Difference between revisions of "Blog articles/Mathematics"
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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://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/2006/09/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] | ||
| Line 35: | Line 62: | ||
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-3.html Part 3: Fixed Precision] | ** [http://augustss.blogspot.com/2007/04/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] | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| + | === 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
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
Geometry
Group Theory
Set Theory
Ring Theory
Number Theory
Cryptography and Coding Theory
- Feistel Ciphers and DES in Haskell
- Arithmetic coding in Haskell
- Two-dimensional spatial hashing with space-filling curves
Logic
Numerics
- The Division Bell
- Overloading Haskell numbers
Theorem Proving
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
Mathematics of Haskell
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.