Description |
1 online resource (xvi, 674 pages) |
Contents |
Cover -- Half-title Page -- Reviews -- Title Page -- Copyright Page -- Dedication -- Contents -- List of Computer Science Connections -- Acknowledgments -- Credits -- 1 On the Point of this Book -- 2 Basic Data Types -- 2.1 Why You Might Care -- 2.2 Booleans, Numbers, and Arithmetic -- 2.3 Sets: Unordered Collections -- 2.4 Sequences, Vectors, and Matrices: Ordered Collections -- 2.5 Functions -- 2.6 Chapter at a Glance -- 3 Logic -- 3.1 Why You Might Care -- 3.2 An Introduction to Propositional Logic -- 3.3 Propositional Logic: Some Extensions -- 3.4 An Introduction to Predicate Logic |
|
3.5 Predicate Logic: Nested Quantifiers -- 3.6 Chapter at a Glance -- 4 Proofs -- 4.1 Why You Might Care -- 4.2 Error-Correcting Codes -- 4.3 Proofs and Proof Techniques -- 4.4 Some Examples of Proofs -- 4.5 Common Errors in Proofs -- 4.6 Chapter at a Glance -- 5 Mathematical Induction -- 5.1 Why You Might Care -- 5.2 Proofs by Mathematical Induction -- 5.3 Strong Induction -- 5.4 Recursively Defined Structures and Structural Induction -- 5.5 Chapter at a Glance -- 6 Analysis of Algorithms -- 6.1 Why You Might Care -- 6.2 Asymptotics -- 6.3 Asymptotic Analysis of Algorithms |
|
6.4 Recurrence Relations: Analyzing Recursive Algorithms -- 6.5 An Extension: Recurrence Relations of the Form T(n)=aT([frac(n)(b)])+cn[sup(k)] -- 6.6 Chapter at a Glance -- 7 Number Theory -- 7.1 Why You Might Care -- 7.2 Modular Arithmetic -- 7.3 Primality and Relative Primality -- 7.4 Multiplicative Inverses -- 7.5 Cryptography -- 7.6 Chapter at a Glance -- 8 Relations -- 8.1 Why You Might Care -- 8.2 Formal Introduction -- 8.3 Properties of Relations: Reflexivity, Symmetry, and Transitivity -- 8.4 Special Relations: Equivalence Relations and Partial/Total Orders -- 8.5 Chapter at a Glance |
|
9 Counting -- 9.1 Why You Might Care -- 9.2 Counting Unions and Sequences -- 9.3 Using Functions to Count -- 9.4 Combinations and Permutations -- 9.5 Chapter at a Glance -- 10 Probability -- 10.1 Why You Might Care -- 10.2 Probability, Outcomes, and Events -- 10.3 Independence and Conditional Probability -- 10.4 Random Variables and Expectation -- 10.5 Chapter at a Glance -- 11 Graphs and Trees -- 11.1 Why You Might Care -- 11.2 Formal Introduction -- 11.3 Paths, Connectivity, and Distances -- 11.4 Trees -- 11.5 Weighted Graphs -- 11.6 Chapter at a Glance -- 12 Looking Forward -- References |
Summary |
Computer science majors taking a non-programming-based course like discrete mathematics might ask 'Why do I need to learn this?' Written with these students in mind, this text introduces the mathematical foundations of computer science by providing a comprehensive treatment of standard technical topics while simultaneously illustrating some of the broad-ranging applications of that material throughout the field. Chapters on core topics from discrete structures - like logic, proofs, number theory, counting, probability, graphs - are augmented with around 60 'computer science connections' pages introducing their applications: for example, game trees (logic), triangulation of scenes in computer graphics (induction), the Enigma machine (counting), algorithmic bias (relations), differential privacy (probability), and paired kidney transplants (graphs). Pedagogical features include 'Why You Might Care' sections, quick-reference chapter guides and key terms and results summaries, problem-solving and writing tips, 'Taking it Further' asides with more technical details, and around 1700 exercises, 435 worked examples, and 480 figures |
Notes |
Vendor-supplied metadata |
Subject |
Computer science -- Mathematics.
|
|
Discrete mathematics.
|
|
Computer science -- Mathematics
|
|
Discrete mathematics
|
Genre/Form |
Electronic books
|
Form |
Electronic book
|
ISBN |
9781009150484 |
|
1009150480 |
|