# Blog articles/Mathematics

### From HaskellWiki

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

− | ** [http://www.alpheccar.org/ | + | ** [http://www.alpheccar.org/content/74.html Part 1] |

− | ** [http://www.alpheccar.org/ | + | ** [http://www.alpheccar.org/content/76.html Part 2] |

− | ** [http://www.alpheccar.org/ | + | ** [http://www.alpheccar.org/content/77.html Part 3] |

* [http://en.wikibooks.org/wiki/Haskell/Category_theory Category theory and Haskell] | * [http://en.wikibooks.org/wiki/Haskell/Category_theory Category theory and Haskell] |

## Revision as of 23:34, 11 October 2011

Articles using Haskell for mathematics, and the mathematics of Haskell.

For further references see the:

## 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

- Haskell, PDF and penrose tilings
- Visualizing 2D convex hull using Gtk and OpenGL in Haskell
- Calculating the reflect-rotate-translate normal form for an isometry of the plane in Haskell, and verifying it with QuickCheck.
- Drawing fractals in Haskell with a cursor graphics DSEL and a cute list representation

### 1.5 Group theory

- Computational Group Theory in Haskell
- Carry bits and group cohomology
- Monads from Algebra and the the Gray Code from Groups
- Infinite lazy Knuth-Bendix completion for monoids in Haskell

### 1.6 Set theory

- Ordinals in Haskell
- Constructability, Uncountability, and ω-Haskell
- Defining a power set in one line

### 1.7 Ring theory

### 1.8 Number theory

- Number theory and Haskell:

### 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

- 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.