Difference between revisions of "Blog articles/Mathematics"

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Haskell and mathematics. See also the [[Haskell_and_mathematics|Haskell math community]].
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Articles using Haskell for mathematics, and the mathematics of Haskell.
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For further references see the:
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* [[Haskell_and_mathematics|Haskell math community]].
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* [[Blog_articles/Monads|Mathematics of monads]]
   
 
== Haskell for mathematics ==
 
== Haskell for mathematics ==
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* [http://sigfpe.blogspot.com/2006/01/eleven-reasons-to-use-haskell-as.html Eleven Reasons to use Haskell as a Mathematician]
 
* [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
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* [http://www.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory libraries ([http://haskellformaths.blogspot.com/ blog], [http://hackage.haskell.org/package/HaskellForMaths hackage])
 
* [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://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought]
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=== Geometry ===
 
=== Geometry ===
* [http://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings]
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* [http://www.alpheccar.org/content/57.html Haskell, PDF and Penrose Tilings]
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* [http://www.kennknowles.com/blog/2007/11/20/visualizing-2d-convex-hull-using-gtk-and-opengl-in-haskell/ Visualizing 2D convex hull using Gtk and OpenGL in Haskell]
=== Group Theory ===
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* [http://www.kennknowles.com/blog/2007/12/03/calculating-the-reflect-rotate-translate-normal-form-for-an-isometry-of-the-plane-in-haskell-and-verifying-it-with-quickcheck/ Calculating the reflect-rotate-translate normal form for an isometry of the plane in Haskell, and verifying it with QuickCheck.]
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* [http://www.kennknowles.com/blog/2008/04/16/drawing-fractals-in-haskell-with-a-cursor-graphics-dsel-and-a-cute-list-representation/ Drawing fractals in Haskell with a cursor graphics DSEL and a cute list representation]
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=== 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]
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* [http://sigfpe.blogspot.com/2007/06/monads-from-algebra-and-the-gray-code.html Monads from Algebra and the the Gray Code from Groups]
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* [http://www.kennknowles.com/blog/2007/12/20/infinite-lazy-knuth-bendix-completion-for-monoids-in-haskell/ Infinite lazy Knuth-Bendix completion for monoids in Haskell]
   
=== Set Theory ===
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=== Set theory ===
* [http://community.livejournal.com/evan_tech/220036.html Powerset oneliner]
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* Ordinals in Haskell
* [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable Ordinals in Haskell]
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** [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable ordinals]
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** [http://japple.blogspot.com/2007/06/ordinals-part-2.html Uncountable ordinals and better representations for countable ordinals]
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** [http://blog.jbapple.com/2007/07/ord-countable-ordinals-and-idea-of.html Ord, Countable Ordinals, and an Idea of sigfpe]
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* [http://japple.blogspot.com/2007/06/constructability-uncountability-and.html Constructability, Uncountability, and ω-Haskell]
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* [http://community.livejournal.com/evan_tech/220036.html Defining a power set in one line]
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** [http://blog.mikedaum.com/2007/06/28/haskell-power/ Commentary on this powerset implementation]
   
=== Ring Theory ===
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=== Ring theory ===
* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials]
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* [http://sambangu.blogspot.com/2006/12/polynomials-as-numbers Polynomials] ([http://sambangu.blogspot.com/2006/12/questions-on-haskell-style-and update])
   
=== Number Theory ===
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=== 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 ===
 
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* Number theory and Haskell:
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** [http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/ The Division Algorithm]
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** [http://cdsmith.wordpress.com/2007/06/03/learning-number-theory-and-haskell-more-quickcheck-and-divisors/ QuickCheck and Divisors]
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** [http://cdsmith.wordpress.com/2007/06/06/learning-number-theory-and-haskell-greatest-common-divisor/ Greatest Common Divisor]
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** [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions]
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** [http://cdsmith.wordpress.com/2007/07/05/learning-haskell-and-number-theory-the-end-of-gcd/ The End of GCD]
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* [http://www.akalin.cx/2007/07/06/a-foray-into-number-theory-with-haskell/ A foray into number theory with Haskell]
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=== 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]
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=== Logic ===
 
=== Logic ===
 
* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
 
* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
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* [https://serokell.io/blog/incomplete-and-utter-introduction-to-modal-logic Incomplete and Utter Introduction to Modal Logic, Pt. 1]
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* [https://serokell.io/blog/incomplete-and-utter-introduction-to-modal-logic Incomplete and Utter Introduction to Modal Logic, Pt. 2]
   
 
=== Numerics ===
 
=== Numerics ===
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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]
   
== Theorem Proving ==
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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 Computing ==
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== 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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* [http://sigfpe.blogspot.com/2007/03/independence-entanglement-and.html Independence, entanglement and decoherence with the quantum monad]
 
* [http://sigfpe.blogspot.com/2007/03/independence-entanglement-and.html Independence, entanglement and decoherence with the quantum monad]
 
* [http://sigfpe.blogspot.com/2007/03/shor-quantum-error-correcting-code-and.html The Shor Quantum Error Correcting Code (and a Monad for Heat)]
 
* [http://sigfpe.blogspot.com/2007/03/shor-quantum-error-correcting-code-and.html The Shor Quantum Error Correcting Code (and a Monad for Heat)]
* [http://www.alpheccar.org/en/posts/show/68 The Frame Of Reference Monad]
 
   
 
== Mathematics of Haskell ==
 
== Mathematics of Haskell ==
   
=== Category Theoretic ===
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=== Category theoretic ===
   
 
* Category Theory and the Category of Haskell programs:
 
* Category Theory and the Category of Haskell programs:
** [http://www.alpheccar.org/en/posts/show/74 Category Theory and the category of Haskell programs]
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** [http://www.alpheccar.org/content/74.html Part 1]
** [http://www.alpheccar.org/en/posts/show/76 Part 2]
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** [http://www.alpheccar.org/content/76.html Part 2]
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** [http://www.alpheccar.org/content/77.html Part 3]
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* [http://en.wikibooks.org/wiki/Haskell/Category_theory Category theory and Haskell]
   
 
* [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/2006/10/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 ===
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=== 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 ===
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=== Other formal logics ===
 
* [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation]
 
* [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation]
   
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* [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types]
 
* [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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* [http://disparatemathematician.blogspot.com/2007/07/peanos-axioms-iv-advanced-functions-and.html Peano's Axioms IV: Advanced Functions and Integers]
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* [http://sigfpe.blogspot.com/2005/07/formal-power-series-and-haskell.html Formal Power Series and Haskell]
   
 
[[Category:Tutorials]]
 
[[Category:Tutorials]]
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[[Category:Mathematics|*]]

Latest revision as of 07:20, 16 April 2020

Articles using Haskell for mathematics, and the mathematics of Haskell.

For further references see the:

Haskell for mathematics

General

Calculus and Differential Geometry

Algebraic Topology and Geometry

Geometry

Group theory

Set theory

Ring theory

Number theory

Cryptography and coding theory

Logic

Numerics

Theorem proving

Quantum computing

Mathematics of Haskell

Category theoretic

Lambda and combinator calculi

Other formal logics

Miscellaneous