Sets Logic And Maths For Computing 2ed David Makinson by David Makinson 9781447125006, 1447125002 instant download after payment.

This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions. Read more... Sets, Logic and Mathsfor Computing; Preface; For the Student; What Is in This Book?; How Should You Use It?; For the Instructor; Manner of Presentation; Choice of Topics; Courses Outside Computer Science; The Second Edition; Acknowledgements; Contents; List of Figures; 1 Collecting Things Together: Sets; 1.1 The Intuitive Concept of a Set; 1.2 Basic Relations Between Sets; 1.2.1 Inclusion; 1.2.2 Identity and Proper Inclusion; 1.2.3 Diagrams; 1.2.4 Ways of Defining a Set; 1.3 The Empty Set; 1.3.1 Emptiness; 1.3.2 Disjoint Sets; 1.4 Boolean Operations on Sets; 1.4.1 Intersection; 1.4.2 Union 1.4.3 Difference and Complement1.5 Generalized Union and Intersection; 1.6 Power Sets; Selected Reading; 2 Comparing Things: Relations; 2.1 Ordered Tuples, Cartesian Products and Relations; 2.1.1 Ordered Tuples; 2.1.2 Cartesian Products; 2.1.3 Relations; 2.2 Tables and Digraphs for Relations; 2.2.1 Tables; 2.2.2 Digraphs; 2.3 Operations on Relations; 2.3.1 Converse; 2.3.2 Join, Projection, Selection; 2.3.3 Composition; 2.3.4 Image; 2.4 Reflexivity and Transitivity; 2.4.1 Reflexivity; 2.4.2 Transitivity; 2.5 Equivalence Relations and Partitions; 2.5.1 Symmetry; 2.5.2 Equivalence Relations 2.5.3 Partitions2.5.4 The Partition/Equivalence Correspondence; 2.6 Relations for Ordering; 2.6.1 Partial Order; 2.6.2 Linear Orderings; 2.6.3 Strict Orderings; 2.7 Closing with Relations; 2.7.1 Transitive Closure of a Relation; 2.7.2 Closure of a Set Under a Relation; Selected Reading; 3 Associating One Item with Another:Functions; 3.1 What Is a Function?; 3.2 Operations on Functions; 3.2.1 Domain and Range; 3.2.2 Restriction, Image, Closure; 3.2.3 Composition; 3.2.4 Inverse; 3.3 Injections, Surjections, Bijections; 3.3.1 Injectivity; 3.3.2 Surjectivity; 3.3.3 Bijective Functions 3.4 Using Functions to Compare Size3.4.1 Equinumerosity; 3.4.2 Cardinal Comparison; 3.4.3 The Pigeonhole Principle; 3.5 Some Handy Functions; 3.5.1 Identity Functions; 3.5.2 Constant Functions; 3.5.3 Projection Functions; 3.5.4 Characteristic Functions; 3.6 Families and Sequences; 3.6.1 Families of Sets; 3.6.2 Sequences and Suchlike; Selected Reading; 4 Recycling Outputs as Inputs: Induction and Recursion; 4.1 What Are Induction and Recursion?; 4.2 Proof by Simple Induction on the Positive Integers; 4.2.1 An Example; 4.2.2 The Principle Behind the Example 4.3 Definition by Simple Recursion on the Positive Integers4.4 Evaluating Functions Defined by Recursion; 4.5 Cumulative Induction and Recursion; 4.5.1 Cumulative Recursive Definitions; 4.5.2 Proof by Cumulative Induction; 4.5.3 Simultaneous Recursion and Induction; 4.6 Structural Recursion and Induction; 4.6.1 Defining Sets by Structural Recursion; 4.6.2 Proof by Structural Induction; 4.6.3 Defining Functions by Structural Recursion on Their Domains; 4.7 Recursion and Induction on Well-Founded Sets*; 4.7.1 Well-Founded Sets; 4.7.2 Proof by Well-Founded Induction