Blog articles/Mathematics
From HaskellWiki
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=== Haskell for mathematics === | === Haskell for mathematics === | ||
| + | ==== General ==== | ||
| + | |||
| + | * [http://sigfpe.blogspot.com/2006/01/eleven-reasons-to-use-haskell-as.html Eleven Reasons to use Haskell as a Mathematician] | ||
| + | * [http://www.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory libraries | ||
* [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] | ||
| + | * [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought] | ||
| + | * [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?] | ||
| + | |||
| + | ==== Calculus and Differential Geometry ==== | ||
| + | |||
* [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] | ||
| - | * [http:// | + | * [http://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell] |
| + | |||
| + | ==== Algebraic Topology and Geometry ==== | ||
| + | |||
* [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] | ||
| - | * [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!] | ||
| - | + | ||
| - | + | ==== Geometry ==== | |
| - | * [http:// | + | * [http://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings] |
| - | + | ||
| + | ==== Group Theory ==== | ||
| + | |||
* [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] | ||
* [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] | ||
| - | * [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials | + | |
| - | * [http:// | + | ==== Set Theory ==== |
| + | * [http://community.livejournal.com/evan_tech/220036.html Powerset oneliner] | ||
| + | * [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable Ordinals in Haskell] | ||
| + | |||
| + | ==== Ring Theory ==== | ||
| + | * [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials] | ||
| + | |||
| + | ==== Number Theory ==== | ||
| + | * [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions] | ||
| + | |||
| + | ==== Cryptography and Coding Theory ==== | ||
* [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] | ||
* [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] | ||
| - | |||
* [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] | ||
| - | * [http:// | + | |
| - | + | ==== Logic ==== | |
| + | * [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion] | ||
| + | |||
| + | ==== Numerics ==== | ||
* The Division Bell | * The Division Bell | ||
** [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)] | ||
** [http://praisecurseandrecurse.blogspot.com/2006/12/divisive-aftermath.html The Divisive Aftermath] | ** [http://praisecurseandrecurse.blogspot.com/2006/12/divisive-aftermath.html The Divisive Aftermath] | ||
| - | + | ||
* Overloading Haskell numbers | * Overloading Haskell numbers | ||
** [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] | ||
** [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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| + | === Theorem Proving === | ||
* [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] | ||
| - | === 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 === | ||
| + | |||
| + | ==== Category Theoretic ==== | ||
| + | |||
| + | * Category Theory and the Category of Haskell programs: | ||
| + | ** [http://www.alpheccar.org/en/posts/show/74 Category Theory and the category of Haskell programs] | ||
| + | ** [http://www.alpheccar.org/en/posts/show/76 Part 2] | ||
* [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?] | ||
* [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] | ||
* [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...] | ||
| - | |||
* [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.] | ||
| + | |||
| + | ==== Lambda and Combinator Calculi ==== | ||
* [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] | ||
| - | |||
* [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] | ||
| + | |||
| + | ==== Other Formal Logics ==== | ||
| + | * [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation] | ||
| + | |||
| + | ==== Miscellaneous ==== | ||
* [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] | ||
| + | * [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types] | ||
* [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
Contents |
1 Maths
1.1 Haskell for mathematics
1.1.1 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?
1.1.2 Calculus and Differential Geometry
1.1.3 Algebraic Topology and Geometry
1.1.4 Geometry
1.1.5 Group Theory
1.1.6 Set Theory
1.1.7 Ring Theory
1.1.8 Number Theory
1.1.9 Cryptography and Coding Theory
- Feistel Ciphers and DES in Haskell
- Arithmetic coding in Haskell
- Two-dimensional spatial hashing with space-filling curves
1.1.10 Logic
1.1.11 Numerics
- The Division Bell
- Overloading Haskell numbers
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
1.4.1 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.
