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13-48-64-1-10-20181122

Name: 13-48-64-1-10-20181122
ISBN: 978-94-6366-083-9

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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
- 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 *
- Looking Beyond *
- Further Reading
- Index
PDF Hugtenburg & Yorke-Smith - Back