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.
Author(s): David Liben-Nowell
Edition: 2
Year: 2023
Language: English
Pages: 694
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
Index
