Blog articles/Mathematics: Difference between revisions

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

Geometric Algebra for Free!

Geometry

Haskell, PDF and penrose tilings

Group Theory

Set Theory

Ring Theory

Polynomials

Number Theory

GCD and Higher Order Functions

Cryptography and Coding Theory

Quantum Computing

Mathematics of Haskell

Category Theoretic

Category Theory and the Category of Haskell programs:
- Category Theory and the category of Haskell programs
- Part 2

Lambda and Combinator Calculi

Other Formal Logics

From Löb's Theorem to Spreadsheet Evaluation

@@ Line 3: / Line 3: @@
 === 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://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/ <math>A_\infty</math>-algebras and group cohomology]
+* [http://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings]
-* [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought]
+==== 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://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell]
+==== 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/2007/01/07/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]
+==== Numerics ====
 * The Division Bell
 ** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One]
@@ Line 29: / Line 56: @@
 ** [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 62: @@
 ** [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://community.livejournal.com/evan_tech/220036.html Powerset oneliner]
-=== 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 53: / Line 76: @@
 === 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/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 Löb'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]
-* 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]