# Blog articles/Mathematics

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− | == Maths == |
+ | Haskell and mathematics. See also the [[Haskell_and_mathematics|Haskell math community]]. |

− | === Haskell for mathematics === |
+ | == Haskell for mathematics == |

− | ==== General ==== |
+ | === General === |

* [http://sigfpe.blogspot.com/2006/01/eleven-reasons-to-use-haskell-as.html Eleven Reasons to use Haskell as a Mathematician] |
* [http://sigfpe.blogspot.com/2006/01/eleven-reasons-to-use-haskell-as.html Eleven Reasons to use Haskell as a Mathematician] |
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* [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?] |
* [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?] |
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− | ==== Calculus and Differential Geometry ==== |
+ | === Calculus and Differential Geometry === |

* [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry] |
* [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry] |
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* [http://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell] |
* [http://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell] |
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− | ==== Algebraic Topology and Geometry ==== |
+ | === Algebraic Topology and Geometry === |

* [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell] |
* [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell] |
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* [http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html More Low Cost Geometric Algebra] |
* [http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html More Low Cost Geometric Algebra] |
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− | |||

* [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!] |
* [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!] |
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− | ==== Geometry ==== |
+ | === Geometry === |

* [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] |
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− | ==== Group Theory ==== |
+ | === 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] |
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* [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] |
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− | ==== Set Theory ==== |
+ | === Set Theory === |

* [http://community.livejournal.com/evan_tech/220036.html Powerset oneliner] |
* [http://community.livejournal.com/evan_tech/220036.html Powerset oneliner] |
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* [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] |
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− | ==== Ring Theory ==== |
+ | === Ring Theory === |

* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials] |
* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials] |
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− | ==== Number Theory ==== |
+ | === 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] |
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− | ==== Cryptography and Coding Theory ==== |
+ | === 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] |
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* [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] |
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* [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves] |
* [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves] |
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− | ==== Logic ==== |
+ | === Logic === |

* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion] |
* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion] |
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− | ==== Numerics ==== |
+ | === Numerics === |

* The Division Bell |
* The Division Bell |
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** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One] |
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One] |
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** [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] |
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− | === Theorem Proving === |
+ | == 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] |
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− | === Quantum Computing === |
+ | == 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] |
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* [http://www.alpheccar.org/en/posts/show/68 The Frame Of Reference Monad] |
* [http://www.alpheccar.org/en/posts/show/68 The Frame Of Reference Monad] |
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− | === Mathematics of Haskell === |
+ | == Mathematics of Haskell == |

− | ==== Category Theoretic ==== |
+ | === Category Theoretic === |

* Category Theory and the Category of Haskell programs: |
* Category Theory and the Category of Haskell programs: |
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* [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.] |
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− | ==== Lambda and Combinator Calculi ==== |
+ | === 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] |
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* [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] |
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− | ==== Other Formal Logics ==== |
+ | === 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] |
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− | ==== Miscellaneous ==== |
+ | === Miscellaneous === |

* [http://www.rubrication.net/2007/04/21/how-a-real-module-system-should-work/ ML, Haskell and Coq] |
* [http://www.rubrication.net/2007/04/21/how-a-real-module-system-should-work/ ML, Haskell and Coq] |
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* [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types] |
* [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types] |
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* [http://www.alpheccar.org/en/posts/show/70 Djinn, Coq, Monad and a bit of Haskell] |
* [http://www.alpheccar.org/en/posts/show/70 Djinn, Coq, Monad and a bit of Haskell] |
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+ | |||

+ | [[Category:Tutorials]] |

## Revision as of 07:35, 29 June 2007

Haskell and mathematics. See also the Haskell math community.

## Contents |

## 1 Haskell for mathematics

### 1.1 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?

### 1.2 Calculus and Differential Geometry

### 1.3 Algebraic Topology and Geometry

### 1.4 Geometry

### 1.5 Group Theory

### 1.6 Set Theory

### 1.7 Ring Theory

### 1.8 Number Theory

### 1.9 Cryptography and Coding Theory

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

### 1.10 Logic

### 1.11 Numerics

- The Division Bell

- Overloading Haskell numbers

## 2 Theorem Proving

## 3 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

## 4 Mathematics of Haskell

### 4.1 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.