Blog articles/Mathematics

Maths

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
• $A_{\mathrm{\infty }}$-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
  • Part One
  • Part Two
  • Part Three
  • Part Four (Conclusion)
  • The Divisive Aftermath
• Haskell, PDF and penrose tilings
• Overloading Haskell numbers
  • Part 1: symbolic expressions
  • Part 2: Forward Automatic Differentiation
  • Part 3: Fixed Precision
  • Dynamic epsilons in Haskell with a bit of type hackery
• Number theory
  • GCD and Higher Order Functions
• Powerset oneliner

Theorem proving

• Quick and Dirty Theorem Prover

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

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