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Currying

2011-09-20T04:45:17Z

Pmgarvey: Redirected page to Curried Function

#Redirect[[Curried Function]]

Curried Function

2011-09-20T04:43:53Z

Pmgarvey: Created page with "A '''Curried Function''' is a concept in Computer Science and programming related to how a function takes in an argument and gives out a value. It is named for the logici..."

A '''Curried Function''' is a concept in [[Computer Science]] and [[programming]] related to how a function takes in an argument and gives out a value. It is named for the logician Haskell Curry.

==An Example of Why and How==

Imagine we have a [[function]] that multiplies two numbers together, call it ''multiply''. Clearly it must take two numbers as an argument (we'll just stick with [[integers]] for simplicity).. However we're restricted by functional languages which only let us give one value as input to a function. The obvious answer is to package the two numbers together as a new value, called a [[tuple]]. This function would be written in Haskell as

multiply :: (Integer,Integer) -> Integer
multiply (x,y) = x * y

Now let's say we multiply things by two a lot in our program, so rather than writing this out repeatedly we'll define a new function, which we'll call ''double''. We want to use our old function as we've already defined it (obviously it's not too much effort with multiplication, but the principles apply to complicated functions as well).

However we have a problem, there isn't a way of doing this. We don't have a tuple to give multiply. However, imagine if we defined multiply a new way.

Rather than giving multiply a tuple with two numbers, what if we only gave multiply one number. This function would then return another function, which took another number. This second function would then return the answer.

For example if we were multiplying 3 and 2, multiply would take 3, return a new function called ''multiply 3'' which takes 2 as its argument and returns 6.

In Haskell syntax we would define this as

multiply :: Integer -> Integer -> Integer
multiply x y = x * y

With this new defintion we can just set out function double to be multiply 2. In Haskell this is

double :: Integer -> Integer
double x = multiply 2 x

or if preferred

double = multiply 2

This latter style is called [[points free programming]].

This is called partial function application and is one of the greatest strengths of [[functional programming]].

Haskell

2011-09-20T04:30:45Z

Pmgarvey: Forgot functions as values

'''Haskell''' is a pure [[functional programming languages|functional programming language]] with roots in [[category theory]]. Free and [[open source]] implementations are available for a variety of operating systems.

==Functions in Haskell==

Functions are the most important idea in Haskell. A function takes a single value as input and returns a single value as output. Clearly it is often desirable to take in more than one argument or give out more than one. This can be done using [[tuples]] or [[lists]] but there is a very mathematically elegant and useful method called [[currying]], named for the logician Haskell Curry.

Functions in Haskell are also values in themselves, allowing Haskell to use [[higher-order functions]].

== Hello World ==

(display "hello world\n")

===External Links===
* [http://www.haskell.org| The HaskellWiki]

[[Category: Programming Languages]]

Haskell

2011-09-20T04:20:42Z

Pmgarvey: Added a section on functions, also Haskell (unlike Lisp) is category theory based rather than lambda calculus based.

'''Haskell''' is a pure [[functional programming languages|functional programming language]] with roots in [[category theory]]. Free and [[open source]] implementations are available for a variety of operating systems.

==Functions in Haskell==

Functions are the most important idea in Haskell. A function takes a single value as input and returns a single value as output. Clearly it is often desirable to take in more than one argument or give out more than one. This can be done using [[tuples]] or [[lists]] but there is a very mathematically elegant and useful method called [[currying]], named for the logician Haskell Curry.

== Hello World ==

(display "hello world\n")

===External Links===
* [http://www.haskell.org| The HaskellWiki]

[[Category: Programming Languages]]

Topology

2011-06-10T23:40:47Z

Pmgarvey: Added a section that introduces those who have not met topology before to it in a non-rigorous way, free of jargon

'''Topology''' is a branch of advanced [[mathematics]] devoted to spatial relationships. It can also be described as the manipulation and [[mapping]] of sets. Traditionally the field was divided into the fields of [[continuous topology]] and [[geometric topology]]. Now, however, the subject of topology is divided into:

*[[algebraic topology]]
*[[point-set topology]]

Topology also has a specific mathematical definition as a collection of [[open set]]s in a [[topological space]]. The open sets can be manipulated, forming the [[basis]] of the topology. The opposite of open sets are [[closed set]]s. Topology may also be defined in terms of closed sets, but this yields an [[equivalence relation|equivalent]] definition.

In topology, a ''[[genus (mathematics)|genus]]'' of a surface is the greatest number of distinct, [[continuous]] [[closed_set|closed]] [[curve]]s that may be drawn on it without separating the surface into distinct regions. The closed curves cannot be self-intersecting. The genus of the surface of a [[sphere]] is 0, while the genus of a [[torus]] (doughnut shape) is 1.

If you draw a circle on a sphere, then you can put a point A inside the circle and a point B outside the circle. The only way to connect A to B would have to cross the circle. So drawing the circle divides the surface of the sphere into two regions. But you can draw a circle around the edge (rim) of a torus without creating two regions. You can get from point A on one side of the line to point B on the other side, by going through the hole in the center.

==Introduction==

Topology is a branch of mathematics. Like geometry, it studies shapes, but it focuses on certain properties of them. For example, length is not a topological property, so to a topologist, a line of length 20 metres and one of length 2 metres are the same. Nor are angles, or curvature, so a topologist would say that triangles and circles are also undistinguishable.

A way of thinking about topology (albeit a non-rigorous one) is that two shapes are topologically the same, if they can be transformed into one another if one can be turned into the other by stretching it (or parts of it), but there must be no cutting of the shape. If you imagine the objects are made of clay then you can stretch or compress the clay or pull it around, but you cannot tear it at any point.

[[category:mathematics]][[Category:Topology]]

New Testament

2011-06-10T22:02:30Z

Pmgarvey: added a note about the language of the new testament

{{Bible}}

The '''New Testament''' is a collection of biblical books written by various authors between 45 AD and 100 AD, revolving around the life and work of [[Jesus]] of Nazareth and His apostles, as well as the history of the early church.

The books are traditionally classified into categories:

*The four [[Gospel]]s (literally "Good news"): [[Alleged Bible contradictions|varying]] accounts of the life and ministry of [[Jesus]], consisting of the gospels attributed to [[Saint Matthew|Matthew]], [[Gospel of Mark|Mark]], [[Luke]], and [[John the Apostle|John]].

*[[The Acts of the Apostles]] (or just "Acts") (which J. B. Phillips evocatively called "The Young Church In Action,") which concerns the ministry of the Apostles after the death of Christ. It is similar in language and style to, and reads as a continuation of, the Gospel of [[Luke]].

*[[The Epistles]] (which J. B. Phillips called "Letters to Young Churches,") ''Romans'' through ''Jude'', consisting of fourteen letters attributed to St. Paul and seven by other writers including James, [[Saint Peter|Peter]], John, and Jude. The writer of Hebrews is unknown.

*[[The Book of Revelation]] (or just "Revelation,") the prophetic book which ends the New Testament. It is also known as "the Apocalypse" (Greek for 'revelation'). It is somewhat similar in style to the [[Old Testament]] book of [[Daniel]] (and indeed weaves common prophecy), and tells of the end of the world, including [[Armageddon]], Judgment Day, and the arrival of the Kingdom of Heaven. Despite Jesus' thrice repeated promise in it that 'I shall come very soon', opinions vary as to whether it refers to imminent events set amid the then Roman Empire or to the far future.

As with the Old Testament, the chapter and verse divisions of the various books are not original, but were added in medieval times for greater understanding.

The oldest books in the New Testament are the letters of [[Paul]], or possibly the book of [[St. James the Less|James]].

==Books of the New Testament Canon==
[[Image:Rylands papyrus verso.jpg|thumb|Rylands papyrus, verso, (P52); containing on the one side part of St. John's Gospel verses 31-33, on the other of verses 37-38 of chapter xviii.]]
*[[Gospel of Matthew]]
*[[Gospel of Mark]]
*[[Gospel of Luke]]
*[[Gospel of John]]
*[[Acts of the Apostles]]
*[[Epistle to the Romans]]
*[[First Epistle to the Corinthians]]
*[[Second Epistle to the Corinthians]]
*[[Epistle to the Galatians]]
*[[Epistle to the Ephesians]]
*[[Epistle to the Philippians]]
*[[Epistle to the Colossians]]
*[[First Epistle to the Thessalonians]]
*[[Second Epistle to the Thessalonians]]
*[[First Epistle to Timothy]]
*[[Second Epistle to Timothy]]
*[[Epistle to Titus]]
*[[Epistle to Philemon]]
*[[Epistle to the Hebrews]]
*[[Epistle of James]]
*[[First Epistle of Peter]]
*[[Second Epistle of Peter]]
*[[First Epistle of John]]
*[[Second Epistle of John]]
*[[Third Epistle of John]]
*[[Epistle of Jude]]
*[[Book of Revelation|Revelation]]

== See also ==

*[[The Twelve Apostles]]
*[[Virgin Mary]]
*[[New Testament understanding through the Jewish perspective]]
*[[Famous Bible paintings]]

==References==
<references/>

==Sources==

* Cruden, A., ''Complete Concordance to the Old and New Testaments'' (Lutterworth, 1930)
* Cross, C., ''Who Was Jesus?'' (Hodder & Stoughton, 1970)
* ''The Holy Bible'' (King James Version)
* James, M. R., ''The Apocryphal New Testament'' (Clarendon, Oxford, 1953)
* ''The New English Bible'' (Oxford & Cambridge University Presses, 1970)
* ''The New Jerusalem Bible'' (Darton, Longman & Todd, 1990)
* Lemesurier, P., ''The Armageddon Script'' (Element Books, 1981)
* Peake, A. S., ''Commentary on the Bible'' (Nelson, 1962)
* Schonfield, H. J., ''The Authentic New Testament'' (Dobson, n.d.)
* Schonfield, H. J., ''The Passover Plot'' (Hutchinson, 1965)
* Schonfield, H. J., ''The Pentecost Revolution'' (Macdonald, 1974)
* Schonfield, H. J., ''Those Incredible Christians'' (Bernard Geis, New York, 1968)
* Vermes, G., ''Jesus the Jew'' (Collins, 1973)
* Young, R., ''Analytical Concordance to the Holy Bible'' (Lutterworth, 1939)

==Language==
The books of the New Testament are written in [[Koine Greek]], a form of Greek used as a lingua franca around the eastern part of the Roman Empire at the time, rather than the [[Aramaic]] that would have actually been spoken in the events described.

== External Links ==

*[http://www.swartzentrover.com/cotor/E-Books/papers/acceptnt.htm Acceptance of the New Testament Canon]
*[http://www.swartzentrover.com/cotor/E-Books/christ/Interliner/Greekindex.htm The Interlinear Translation of the Greek New Testament]
*[http://www.swartzentrover.com/cotor/E-Books/christ/bruce/ntdocindex.htm THE NEW TESTAMENT DOCUMENTS Are they Reliable?]
*[http://www.swartzentrover.com/cotor/Bible/Bible/NT/Chorology%20of%20Important%20New%20Testament%20Manuscripts.htm Chorology of Important New Testament Manuscripts]

[[Category:Christianity]]
[[Category:New Testament| ]]

Computer science

2011-06-10T21:46:59Z

Pmgarvey: added some info on algorithms, and the pioneers of the subject

'''Computer science''' is the study of various aspects of [[computers]]. It is a common course of study and degrees at the college level and beyond.

Studies can range from the very practical, such as learning [[programming language]]s, to the highly theoretical.

Students who plan to study computer science should take as many [[mathematics]] courses as possible. While not all of computer science is directly mathematical, the mental discipline that comes from studying math is very useful in studying computers. Computer Science was originally (and still by some) viewed as a branch of mathematics, the earliest discoveries in the discipline being made by mathematicians. Some of the earliest pioneers were [[Alan Turing]], [[Alonzo Church]] and [[John von Neumann]], all mathematicians.

==Algorithms==
An [[algorithm]] is the fundamental concept of Computer Science. An algorithm is simply a finite set of instructions to accomplish any task. A computer is simply a machine to carry out algorithms so you don't have to. The [[MIT]] book, Introduction to Algorithms, is viewed as the canonical basic reference and would be good for anyone interested. It is however expensive.

==Common programming languages in Computer Science==
*[[Java]]
*[[C++|C/C++]]
*[[C#]]
*[[Python]], and its [[Java]] implementation [[Jython]]
*[[Matlab]]

==Theoretical Computer Science==
[[Theoretical computer science]] is the mathematical study of what can and cannot in principle be computed under various constraints. For example, [[Alan Turing]] [[halting problem|proved]] that it is impossible to write a computer program that can determine whether other computer programs will ever ''halt'', or whether they will run forever. Other problems which can be solved in principle seem impossible to solve efficiently. For example, the famous P vs. NP problem asks whether there exists a polynomial time algorithm to solve any NP-complete problem, like the [[travelling salesman problem]]. There is a $1,000,000 prize for the solution to the P vs. NP problem.

[[Category:Information technology]]
[[Category:Computer Science]]