# Blog articles/Mathematics

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## Revision as of 06:45, 29 June 2007

## Contents |

## 1 Maths

### 1.1 Haskell for mathematics

- Learn Maths with Haskell
- Practical Synthetic Differential Geometry
- More Low Cost Geometric Algebra
- Algebraic Topology in Haskell
- Infinitesimal Types
- Geometric Algebra for Free!
- Eleven Reasons to use Haskell as a Mathematician
- Laws of Form: An Opinion
- -algebras and group cohomology
- Prototyping thought
- Computational Group Theory in Haskell
- Carry bits and group cohomology
- Polynomials as numbers
- Non-standard analysis, automatic differentiation, Haskell
- Feistel Ciphers and DES in Haskell
- Arithmetic coding in Haskell
- Haskell for Maths: commutative algebra, combinatorics, number theory, and group theory
- Two-dimensional spatial hashing with space-filling curves
- Countable Ordinals in Haskell
- Polynomials as numbers
- The Division Bell
- Haskell, PDF and penrose tilings
- Overloading Haskell numbers
- Number theory
- Powerset oneliner

### 1.2 Theorem proving

### 1.3 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

### 1.4 Mathematics of Haskell

- Why isn't ListT list a monad?
- Reverse Engineering Machines with the Yoneda Lemma
- Variable substitution gives a...
- From Löb's Theorem to Spreadsheet Evaluation
- Games, Strategies and the Self-Composition of the List Monad.
- Programs are Proofs: Models and Types in Lambda Calculus
- Why Haskell?
- Don't need the Y combinator
- ML, Haskell and Coq
- Djinn, Coq, Monad and a bit of Haskell
- Category Theory and the category of Haskell programs