithmic notation used in the book on the inside covers.     Breadth of examples and exercises help students master introductory discrete mathematics   Nearly 4,500 exercises and 650 worked examples. EXPANDED! More than 300 new exercises increase the total to nearly 4,500. The previous edition featured approximately 4,200. UPDATED! Nearly 650 worked problems examples show students how to tackle problems, demonstrate applications of the theory, and clarify proofs. UPDATED! Chapter self-test exercises read more like real exams, no longer identifying relevant sections within the exercises. Hints to these exercises identify relevant sections for further reference. EXPANDED! Additional real-world examples provide more context for complex ideas and concepts. Additional exercises give examples of algebraic systems in which prime factorisation does not hold.