Free

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

You May Also Like

Transactions of the American Society of Civil Engineers, vol. LXX, Dec. 1910 Federal Investigations of Mine Accidents, Structural Materials and Fuels. Paper No. 1171

By Herbert M. (Herbert Michael) Wilson

Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 Address at the 42d Annual Convention, Chicago, Illinois, June 21st, 1910, Paper No. 1178

By J. A. (John Anderson) Bensel

The Mechanical Properties of Wood Including a Discussion of the Factors Affecting the Mechanical Properties, and Methods of Timber Testing

By Samuel J. (Samuel James) Record

Samuel F. B. Morse, His Letters and Journals In Two Volumes, Volume II

By Samuel Finley Breese Morse