View source for Blog articles/Mathematics

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

For further references see the:

* [[Haskell_and_mathematics|Haskell math community]].
* [[Blog_articles/Monads|Mathematics of monads]]

== 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://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://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://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/2006/09/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!]

=== Geometry ===
* [http://www.alpheccar.org/content/57.html Haskell, PDF and Penrose Tilings]
* [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]
* [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.]
* [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]
 
=== 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/2006/07/carry-bits-and-group-cohomology/ Carry bits and group cohomology]
* [http://sigfpe.blogspot.com/2007/06/monads-from-algebra-and-the-gray-code.html Monads from Algebra and the the Gray Code from Groups]
* [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 ===
* Ordinals in Haskell
** [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable ordinals]
** [http://japple.blogspot.com/2007/06/ordinals-part-2.html Uncountable ordinals and better representations for countable ordinals]
** [http://blog.jbapple.com/2007/07/ord-countable-ordinals-and-idea-of.html Ord, Countable Ordinals, and an Idea of sigfpe]
* [http://japple.blogspot.com/2007/06/constructability-uncountability-and.html Constructability, Uncountability, and &omega;-Haskell]
* [http://community.livejournal.com/evan_tech/220036.html Defining a power set in one line]
** [http://blog.mikedaum.com/2007/06/28/haskell-power/ Commentary on this powerset implementation]

=== Ring theory ===
* [http://sambangu.blogspot.com/2006/12/polynomials-as-numbers Polynomials] ([http://sambangu.blogspot.com/2006/12/questions-on-haskell-style-and update])

=== Number theory ===

* Number theory and Haskell:
** [http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/ The Division Algorithm]
** [http://cdsmith.wordpress.com/2007/06/03/learning-number-theory-and-haskell-more-quickcheck-and-divisors/ QuickCheck and Divisors]
** [http://cdsmith.wordpress.com/2007/06/06/learning-number-theory-and-haskell-greatest-common-divisor/ Greatest Common Divisor]
** [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions]
** [http://cdsmith.wordpress.com/2007/07/05/learning-haskell-and-number-theory-the-end-of-gcd/ The End of GCD]

* [http://www.akalin.cx/2007/07/06/a-foray-into-number-theory-with-haskell/ A foray into number theory with Haskell]

=== 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/2007/01/07/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]

=== Logic ===
* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
* [https://serokell.io/blog/incomplete-and-utter-introduction-to-modal-logic Incomplete and Utter Introduction to Modal Logic, Pt. 1]
* [https://serokell.io/blog/incomplete-and-utter-introduction-to-modal-logic Incomplete and Utter Introduction to Modal Logic, Pt. 2]

=== Numerics ===
* 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-part-two.html Part Two]
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me-part-three.html Part Three]
** [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]

* 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-2.html Part 2: Forward Automatic Differentiation]
** [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]

== Theorem proving ==
* [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover]

== Quantum computing ==

* [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing]
* [http://sigfpe.blogspot.com/2007/02/monads-for-vector-spaces-probability.html Monads for vector spaces, probability and quantum mechanics pt. I]
* [http://sigfpe.blogspot.com/2007/03/monads-vector-spaces-and-quantum.html Monads, Vector Spaces and Quantum Mechanics pt. II]
* [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)]

== Mathematics of Haskell ==

=== Category theoretic ===

* Category Theory and the Category of Haskell programs:
** [http://www.alpheccar.org/content/74.html Part 1]
** [http://www.alpheccar.org/content/76.html Part 2]
** [http://www.alpheccar.org/content/77.html Part 3]

* [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/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/2006/10/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://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://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://disparatemathematician.blogspot.com/2007/07/peanos-axioms-iv-advanced-functions-and.html Peano's Axioms IV: Advanced Functions and Integers] 
* [http://sigfpe.blogspot.com/2005/07/formal-power-series-and-haskell.html Formal Power Series and Haskell]

[[Category:Tutorials]]
[[Category:Mathematics|*]]