# Difference between revisions of "Blog articles/Mathematics"

From HaskellWiki

RossPaterson (talk | contribs) (update polynomials link) |
BrettGiles (talk | contribs) m (Case) |
||

Line 25: | Line 25: | ||

* [http://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings] | * [http://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings] | ||

− | === Group | + | === Group theory === |

* [http://blog.mikael.johanssons.org/archive/2006/10/computational-group-theory-in-haskell-1-in-a-series/ Computational Group Theory in Haskell] | * [http://blog.mikael.johanssons.org/archive/2006/10/computational-group-theory-in-haskell-1-in-a-series/ Computational Group Theory in Haskell] | ||

* [http://blog.mikael.johanssons.org/archive/2006/07/carry-bits-and-group-cohomology/ Carry bits and group cohomology] | * [http://blog.mikael.johanssons.org/archive/2006/07/carry-bits-and-group-cohomology/ Carry bits and group cohomology] | ||

− | === Set | + | === Set theory === |

* [http://community.livejournal.com/evan_tech/220036.html Powerset oneliner] | * [http://community.livejournal.com/evan_tech/220036.html Powerset oneliner] | ||

* [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable Ordinals in Haskell] | * [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable Ordinals in Haskell] | ||

− | === Ring | + | === Ring theory === |

* [http://sambangu.blogspot.com/2006/12/polynomials-as-numbers Polynomials] ([http://sambangu.blogspot.com/2006/12/questions-on-haskell-style-and update]) | * [http://sambangu.blogspot.com/2006/12/polynomials-as-numbers Polynomials] ([http://sambangu.blogspot.com/2006/12/questions-on-haskell-style-and update]) | ||

− | === Number | + | === Number theory === |

* [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions] | * [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions] | ||

− | === Cryptography and | + | === Cryptography and coding theory === |

* [http://vandreev.wordpress.com/2007/06/18/feistel-ciphers-and-des-in-haskell/ Feistel Ciphers and DES in Haskell] | * [http://vandreev.wordpress.com/2007/06/18/feistel-ciphers-and-des-in-haskell/ Feistel Ciphers and DES in Haskell] | ||

* [http://vandreev.wordpress.com/2007/01/07/arithmetic-coding/ Arithmetic coding in Haskell] | * [http://vandreev.wordpress.com/2007/01/07/arithmetic-coding/ Arithmetic coding in Haskell] | ||

Line 62: | Line 62: | ||

** [http://augustss.blogspot.com/2007/05/i-was-asked-if-my-fixed-number-module.html Dynamic epsilons in Haskell with a bit of type hackery] | ** [http://augustss.blogspot.com/2007/05/i-was-asked-if-my-fixed-number-module.html Dynamic epsilons in Haskell with a bit of type hackery] | ||

− | == Theorem | + | == Theorem proving == |

* [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover] | * [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover] | ||

− | == Quantum | + | == Quantum computing == |

* [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing] | * [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing] | ||

Line 76: | Line 76: | ||

== Mathematics of Haskell == | == Mathematics of Haskell == | ||

− | === Category | + | === Category theoretic === |

* Category Theory and the Category of Haskell programs: | * Category Theory and the Category of Haskell programs: | ||

Line 87: | Line 87: | ||

* [http://sigfpe.blogspot.com/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.] | * [http://sigfpe.blogspot.com/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.] | ||

− | === Lambda and | + | === Lambda and combinator calculi === |

* [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus] | * [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus] | ||

* [http://www.onebadseed.com/blog/?p=51 Don't need the Y combinator] | * [http://www.onebadseed.com/blog/?p=51 Don't need the Y combinator] | ||

− | === Other | + | === Other formal logics === |

* [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation] | * [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation] | ||

## Revision as of 19:58, 29 June 2007

Haskell and mathematics. See also the Haskell math community.

## Haskell for mathematics

### General

- Eleven Reasons to use Haskell as a Mathematician
- Haskell for Maths: commutative algebra, combinatorics, number theory, and group theory libraries
- Learn Maths with Haskell
- Prototyping thought
- Why Haskell?

### Calculus and Differential Geometry

### Algebraic Topology and Geometry

### Geometry

### Group theory

### Set theory

### Ring theory

### Number theory

### Cryptography and coding theory

- Feistel Ciphers and DES in Haskell
- Arithmetic coding in Haskell
- Two-dimensional spatial hashing with space-filling curves

### Logic

### Numerics

- The Division Bell

- Overloading Haskell numbers

## Theorem proving

## Quantum computing

- The Essence of Quantum Computing
- Monads for vector spaces, probability and quantum mechanics pt. I
- Monads, Vector Spaces and Quantum Mechanics pt. II
- Independence, entanglement and decoherence with the quantum monad
- The Shor Quantum Error Correcting Code (and a Monad for Heat)
- The Frame Of Reference Monad

## Mathematics of Haskell

### Category theoretic

- Category Theory and the Category of Haskell programs:

- Why isn't ListT list a monad?
- Reverse Engineering Machines with the Yoneda Lemma
- Variable substitution gives a...
- Games, Strategies and the Self-Composition of the List Monad.