Difference between revisions of "Computer science"

''Computer Science is no more about computers than astronomy is about telescopes''.

-- E. W. Dijkstra

__TOC__

== Introduction ==

Wikipedia's [http://en.wikipedia.org/wiki/Computer_science Computer science].

[http://www.cs.bham.ac.uk/~mhe/ Martín Escardó] maintains a [http://www.math.niu.edu/~rusin/known-math/index/68-XX.html Computer science] page, being both detailed and comprehensive. The Dijkstra-quotation cited above comes from this page.

[http://mitpress.mit.edu/sicp/full-text/book/book.html Structure and Interpretation of Computer Programs] (by Harold Abelson and Gerald Jay Sussman

with Julie Sussman, foreword by Alan J. Perlis).

== Computability theory ==

Wikipedia's [http://en.wikipedia.org/wiki/Computability_theory Computability theory].

An interesting area related to computabilty theory: [[Exact real arithmetic]]. For me, it was surprising, how it connected problems in mathematical analysis, arithmetic and computability theory.

== To do ==

There are several (equivalent) definitions to the concept of ''algorithm'':

* [[Turing machine]]

* [[Combinatory logic]]

* [http://en.wikipedia.org/wiki/Markov_algorithm Markov algorithm]

* [http://en.wikipedia.org/wiki/Post_system Post system]

* [[Recursive function theory]]

* ...

These can be conceived also as computer programming languages -- there should be implemented as many of them as possible.

And some of them can be very good for making such jokes as

* [[Combinatory logic#Self-replication.2C_quines.2C_reflective_programming|self replication programs or self-representing formulas]]

* metacircular interpreters.

At least

* to write a combinatory logic expression which is equivalent to its own quotation (term representation)

* to specify and implement a programming language, which could be seen as an experimentable, playable incarnation of [[recursive function theory]] -- it could yield a playground for learning concepts like [http://www.madore.org/~david/computers/quine.html iteration theorem, recursion theorem, fixed point theorem]

Although there are many differences between [[Combinatory logic]] and recursive function theory, I suspect they have some important common features

* both of them allow us to avoid the concept of variable

* both of them can be used well for metaprogramming

[[Algorithmic information theory]] may exemplify relatedness of computer science to [http://en.wikipedia.org/wiki/Philosophy_of_mathematics philosophical] and [http://en.wikipedia.org/wiki/Foundations_of_mathematics foundational] questions of [[mathematics]].

[[Category:Theoretical foundations]]