# Blog articles/Mathematics

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## Revision as of 06:04, 16 July 2007

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

### 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

- 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.