Blog articles/Mathematics: Difference between revisions

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

Eleven Reasons to use Haskell as a Mathematician
Haskell for Maths: commutative algebra, combinatorics, number theory, and group theory libraries (blog, hackage)
Learn Maths with Haskell
Prototyping thought
Why Haskell?

Calculus and Differential Geometry

Algebraic Topology and Geometry

Geometry

Group theory

Set theory

Ring theory

Polynomials (update)

Number theory

Number theory and Haskell:

A foray into number theory with Haskell

Cryptography and coding theory

Logic

Numerics

The Division Bell

Overloading Haskell numbers

Theorem proving

Quick and Dirty Theorem Prover

Quantum computing

Mathematics of Haskell

Category theoretic

Category Theory and the Category of Haskell programs:
- Part 1
- Part 2
- Part 3

Category theory and Haskell

Lambda and combinator calculi

Other formal logics

From Löb's Theorem to Spreadsheet Evaluation

Miscellaneous

@@ Line 1: / Line 1: @@
-== Maths ==
+Articles using Haskell for mathematics, and the mathematics of Haskell.
-=== Haskell for mathematics ===
+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/algebraic-topology-in-haskell.html Algebraic Topology in Haskell]
-* [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types]
 * [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!]
-* [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/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
+=== Geometry ===
-* [http://blog.mikael.johanssons.org/archive/2006/11/a-algebras-and-group-cohomology/ A-algebras and group cohomology]
+* [http://www.alpheccar.org/content/57.html Haskell, PDF and Penrose Tilings]
-* [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought]
+* [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://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers]
+* [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://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell]
+* [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.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory
 * [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://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable Ordinals in Haskell]
-* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers]
+=== 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]
@@ Line 29: / Line 80: @@
 ** [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://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings]
 * Overloading Haskell numbers
 ** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-1.html Part 1: symbolic expressions]
@@ Line 35: / Line 86: @@
 ** [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]
-* Number theory
-** [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions]
-* [http://www.alpheccar.org/en/posts/show/74 Category theory 1]
-* [http://www.alpheccar.org/en/posts/show/76 Category theory 2]
-=== Theorem proving ===
+== Theorem proving ==
 * [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover]
-=== Quantum computing ===
+== Quantum computing ==
 * [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing]
@@ Line 51: / Line 97: @@
 * [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://www.alpheccar.org/en/posts/show/68 The Frame Of Reference Monad]
-=== Mathematics of Haskell ===
+== 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/2006/11/from-l-theorem-to-spreadsheet.html From Lb's Theorem to Spreadsheet Evaluation]
 * [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/2006/11/why_haskell.php Why Haskell?]
 * [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://www.alpheccar.org/en/posts/show/74 Category Theory and the category of Haskell programs]
+* [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|*]]