# Blog articles/Mathematics

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DonStewart (Talk | contribs) (→Set theory) |
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* [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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+ | * [http://sigfpe.blogspot.com/2007/06/monads-from-algebra-and-the-gray-code.html Monads from Algebra and the the Gray Code from Groups] |
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=== Set theory === |
=== Set theory === |

## Revision as of 01:36, 2 July 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

- Computational Group Theory in Haskell
- Carry bits and group cohomology
- Monads from Algebra and the the Gray Code from Groups

### 1.6 Set theory

- Uncountable ordinals in Haskell
- Constructability, Uncountability, and �-Haskell
- Defining a power set in one line

### 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.