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Full Description
Written exclusively with computer science students in mind, Discrete Mathematics for Computer Science provides a comprehensive treatment of standard course topics for the introductory discrete mathematics course with a strong emphasis on the relationship between the concepts and their application to computer science. The book has been crafted to enhance teaching and learning ease and includes a wide selection of exercises, detailed exploration problems, examples and problems inspired by wide-ranging applications of computer science and handy quick reference guides for key technical topics throughout. Discrete Mathematics for Computer Science provides a lucidly written introduction to discrete mathematics with abundant support for learning, including over 450 examples, thorough chapter summaries, simple quizzes, and approximately 1600 homework exercises of widely varying difficulty. Each chapter begins with motivational content that relates the chapter topic to computer science practice and the book also includes over fifty "Computer Science Connections" which discuss applications to computer science such as Rotation Matrices; Game Trees, Logic, and Winning Tic-Tac(-Toe); Moore's Law; Secret Sharing; The Enigma Machine and the First Computer; Bayesian Modeling and Spam Filtering; and Quantum Computing.
Contents
1 On the Point of this Book 1012 Basic Data Types 2012.1 Why You Might Care 2022.2 Booleans, Numbers, and Arithmetic 2032.3 Sets: Unordered Collections 2222.4 Sequences, Vectors, and Matrices: Ordered Collections 2372.5 Functions 2532.6 Chapter at a Glance 2703 Logic 3013.1 Why You Might Care 3023.2 An Introduction to Propositional Logic 3033.3 Propositional Logic: Some Extensions 3173.4 An Introduction to Predicate Logic 3313.5 Predicate Logic: Nested Quantifiers 3493.6 Chapter at a Glance 3624 Proofs 4014.1 Why You Might Care 4024.2 Error-Correcting Codes 4034.3 Proofs and Proof Techniques 4234.4 Some Examples of Proofs 4414.5 Common Errors in Proofs 4584.6 Chapter at a Glance 4695 Mathematical Induction 5015.1 Why You Might Care 5025.2 Proofs by Mathematical Induction 5035.3 Strong Induction 5215.4 Recursively Defined Structures and Structural Induction 5335.5 Chapter at a Glance 5466 Analysis of Algorithms 6016.1 Why You Might Care 6026.2 Asymptotics 6036.3 Asymptotic Analysis of Algorithms 6176.4 Recurrence Relations: Analyzing Recursive Algorithms 6316.5 Recurrence Relations: The Master Method 6476.6 Chapter at a Glance 6577 Number Theory 7017.1 Why You Might Care 7027.2 Modular Arithmetic 7037.3 Primality and Relative Primality 7177.4 Multiplicative Inverses 7347.5 Cryptography 7457.6 Chapter at a Glance 7568 Relations 8018.1 Why You Might Care 8028.2 Formal Introduction 8038.3 Properties of Relations: Reflexivity, Symmetry, and Transitivity 8188.4 Special Relations: Equivalence Relations and Partial/Total Orders 8338.5 Chapter at a Glance 8509 Counting 9019.1 Why You Might Care 9029.2 Counting Unions and Sequences 9039.3 Using Functions to Count 9269.4 Combinations and Permutations 9449.5 Chapter at a Glance 96510 Probability 100110.1 Why You Might Care 100210.2 Probability, Outcomes, and Events 100510.3 Independence and Conditional Probability 102110.4 Random Variables and Expectation 104110.5 Chapter at a Glance 106711 Graphs and Trees 110111.1 Why You Might Care 110211.2 Formal Introduction 110311.3 Paths, Connectivity, and Distances 112911.4 Trees 114711.5 Weighted Graphs 116411.6 Chapter at a Glance 117712 Index 1201
