Difference between revisions of "Blog articles/Mathematics"
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=== Haskell for mathematics === |
=== Haskell for mathematics === |
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+ | ==== General ==== |
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* [http://sigfpe.blogspot.com/2006/09/learn-maths-with-haskell.html Learn Maths with Haskell] |
* [http://sigfpe.blogspot.com/2006/09/learn-maths-with-haskell.html Learn Maths with Haskell] |
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+ | ==== Calculus and Differential Geometry ==== |
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* [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry] |
* [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry] |
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+ | ==== Algebraic Topology and Geometry ==== |
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+ | |||
* [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell] |
* [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell] |
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− | * [http://sigfpe.blogspot.com/2006/09/ |
+ | * [http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html More Low Cost Geometric Algebra] |
+ | |||
* [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!] |
* [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!] |
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+ | ==== Geometry ==== |
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− | * [http://blog.mikael.johanssons.org/archive/2006/11/a-algebras-and-group-cohomology/ <math>A_\infty</math>-algebras and group cohomology] |
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+ | ==== Group 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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+ | |||
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+ | ==== Set Theory ==== |
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+ | |||
+ | ==== Ring Theory ==== |
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+ | |||
+ | ==== Number Theory ==== |
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+ | |||
+ | ==== Cryptography and Coding Theory ==== |
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* [http://vandreev.wordpress.com/2007/06/18/feistel-ciphers-and-des-in-haskell/ Feistel Ciphers and DES in Haskell] |
* [http://vandreev.wordpress.com/2007/06/18/feistel-ciphers-and-des-in-haskell/ Feistel Ciphers and DES in Haskell] |
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* [http://vandreev.wordpress.com/2007/01/07/arithmetic-coding/ Arithmetic coding in Haskell] |
* [http://vandreev.wordpress.com/2007/01/07/arithmetic-coding/ Arithmetic coding in Haskell] |
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* [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves] |
* [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves] |
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+ | |||
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+ | ==== Logic ==== |
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− | * [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers] |
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+ | |||
+ | ==== Numerics ==== |
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* The Division Bell |
* The Division Bell |
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** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One] |
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One] |
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** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me-part-four.html Part Four (Conclusion)] |
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me-part-four.html Part Four (Conclusion)] |
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** [http://praisecurseandrecurse.blogspot.com/2006/12/divisive-aftermath.html The Divisive Aftermath] |
** [http://praisecurseandrecurse.blogspot.com/2006/12/divisive-aftermath.html The Divisive Aftermath] |
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* Overloading Haskell numbers |
* Overloading Haskell numbers |
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** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-1.html Part 1: symbolic expressions] |
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-1.html Part 1: symbolic expressions] |
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** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-3.html Part 3: Fixed Precision] |
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-3.html Part 3: Fixed Precision] |
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** [http://augustss.blogspot.com/2007/05/i-was-asked-if-my-fixed-number-module.html Dynamic epsilons in Haskell with a bit of type hackery] |
** [http://augustss.blogspot.com/2007/05/i-was-asked-if-my-fixed-number-module.html Dynamic epsilons in Haskell with a bit of type hackery] |
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− | * Number theory |
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* [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover] |
* [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover] |
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− | === Quantum |
+ | === Quantum Computing === |
* [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing] |
* [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing] |
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=== Mathematics of Haskell === |
=== Mathematics of Haskell === |
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+ | |||
+ | ==== Category Theoretic ==== |
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* [http://sigfpe.blogspot.com/2006/11/why-isnt-listt-monad.html Why isn't ListT list a monad?] |
* [http://sigfpe.blogspot.com/2006/11/why-isnt-listt-monad.html Why isn't ListT list a monad?] |
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* [http://sigfpe.blogspot.com/2006/11/yoneda-lemma.html Reverse Engineering Machines with the Yoneda Lemma] |
* [http://sigfpe.blogspot.com/2006/11/yoneda-lemma.html Reverse Engineering Machines with the Yoneda Lemma] |
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* [http://sigfpe.blogspot.com/2006/11/variable-substitution-gives.html Variable substitution gives a...] |
* [http://sigfpe.blogspot.com/2006/11/variable-substitution-gives.html Variable substitution gives a...] |
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* [http://sigfpe.blogspot.com/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.] |
* [http://sigfpe.blogspot.com/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.] |
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+ | |||
+ | ==== Lambda and Combinator Calculi ==== |
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* [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus] |
* [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus] |
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* [http://www.onebadseed.com/blog/?p=51 Don't need the Y combinator] |
* [http://www.onebadseed.com/blog/?p=51 Don't need the Y combinator] |
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+ | ==== Other Formal Logics ==== |
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+ | ==== Miscellaneous ==== |
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* [http://www.rubrication.net/2007/04/21/how-a-real-module-system-should-work/ ML, Haskell and Coq] |
* [http://www.rubrication.net/2007/04/21/how-a-real-module-system-should-work/ ML, Haskell and Coq] |
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* [http://www.alpheccar.org/en/posts/show/70 Djinn, Coq, Monad and a bit of Haskell] |
* [http://www.alpheccar.org/en/posts/show/70 Djinn, Coq, Monad and a bit of Haskell] |
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Revision as of 07:25, 29 June 2007
Maths
Haskell for mathematics
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?
Calculus and Differential Geometry
Algebraic Topology and Geometry
Geometry
Group Theory
Set Theory
Ring Theory
Number Theory
Cryptography and Coding Theory
- Feistel Ciphers and DES in Haskell
- Arithmetic coding in Haskell
- Two-dimensional spatial hashing with space-filling curves
Logic
Numerics
- The Division Bell
- Overloading Haskell numbers
Theorem Proving
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
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.