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Book Description

Table of Contents

- PDF Hugtenburg & Yorke-Smith - Front
- Delftse FoC v1.0.2
- Introduction
- Logic
- Propositional Logic
- Propositions
- Logical operators
- Precedence rules
- Logical equivalence
- More logical operaters
- Implications in English
- More forms of implication
- Exclusive or
- Universal operators
- Classifying propositions

- Boolean Algebra
- Basics of Boolean Algebra
- Substitution laws
- Simplifications
- More rules of Boolean algebra

- Application: Logic Circuits
- Logic gates *
- Combining gates to create circuits *
- From circuits to propositions *
- Disjunctive Normal Form
- Binary addition *

- Predicate Logic
- Predicates
- Quantifiers
- Operators
- Tarski's world and formal structures
- Logical equivalence

- Deduction
- Arguments
- Valid arguments and proofs
- Proofs in predicate logic

- Propositional Logic
- Proof
- A Little Historical Background
- Mathematical Proof
- How to write a proof
- Some terminology
- Examples

- Proof by Contradiction
- Mathematical Induction
- How to write a proof by induction
- Examples
- More examples

- Strong Mathematical Induction
- Application: Recursion and Induction
- Recursive factorials
- Towers of Hanoi
- Binary trees *

- Recursive Definitions
- Invariants

- Sets, Functions, and Relations
- Basic Concepts
- Elements of sets
- Set-builder notation
- Operations on sets
- Visualising sets
- Sets of sets
- Mathematical induction revisited
- Structural Induction

- The Boolean Algebra of Sets
- Set complement
- Link between logic and set theory

- Application: Programming with Sets *
- Representing sets
- Computing with sets

- Functions
- Formalising the notion of functions
- Operations on functions
- Properties of functions
- First-class objects

- Application: Programming with Functions *
- Functions as first-class objects

- Counting Past Infinity
- Cardinality
- Counting to infinity
- Uncountable sets *
- A final note on infinities *

- Relations
- Properties of relations
- Equivalence relations

- Application: Relational Databases *

- Basic Concepts
- Looking Beyond *
- Further Reading
- Index

- PDF Hugtenburg & Yorke-Smith - Back

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