Some Playing with Derivatives
This is a summary of what I’ve been playing with in case people find it interesting. In general, there are three ways to find the derivative of a function: Do the symbolic manipulation of formulae that we all learned in school when we were 16 years old. This assumes that one has the function as an algebraic expression of some kind in terms of known quantities. Do it numerically, by computing (f(x
Haskell and mathematics - HaskellWiki
Haskell is growing in popularity among mathematicians. As one blogger put it: "after my involving myself in the subject, one thing that stands out is the relatively low distance between thought expressed in my ordinary day-to-day mathematical discourse, and thought expressed in Haskell code." and "How can Haskell not be the programming language that all mathematicians should learn?" This page coll
Blog articles/Mathematics - HaskellWiki
Articles using Haskell for mathematics, and the mathematics of Haskell. For further references see the: Haskell math community. Mathematics of monads 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
evan_tech -- powerset
For those of us who found this somwhat (but not totally) unaccessible, i'd recommend reading [[Schwartzian Transform]] to get into apprximately the right head-space, then [[Monads in functional programming]]. Oh man is that hard for me to grok, mostly because I haven't internalized the list monad. avva and I were puzzling over it too; here's how we figured it out. First, in terms of types, yes, it
Type arithmetic - HaskellWiki
Type arithmetic (or type-level computation) are calculations on the type-level, often implemented in Haskell using functional dependencies to represent functions. A simple example of type-level computation are operations on Peano numbers: data Zero data Succ a class Add a b ab | a b -> ab, a ab -> b instance Add Zero b b instance (Add a b ab) => Add (Succ a) b (Succ ab) Many other representations
The Haskell Road to Logic, Maths and Programming
Sample from the book (table of contents plus first chapter): compressed postscript Addendum to Chapter 9 of the Book: Direct Computation of Polynomial Representations for Sequences: PolAddendum.pdf PolAddendum.hs Errata A list of errata is here. Software Getting Started: GS.hs Talking about Mathematical Objects: TAMO.hs The Use of Logic: Proof: TUOLP.hs Sets, Types and Lists: STAL.hs Database used
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Peano's Axioms IV: Advanced Functions and Integers