Home  - Mathematical_Logic - Recursion Theory
 Images Newsgroups
 Page 1     1-60 of 60    1

1. Recursion Theory - Wikipedia, The Free Encyclopedia
Recursion theory, also called computability theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions
http://en.wikipedia.org/wiki/Recursion_theory
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
##### Recursion theory
Jump to: navigation search For the branch of computer science called computability theory, see Computability theory (computer science) Recursion theory , also called computability theory , is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees . The field has grown to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory The basic questions addressed by recursion theory are "What does it mean for a function from the natural numbers to themselves to be computable?" and "Can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched. Recursion theorists in mathematical logic often study the theory of relative computability, reducibility notions and degree structures described in this article. This contrasts with the theory of subrecursive hierarchies formal methods and formal languages that is common in the study of computability theory in computer science . There is considerable overlap in knowledge and methods between these two research communities, however, and no firm line can be drawn between them.

2. Logic, 8
Notes from the class taught by Prof. Sacks in the Spring of 1998.
http://www.media.mit.edu/physics/pedagogy/babbage/texts/rt.html
 Introduction to Logic and Recursion Theory This is a transcription of relevant notes from the class 18.511 taught by Prof. Sacks in the Spring of 1998, organized and reinterpreted. Homework problems starting with problem 9 are solved in vitro. Notation is indecipherable. Propositional Calculus Propositional calculus is an example of a formal system . One must specify atomic symbols , which consist of letters A n , or symbols, and connectives expression is a finite sequence of atomic symbols. The set of well-formed formulas (WFFs) is defined recursively as follows: (A n g). This lets up build up new propositions from old ones. They are associative, etc. in the commonly held sense of these notions. A truth valuation c to the set of all WFFs, simply given by defining it recursively in the obvious fashion. Two WFFs are semantically equivalent disjunctive normal form semantically complete . It is obvious that we cannot discard the ! symbol, but one can combine the two to make the NAND operator, which is, all by itself, semantically complete, the Schaeffer stroke . In quantum logic, the CNOT is semantically complete, combined with an arbitrary unitary operator.

3. Computability Theory
Information on this site includes a Bibliographic Database for Computability theory, a list of Open Questions in Recursion theory as well as links to many
http://www.nd.edu/~cholak/computability/computability.html
##### Computability Theory
• Bibliographic Database for Computability Theory
• Open Questions in Recursion Theory
• Other Useful Sites:
• People who work (or have worked) in Computability Theory:
• People whose work had great impact on the field:
• Computability Theory E-mailing List
• Research Announcements
• Meetings (see the Association for Symbolic Logic for ASL meetings)
• Research Grants
• Graduate School in Computability Theory
• Job Announcements As with most web pages, this page is a continuously evolving resource. It will only develop into a useful resource for computability theorists if they help by adding information related to computability theory to the web and this page. Therefore computability theorists are encouraged to add information and links to this page. There are two ways of achieving this. The preferred method is to add the information to the web yourself and
• 4. Classical Recursion Theory - Elsevier
1988 marked the first centenary of Recursion theory, since Dedekind s 1888 paper on the nature of number. Now available in paperback, this book is both a
http://www.elsevier.com/wps/product/cws_home/502130
 Home Site map Elsevier websites Alerts ... Classical Recursion Theory Book information Product description Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view CLASSICAL RECURSION THEORY The Theory of Functions and Sets of Natural Numbers To order this title, and for more information, click here By P. Odifreddi Included in series Studies in Logic and the Foundations of Mathematics, 125 Description 1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Contents Recursiveness and Computability. Induction. Systems of Equations. Arithmetical Formal Systems. Turing Machines. Flowcharts. Functions as Rules. Arithmetization. Church's Thesis. Basic Recursion Theory. Partial Recursive Functions. Diagonalization. Partial Recursive Functionals. Effective Operations. Indices and Enumerations. Retraceable and Regressive Sets. Post's Problem and Strong Reducibilities.

5. Program On Computation Prospects Of Infinity - IMS
Open Forum Future on Recursion theory. Tuesday, 2 Aug 2005. 0930am 1030am. Definable ideals and quotient structures in R
http://www.ims.nus.edu.sg/Programs/infinity/activities2.htm
var imgdir = "../../images/"; var urldir = "../../"; Back to Program Overview Workshops/Tutorials
Registration form
MSWord
PDF PS Membership application form
MSWord
PDF PS Enquiries
General

Scientific aspects
##### Computational Prospects of Infinity (20 Jun - 15 Aug 2005)
Organizing Committee Confirmed Visitors Overview Activities ... Membership Application Recursion Theory Schedule of Talks and Tutorials Week 1 Â· Week 2 Week 3 Week 4 Monday, 18 Jul 2005 Tutorial: Algorithmic randomness (Lecture 1)
Rod Downey, Victoria University of Wellington, New Zealand
Lecture notes: PDF... Presentation slides: PDF... - Coffee Break - - Lunch Break - Process on the c.e. sets: Improving and proving the Slaman-Woodin conjecture
Peter Cholak, University of Notre Dame, USA
Presentation slides: PDF... - Coffee Break - A 1-generic degree with a strong minimal cover Masahiro Kumabe, University of the Air, Japan Tuesday, 19 Jul 2005

6. Recursion Theory And Joy
The final section discusses the more practical Recursion combinators of Joy. Previous knowledge of the field of Recursion theory is not assumed.
http://www.latrobe.edu.au/philosophy/phimvt/joy/j05cmp.html
Global Utilities Search: Global Navigation You are here: University home Philosophy Program Home page for Manfred von Thun Recursion Theory and Joy TITLE>Recursion Theory and Joy
##### Recursion Theory and Joy
by Manfred von Thun Abstract: Joy is a functional programming language which is not based on the application of functions to arguments but on the composition of functions. Many topics from the theory of computability are particularly easy to handle within Joy. They include the parameterisation theorem, the recursion theorem and Rice's theorem. Since programs are data, it is possible to define a Y-combinator for recursion and several variants. It follows that there are self-reproducing and self-describing programs in Joy. Practical programs can be written without recursive definitions by using several general purpose recursion combinators which are more intuitive and more efficient than the classical ones. Keywords: functional programming, functionals, computability, diagonalisation, program = data, diagonalisation, self-reproducing and self-describing programs, hierarchy of recursion combinators, elimination of recursive definitions.

7. Recursion Theory, Or Recursive Function Theory (logic) --Â Britannica Online Enc
Kleene, together with Alonzo Church, Kurt GÃ¶del, Alan Turing, and others, developed the field of Recursion theory, which made it possible to prove whether
http://www.britannica.com/eb/topic-493971/recursion-theory
Already a member? LOGIN EncyclopÃ¦dia Britannica - the Online Encyclopedia Home Blog Advocacy Board ... Free Trial Britannica Online Content Related to
this Topic Shopping
Revised, updated, and still unrivaled.
2008 Britannica Ultimate DVD/CD-ROM

The world's premier software reference source.
Great Books of the Western World

The greatest written works in one magnificent collection. Visit Britannica Store
##### recursion theory, or recursive function theory (logic)
A selection of articles discussing this topic. metalogic
##### modern logic
...on what cannot be validly deduced from a set of material hypotheses. One attempts to find structures about which the hypotheses are true and yet for which a particular statement is false. Third is recursion theory, which deals with questions involving the decidability of the question of whether or not a sentence is deducible from a set of premises. This study has led to theories of... No results were returned. Please consider rephrasing your query. For additional help, please review Search Tips Search Britannica for recursion theory About Us Legal Notices ... Test Prep Other Britannica sites: Australia France India Korea ... Encyclopedia

8. LtU Classic Archives
Recursion theory and Joy started 1/13/2003; 50955 AM last post 1/15/2003; 52426 PM Michael Vanier - Re Recursion theory and Joy blueArrow
http://lambda-the-ultimate.org/classic/message5521.html
##### Lambda the Ultimate
Recursion Theory and Joy
started 1/13/2003; 5:09:55 AM - last post 1/15/2003; 5:24:26 PM Ehud Lamm - Recursion Theory and Joy
1/13/2003; 5:09:55 AM (reads: 1792, responses: 6) Recursion Theory and Joy Joy is a functional programming language which is not based on the application of functions to arguments but on the composition of functions. Many topics from the theory of computability are particularly easy to handle within Joy. They include the parameterisation theorem, the recursion theorem and Rice's theorem. Since programs are data, it is possible to define a Y-combinator for recursion and several variants. It follows that there are self-reproducing and self-describing programs in Joy. Practical programs can be written without recursive definitions by using several general purpose recursion combinators which are more intuitive and more efficient than the classical ones. A short discussion of such cool things as fixed point combinators, Kleene's S-m-n theorem, and Rice's theorem. Along the line you are introduced to Goedel numbering and self-reproducing programs.

 9. Oxford University Press: Recursion Theory For Metamathematics: Raymond M. Smully Recursion theory for Metamathematics. Raymond M. Smullyan. bookshot Add to Cart. ISBN13 9780195082326ISBN10 019508232X hardback, 184 pageshttp://www.oup.com/us/catalog/general/subject/?view=usa&sf=toc&ci=019508232X

10. [hep-th/9412048] The Diagonalization Method In Quantum Recursion Theory
The diagonalization method in quantum Recursion theory. Authors Karl Svozil Comments 6 pages, updated and revised, presented at the Workshop Quantum
http://arxiv.org/abs/hep-th/9412048
##### arXiv.orghep-th
Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
Citations
p revious n ... ext
##### Title: The diagonalization method in quantum recursion theory
Authors: Karl Svozil (Submitted on 6 Dec 1994 (v1), last revised 21 Sep 2004 (this version, v2)) Abstract: Due to the continuity of quantum states, classical diagonalization has to be revised for quantum recursion theory. Comments: 6 pages, updated and revised, presented at the Workshop "Quantum Information" (Portoconte, Sardinia, Italy, September 23-25, 2004) Subjects: High Energy Physics - Theory (hep-th) ; Quantum Physics (quant-ph) Cite as: arXiv:hep-th/9412048v2
##### Submission history
From: Svozil Karl [ view email
Tue, 6 Dec 1994 10:32:51 GMT ( not stored
Tue, 21 Sep 2004 18:40:00 GMT (6kb)
Which authors of this paper are endorsers?
Link back to: arXiv form interface contact

11. Recursion Theory
Recursion theory. theory The study of problems that, in principle, cannot be solved by either computers or humans. Proper definition? (199903-01)
http://burks.brighton.ac.uk/burks/foldoc/12/97.htm
The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: recursion Next: recursive
##### recursion theory
theory [Proper definition?]

12. Dr Benedikt Loewe: Recursion Theory (1st Semester 2004/2005)
Content of the courseThis lecture course will cover the basics of Recursion theory (models of computation, limitative theorems) and discuss the connections
http://staff.science.uva.nl/~bloewe/2004-I-RT.html
 Recursion Theory 2004/2005; 1st Semester Universiteit van Amsterdam Instructor: Dr Benedikt LÃ¶we , Dr Maricarmen MartÃ­nez Vakcode: Time and place: Tuesday 13-15, P.014 ; Friday 11-13, P.018 Course language: English Intended Audience: M.Sc. students of Logic and Mathematics Prerequisites: This course assumes mathematical maturity and knowledge about first-order logic. Content of the course: This lecture course will cover the basics of recursion theory (models of computation, limitative theorems) and discuss the connections between recursion theory and the foundations of mathematics (GÃ¶del's Incompleteness Theorem). After that, recursion-theoretic hierarchies (Turing degrees) will be introduced. Literature: Barry Cooper, "Computability Theory" (Chapters 1-10). We will sell the book to enrolled students for EUR 32 in the break of the first lecture on September 7, 2004 (at a substantial discount compared to the list price of \$69.95). Organization: There will be 11 homework assignments for 6 points and one for 10 points, for a total of 76 points . The final grade will depend on the total number of homework points. A total of 40 points will be sufficient to pass the course. You can find your results from homework sets 1-7 listed by student ID

 13. JSTOR Techniques Of Admissible Recursion Theory. Admissible Recursion theory is the generalization of classical Recursion theory to those ordinals satisfying certain closure conditions.http://links.jstor.org/sici?sici=0022-4812(198703)52:1<285:TOART>2.0.CO;2-8

14. Lumpy Pea Coat: Recursion Theory
My Recursion theory was lacking so I finally cracked open Cutland s Computability (that I bought a long time ago and had sitting around the house).
http://nortexoid.blogspot.com/2007/06/recursion-theory.html
##### Lumpy Pea Coat
Logic and Mannequins
##### Recursion theory
My recursion theory was lacking so I finally cracked open Cutland's "Computability" (that I bought a long time ago and had sitting around the house). It's alright. The exercises are too easy (and a number of them too similar to others) and some of the proofs are sort of lame, not to mention nonconstructive. Just kidding about the nonconstructive part. I'm sure the Rogers text is much better, but these target different audiences (in terms of mathematical sophistication) which I hadn't realized when I picked this up.
Anyway, the s-m-n theorem and the Kleene normal form theorem are dope. So is the stuff on reducibility (of decision problems) and degrees of unsolvability. I wish he would've included at least a section on the arithmetical hierarchy. Thankfully it's in Mendelson, which I have.
Ha, some Asian guy just walked into the tea house I'm in and the server started talking Mandarin to him, but he's actually North American, so when he started speaking English she didn't know what the hell he said because she was expecting Chinese. She responds "whu!!". I bet some of these American/Canadian-born Asians have it hard in some parts of Asia, like Korea. Ok, nevermindyou had to be here, and be me.
I can't wait to be doing logic and philosophy full-time again. Teaching ESL sucks!!! Well, the money is better than anything I could've been doing back home on short notice (since I'm leaving in Sept.), but six days a week is killing me. However, I'm teaching the world a variety of semantic paradoxes one class at a time. (They just look strangely at meno joke.) And everybody thinks that the contradictory of "Everything is P" is "Nothing is P", unless I show them that both can be false. They baffle for a minute, think some more, nothing happens, then...burp.

15. FOM: Concepts Of Recursion Theory
In some recent communications, Steve has lamented that Recursion theory has gone astray. He says that in the beginning, computability was the central
http://cs.nyu.edu/pipermail/fom/1998-August/002024.html
##### FOM: Concepts of Recursion Theory
Joseph Shoenfield jrs at math.duke.edu

 16. A K Peters, Ltd. - Recursion Theory This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to Recursion theory.http://www.akpeters.com/product.asp?ProdCode=1497

17. Test Of Recursion Theory Of Localization: Numerical Evidence Of A Phase Transiti
Test of Recursion theory of Localization Numerical Evidence of a Phase Transition in Disordered TwoDimensional Potentials
http://www.iop.org/EJ/abstract/0295-5075/14/2/008
Create account
##### Test of Recursion Theory of Localization: Numerical Evidence of a Phase Transition in Disordered Two-Dimensional Potentials
T. J. Godin et al Europhys. Lett. 137-143 doi:10.1209/0295-5075/14/2/008 PDF (574 KB) References Articles citing this article
T. J. Godin
and R. Haydock
Department of Physics and Materials Science Institute, University of Oregon, Eugene, OR 97403, USA
Present address: Molecular Science Research Center K2-18, Battelle Pacific Northwest Laboratory, P.O. Box 999, Richland, WA 99352, USA Abstract. We report results of new calculations, highly resolved in energy, of quantum transmittance of disordered two-dimensional potentials using the block recursion method. Comparison is made to predictions of analytic calculations based on the recursion method. Consistent with these predictions, we find strong evidence that a kink, similar to a band edge singularity, exists in the inverse localization length as a function of energy. This feature is located near, but well inside, the band edge. A steep drop in the transmittance, similar to that of a crystal at the band edge, thus occurs at this energy. Such a "pseudo-mobility edge" (weak insulator-strong insulator transition) can be thought of as intermediate between 1D and 3D behavior. PACS numbers: 71.55.Jv, 72.15.Rn, 73.20.-r

18. Recursion Theory
Odifreddi, Classical Recursion theory; 2. Cutland, An Introduction to Recursive Function theory; 3. Rogers, theory of Recursive Functions and Effective
##### Recursion Theory
Odifreddi, Classical Recursion Theory
Cutland, An Introduction to Recursive Function Theory
Rogers, Theory of Recursive Functions and Effective Computability
The books listed above are only the most frequently recommended texts. There are many others that may be quite good.
root

19. Interdisciplines : Issues In Coevolution Of Language
Recursion, theory of mind and communication Anne Reboul May 17, 2004 834 UT I would like to begin by saying how much I enjoyed de Villiers paper.
http://www.interdisciplines.org/coevolution/papers/5/2
 and Theory of Mind : Why language first? English Conferences Bibliography Search ... About Us Why language first? Jill De Villiers Moderators: Peter Ford F. Dominey Anne Reboul Gloria Origgi Meme or Module? Two strikingly different opinions exist about the origins and ontogenesis of theory of Mind. One position posits it as a culturally transmitted meme, a theory of naÂ¯ve psychology that has proved sufficiently useful so as to occur to most if not all the human groups. The second posits a module genetically specialized for the understanding of mind-reading, sprung forth anew in every infant by virtue of being human (or maybe just a social primate). The meme view explains the four-year delay for false belief reasoning , though perhaps not the surprising invariance in the timetable. The module view explains the uniformity, but only at the cost of positing a moderating influence of Ã¢ÂÂprocessing capacityÃ¢ÂÂ or its kin, executive control, which must mature. Not surprisingly, two parallel opinions also exist about the origins and ontogenesis of human language. One position posits a cultural transmission, the other a genetic module. On the first view language learning will take time and experience, on the second it wonÃ¢ÂÂt, except for the vexing issues of the time needed to learn a arbitrary lexicon, and to sort out from primary data which set of parameters is appropriate.

20. Mathematical Logic - Math.umn.edu
Wayne Richter richter@math.umn.edu Associate Professor , Ph.D. 1963 Princeton University Recursion theory, set theory, finite model theory
Institute of Technology One Stop Directories Search U of M ...
##### Mathematical Logic
math page grad page research page
• Karel Prikry prikry@math.umn.edu
Professor , Ph.D. 1968 University of California Berkeley
set theory, measure theory, boolean algebras
• Wayne Richter richter@math.umn.edu
Associate Professor , Ph.D. 1963 Princeton University
recursion theory, set theory, finite model theory
Director of Graduate Studies in Mathematics
127 Vincent Hall
206 Church St. S.E.
Minneapolis, MN 55455 USA
The University of Minnesota is an equal opportunity educator and employer.
Enter keyword search Search Domain math.umn.edu umn.edu edu the internet

21. Books - Classical Recursion Theory - 9780444894830
Buy Classical Recursion theory The theory of Functions and Sets of Natural Numbers - Price Range \$65.95 - \$73.88 from 3 sellers.
http://www.pricegrabber.com/search_getprod.php/isbn=9780444894830
Go back to home page Login Register SHOP FOR IN All Products Appliances Auto Parts Books Cameras Clothing Computers Electronics Furniture Indoor Living Magazines Movies Music Musical Instruments Office Outdoor Living Software Sporting Goods Toys Video Games SEARCH Sell Yours Save Product to Your List(s) (Javascript required) Set Price Alert
##### Classical Recursion Theory (English)
(The Theory of Functions and Sets of Natural Numbers - ISBN: 9780444894830) Price range: from 5 Sellers Publisher: North-Holland Format: Paperback MSRP: \$ 65.95 Synopsis: 1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalen... Read More User Reviews Not Rated Write a Review New (1 Seller for \$73.88) View All Conditions Enter Zip Code* Seller Price (USD) Tax* Shipping* BottomLinePrice* Availability Seller Rating
Merchant Info

10% off
Free In Stock Fewer than 10 reviews
Amazon.com

22. Recursion Theory - Wiktionary
Recursion theory (uncountable). An alternate name for computability theory. Retrieved from http//en.wiktionary.org/wiki/Recursion_theory
http://en.wiktionary.org/wiki/recursion_theory
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wiktionary";
##### edit Noun
recursion theory uncountable
• An alternate name for computability theory

23. Phys. Rev. A 25 (1982): Yoram Tal And Mel Levy - Recursion Theory For Nonrelativ
A Recursion theory for the determination of binding energies and expectation values of r1 is presented and discussed for neutral atoms.
 Physical Review Online Archive Physical Review Online Archive AMERICAN PHYSICAL SOCIETY Home Browse Search Members ... Help Abstract/title Author: Full Record: Full Text: Title: Abstract: Cited Author: Collaboration: Affiliation: PACS: Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST PER Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article: MyArticles: View Collection Help (Click on the to add an article.) Phys. Rev. A 25, 1838 - 1845 (1982) Previous article Next article Issue 4 View Page Images PDF (1098 kB), or Buy this Article Use Article Pack Export Citation: BibTeX EndNote (RIS) Recursion theory for nonrelativistic ground-state atomic energies and expectation values of r Yoram Tal Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada Mel Levy Department of Chemistry, Tulane University, New Orleans, Louisiana 70118 Received 5 June 1981 A recursion theory for the determination of binding energies and expectation values of r is presented and discussed for neutral atoms. The derived recursion relations are parameter free and provide accurate estimates of

24. Recursion Theory - Wiki Browser By Chainofthoughts.com
Linear logic Firstorder logic Reduction (Recursion theory) Second-order arithmetic Reasoning Natural number List of set theory topics Computability logic
http://wiki.chainofthoughts.com/dt/en/Recursion theory
##### Recursion theory
Linear logic First-order logic Reduction (recursion theory) ... merkl

 25. Higher Recursion Theory Classical Recursion theory (CRT) applies to essentially finite sets of natural numbers. CRT predicates can be defined using the firstorder predicatehttp://portal.acm.org/citation.cfm?id=95355

26. UniTO-CS Dept: Complexity, Logic And Recursion Theory
Complexity, Logic and Recursion theory. Computer Science Dept. Univ. of Torino. The People. Lavinia Egidi Gabriele Lolli Piergiorgio Odifreddi
http://www.di.unito.it/WWW/comprec/homeCLR.html
##### Complexity, Logic and Recursion Theory
Computer Science Dept. -Univ. of Torino
##### The People:

27. CIDEC Library: Shoenfield * Recursion Theory
Recursion theory; Rekursive Funktionen; Hierarchietheorie; Unentscheidbare Theorien. M13100 Logic,Foundations,Set theory; M18021 Algebraic Geometry
http://cs.ioc.ee/yik/lib/1/Shoenfield1.html
Subject Area: CS Basics (Logics, Discrete Mathematics) in CIDEC Library
##### RECURSION THEORY
Joseph Robert SHOENFIELD , 1927- , Duke University, Durham, NC, USA Series: Lecture Notes in Logic . Vol. 1
Eds.: K. Fine; J.-Y. Girard; A. Lachlan; T. Slaman; H. Woodin. Publisher : Springer-Verlag - Berlin ; New York Bibliographic :
• Softcover 150g (acid-free)
• ISBN: 3-540-57093-4
• VII, 84 p. ; 24 cm
• Dewey No.: 511.3/5 20
• Recursion theory
• Rekursive Funktionen; Hierarchietheorie; Unentscheidbare Theorien
• M13100 Logic,Foundations,Set Theory
• M18021 Algebraic Geometry
• I16048 Mathematical Logic and Formal Languages
DESCRIPTION: This is an introduction to recursive functions intended for graduate students. It presupposes some mathematical maturity and a slight aquaintance with some important topics, such as group theory and topology. Some acquaintance with logic is desirable but not essential. It introduces the main topics of recusion theory, such as hierarchy theory, RE sets, and undecidable theories, without going very deeply into any of them. CONTENTS: Includes index.

28. Arithmetical Independence Results Using Higher Recursion Theory
Arithmetical independence results using higher Recursion theory. Andrew Arana. Source J. Symbolic Logic Volume 69, Issue 1 (2004), 18.
http://projecteuclid.org/handle/euclid.jsl/1080938820
##### Arithmetical independence results using higher recursion theory
Andrew Arana Source: J. Symbolic Logic Volume 69, Issue 1 (2004), 1-8.
##### References
Andrew Arana Solovay's theorem cannot be simplified Annals of Pure and Applied Logic , vol. 112 (2001), no. 1, pp. 2741.

29. Recursion Theory On The Reals And Continuous-Time Computation
Author(s) Cristopher Moore. 1995 Abstract We define a case of recursive functions on the reals analogous to the classical recursive functions on the
http://ideas.repec.org/p/wop/safiwp/95-09-079.html
##### This file is part of IDEAS , which uses RePEc data
Papers Articles Software Books ... Help!
##### Recursion Theory on the Reals and Continuous-Time Computation
Author info Abstract Publisher info Download info ... Statistics Author Info Cristopher Moore
Abstract

We define a case of recursive functions on the reals analogous to the classical recursive functions on the natural numbers, corresponding to a conceptual analog computer that operates in continuous time. This class turns out to be surprisingly large, and includes many functions which are uncomputable in the traditional sense. We stratify this class of functions into a hierarchy, according to the number of uses of the zero-finding operator mu. At the lowest level are continuous functions that are differentially algebraic, and computable by Shannon's General Purpose Analog Computer. At higher levels are increasingly discontinuous and complex functions. We relate this mu-hierarchy to the Arithmetical and Analytical Hierarchies of classical recursion theory. Download Info To our knowledge, this item is not available for download

 30. Recursion Theory @ Computer-Dictionary-Online.org Recursion theory @ Computer Dictionary Online. Computer terminology definitions including hardware, software, equipment, devices, jargon abbreviations andhttp://www.computer-dictionary-online.org/recursion theory.htm?q=recursion theor

 31. Recursion Theory From FOLDOC Nearby terms rectangle slinger Â« recurse Â« Recursion Â« Recursion theory Â» recursive Â» recursive acronym Â» recursive definition.http://foldoc.org/?recursion theory

32. From Danupam@stanford.edu Wed Jan 31 091601 2007 Date Wed, 31
(4) Optional reading Chapter 1 of the classic text on Recursion theory by Hartley Rogers, Jr. is recommended. You will find examples of primitive recursive
http://www.stanford.edu/class/cs258/recursion.txt
 From danupam@stanford.edu Wed Jan 31 09:16:01 2007 Date: Wed, 31 Jan 2007 09:15:22 -0800 (PST) From: Anupam Datta To: cs258-win0607-students@mailman.stanford.edu Cc: Arnab Roy , Anupam Datta

33. Richard A. Shore: Curriculum Vitae
Survey Lecture, 2nd Symposium on Generalized Recursion theory, Oslo, June 1977. Lecture Series, AMS Summer Research Institute in Recursion theory,
http://www.math.cornell.edu/~shore/vitae.html
##### Richard A. Shore : Curriculum Vitae
• Education
• Employment
• Invited Talks
• Grants ...
• Publications
##### Education
• A. B. Summa cum laude in Mathematics, Harvard University, 1968.
• Ph.D. in Mathematics, M.I.T., 1972.
##### Employment
• M.I.T., Teaching Assistant, 9/68-6/72.
• University of Chicago, Instructor, 10/72-9/74.
• Cornell University, Assistant Prof., 7/74-6/78; Associate Prof., 7/78-3/83; Prof., 4/83-.
• University of Illinois, Chicago, Assistant Professor, 1/77-8/77.
• University of Connecticut, Storrs, Visiting Associate Professor, 9/79-12/79.
• M.I.T., Visiting Associate Professor, 1/80-5/80.
• Hebrew University of Jerusalem, Visiting Professor, 9/82-6/83.
• University of Chicago, Visiting Professor, 2/87.
• University of Sienna, Italy, Visiting Professor, 5/87.
• MSRI, Berkeley, Member, 1989-1990.
• Harvard University, Visiting Scholar, 1/97-6/97.
• M.I.T., Visiting Scholar, 1/97-6/97.
• National University of Singapore, Distinguished Visiting Professor, 12/99-1/00.
• Harvard University, Visiting Scholar, 1/02-7/02.
##### Invited Talks
• Survey Lecture, Annual Meeting of the Assoc. for Symbolic Logic, Washington, D.C., January 1975.
• 20-minute talk, Special Session on Recursively Enumerable Sets and Degrees, AMS, Toronto, August 1976.
• 34. Recursion Theory F2003
We focused our attention on the fundamental results of Recursion theory the Normal Form, Enumeration, Parametre, and Recursion theorems, as reinforced by
http://www.it-c.dk/people/volodya/RTF2003.html
##### Seminar / reading group / project / PhD course
The exam (for the 12-week project, not the PhD course) takes place on Tuesday, June 24 in room starting at . Our internal censor is Lars Birkedal Literature. J. R. Shoenfield. Recursion Theory. Springer-Verlag 1993 (reprinted by A K Peters 2000, ISBN 1-56881-149-7). Episode 1, February 6, 2003. Sections 1 to 4 presented. Homework Exercises (corrected February 10) available for download. Nina's solution to Exercise 6 is now written up. Episode 2, February 13, 2003. We have discussed sections 5 through 7. The discussion unearthed an interesting question about whether there is a single `function algebra term' describing definition by cases for partial (recursive) functions. This question became Exercise 6 in Homework Exercises (corrected February 20). Episode 3, February 20, 2003. We have discussed homework exercises, as well as sections 8 and 9 from the textbook. We focused our attention on the fundamental results of Recursion Theory: the Normal Form, Enumeration, Parametre, and Recursion theorems, as reinforced by Homework Exercises . We have also agreed to accept Church's Thesis as a working hypothesis, at least unless and untill proven wrong.

35. Recursion Theory
Recursion theory. The field of recursive analysis develops natural number computation into a framework appropriate for the real numbers.
http://mulhauser.net/research/tutorials/computability/recursion.html
You have reached part of the Mulhauser Consulting legacy site. Please note that the legacy pages of the Mulhauser Consulting site have not been actively maintained since 2003. Please click to visit the current home page of Mulhauser Consulting, Ltd.
Sections Available: Computability Theory
• Classical/Halting
• Recursive Analysis
• Super-Turing ... Counselling
##### Scientific Research
Web mulhauser.net This article outlines a standard definition of computability for the real numbers.
##### Introduction
another short paper on the topic . The basic problem of incompleteness has been extended to its most general form by Greg Chaitin, and the theory of Turing computation over the naturals can be usefully developed to include algebra and fields ( Rabin 1960 ). But the fact that real physical systems are normally described by functions which take on real values motivates the extension of Turing computation to cover the real numbers

36. IngentaConnect A Blend Of Methods Of Recursion Theory And Topology: A 10 Tree Of
A blend of methods of Recursion theory and topology A 10 tree of shadow points. Authors Kalantari, Iraj1; Welch, Larry2. Source Archive for Mathematical
http://www.ingentaconnect.com/content/klu/153/2004/00000043/00000008/art00004
var tcdacmd="dt";
• Home About Ingenta Ingenta Labs Ingenta Blog ...
• Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers For Researchers For Librarians CM8ShowAd("HorizontalBanner");
Authors: Kalantari, Iraj ; Welch, Larry Source: Archive for Mathematical Logic , Volume 43, Number 8, November 2004 , pp. 991-1008(18) Publisher: Springer Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: tree of avoidable points tree of shadow points . This tree is a tree of sharp filters, where a sharp filter is a nested sequence of basic open sets converging to a point. In the construction we assign to each basic open set on the tree an address in 2 ) is isomorphic to the tree of addresses (a subtree of 2 ), the tree of addresses is recursively enumerable but not recursive. To achieve this end we use a finite injury priority argument.

37. Recursion Theory Â» Wikirage: What's Hot Now On Wikipedia
This site lists the pages in Wikipedia which are receiving the most edits per unique editor over various periods of time. Not to be confused with Wiki Rage
http://www.wikirage.com/wiki/Recursion_theory/
This site lists the pages in Wikipedia which are receiving the most edits per unique editor over various periods of time. 1-25 for Akatsuki (Naruto) I Am Legend (film) Nancy Reagan The Amazing Race 12 ... 2007 NFL season Summary from Wikipedia
##### Recent Edits
12:32, 21 December 2007 Jdrewitt Talk contribs (40,252 bytes) Undid revision 179379870 by talk 12:32, 21 December 2007 Talk (40,253 bytes) Frequency computation 12:31, 21 December 2007 Talk (40,252 bytes) Frequency computation 12:30, 21 December 2007 Talk (40,253 bytes) Inductive inference 08:50, 18 December 2007 Talk (40,255 bytes) Research papers and collections - +ja) 20:59, 28 November 2007 JMK Talk contribs m (40,235 bytes) 16:41, 28 October 2007 Talk (40,237 bytes) (interwiki) 16:35, 24 October 2007 Talk (40,215 bytes) Generalizations of Turing computability var AdBrite_Title_Color = '0000FF'; var AdBrite_Text_Color = '000000'; var AdBrite_Background_Color = 'FFFFFF'; var AdBrite_Border_Color = 'FFFFFF';
##### Historical Top Edits Rankings
1 Hours 3 Hours 6 Hours 12 Hours 24 Hours 48 Hours 72 Hours 168 Hours 336 Hours 672 Hours
##### Number of Unique Editors per 12 hour segments over last 28 days

 38. UM Mathematics My main area of interest is the subarea of Mathematical Logic known as Recursion theory (or, under an increasingly popular renaming, Computability theory).http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=pgh

39. Publications By Carl G. Jockusch
Degrees of generic sets, in Recursion theory its Generalisations and Applications, edited by F. R. Drake and S. S. Wainer, Cambridge University Press,
http://www.math.uiuc.edu/~jockusch/pubs.html
##### Publications by Carl G. Jockusch
• Semirecursive sets and positive reducibility, Trans. Amer. Math. Soc. Supplement to Boone's "Algebraic systems", in Contributions to Mathematical Logic Uniformly introreducible sets, J. Symbolic Logic The degrees of bi-immune sets, Z. Math. Logik Grundlagen Math. Countable retracing functions and P predicates (with T. G. McLaughlin), Pacific J. Math. Relationships between reducibilities, Trans. Amer. Math. Soc. The degrees of hyperhyperimmune sets, J. Symbolic Logic Minimal covers and arithmetical sets (with Robert I. Soare), Proc. Amer. Math. Soc. A minimal pair of P classes (with Robert I. Soare), J. Symbolic Logic P classes and degrees of theories (with Robert I. Soare), Trans. Amer. Math. Soc. Degrees of members of P classes (with Robert I. Soare), Pacific J. Math. Ramsey's theorem and recursion theory, J. Symbolic Logic A reducibility arising from the Boone groups, Mathematica Scandinavica Upward closure of bi-immune degrees, Z. Math. Logik Grundlagen Math. Degrees in which the recursive sets are uniformly recursive, Canad. J. Math.
• 40. Recursion Theory - UvA Course Catalogue - Course Description
Course code MOLRT6 Credits 6 Time Period(s) Semester 1 block 1 and 2 This lecture course will cover the basics of Recursion theory (models of computation,
http://studiegids.uva.nl/web/sgs/en/c/2050.html
var varUrlToOtherLanguage = 'http://studiegids.uva.nl/sgs/WebSite_nl'; var varLanguage='en'; var varCbgId = '2050_p.html'; /* do not remove */ writeHeaderImage('2007-2008'); writeArchiefImg('sgs') Search results
##### Recursion Theory
Course code Admin. code OWII Credits Entry requirements Mathematical maturity, some basic knowledge of first-order logic. Time Period(s) Semester 1 block 1 and 2 Educational institute Information Sciences Lecturer(s) dr. P.H. Rodenburg (co-ordinator) Is part of ... Master's in Mathematics Master's in Logic
##### Contents
This lecture course will cover the basics of recursion theory (models of computation, limitative theorems) and discuss the connections between recursion theory and the foundations of mathematics (GÂ¶del's Incompleteness Theorem). After that, recursion-theoretic hierarchies (Turing degrees) will be introduced.
##### Format
Lectures and Exercise Sessions.
##### Study materials
Barry Cooper, "Computability Theory" (Chapters 1-10).
##### Assessment
Homework; possibly a midterm and/or final exam.

41. Recursion Theory - Computing Reference - ELook.org
Previous Terms, Terms Containing Recursion theory, Next Terms . records Record Separator rectangle slinger recurse Recursion, Stephen Kleene, recursive
http://www.elook.org/computing/recursion-theory.htm
By Letter: Non-alphabet A B C ... Email this page to a friend
##### Recursion theory
[Proper definition?]
Terms Containing recursion theory records
Record Separator

rectangle slinger

recurse
... Contact

42. Bounded Queries In Recursion Theory
In Recursion theory one considers functions which can be computed by an algorithm. Computational complexity theory is dedicated to the study of the
http://www.ici.ro/ici/revista/sic2000_4/art15.htm
 Bounded Queries in Recursion Theory by William I. Gasarch and Georgia A. Martin Progress in Computer Science and Applied Logic: Vol. 16 ISBN 0-8176-3966-7 In recursion theory one considers functions which can be computed by an algorithm. Computational complexity theory is dedicated to the study of the difficulty of computations based on the notion of a measure of computational complexity in terms of the amount of some resources a program uses in a specific computation. An important measure of the complexity of a computable function is the time needed to compute it. Other resources, such as space , have also been considered. The object of the book is to classify functions which are not calculable from the point of view of their difficulty , in a quantitative way. For this, a new notion of complexity that is quantitative is introduced such that it expresses the level of difficulty of a function (such as the Turing degree). This work is a reflection of the contribution of the authors to the foundation and the development of a new direction of research in computational complexity theory. An oracle Turing machine is defined as a Turing machine together with an extra tape, an extra head to be used for reading that tape, and a mechanism to move the extra head and to overwrite characters on the extra tape. This notion is considered as a model of computation which extends the usual model of Turing machine to the power of asking questions - called

43. EconPapers: Recursion Theory On The Reals And Continuous-Time Computation
By Cristopher Moore; Abstract We define a case of recursive functions on the reals analogous to the classical recursive functions on the natural.
http://econpapers.repec.org/paper/wopsafiwp/95-09-079.htm
EconPapers Home
Working Papers
Journal Articles
... Format for printing EconPapers has moved to http://econpapers.repec.org! Please update your bookmarks.
##### Recursion Theory on the Reals and Continuous-Time Computation
Cristopher Moore Working Papers from Santa Fe Institute Abstract: We define a case of recursive functions on the reals analogous to the classical recursive functions on the natural numbers, corresponding to a conceptual analog computer that operates in continuous time. This class turns out to be surprisingly large, and includes many functions which are uncomputable in the traditional sense. We stratify this class of functions into a hierarchy, according to the number of uses of the zero-finding operator mu. At the lowest level are continuous functions that are differentially algebraic, and computable by Shannon's General Purpose Analog Computer. At higher levels are increasingly discontinuous and complex functions. We relate this mu-hierarchy to the Arithmetical and Analytical Hierarchies of classical recursion theory. Date: There are no downloads for this item, see the

44. Recursion Theory - Spock Search
Stephen Cole Kleene, Leo Harrington, Hartley Rogers Jr, Gerald Sacks, RÃ³zsa PÃ©ter, Andrzej Mostowski and other people matching \
http://www.spock.com/q/recursion-theory
 Processing (could take a few minutes)... You should enable javascript to use Spock Name or Email: Tags: Example: badminton Location: Example: San Francisco, CA Age: any to any male female any Must have picture! Click here to see where people you know are on the web Login Sign up Grid ... Stephen Cole Kleene male, deceased Logician Amherst College alumni computable function cleanliness ... Add tag Stephen Cole Kleene was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical... See: Tags (27) Pictures (5) Related People (0) News Web: Wikipedia infoshare1.princeton.edu math.library.wisc.edu nap.edu ... Leo Harrington male ErdÃÂs number 2 Logician ParisÃ¢ÂÂHarrington theorem recursion theory ... Add tag Leo Anthony Harrington is a professor of mathematics at the University of California, Berkeley who works in recursion theory, model theory, and... See: Tags (12) Pictures (0) Related People (0) News Web: Wikipedia math.berkeley.edu

45. Longo Symposium
In this perspective, Longo worked at some aspects of Recursion theory, Higher Type Recursion theory, Domain theory and Category theory as part of a unified
http://www.pps.jussieu.fr/~gc/other/rdp/talks.html
 28-29 June 2007 From Type Theory to Morphologic Complexity: A Colloquium in Honor of Giuseppe Longo In conjunction with RDP 2007 Paris, Conservatoire National des Arts et MÂ©tiers , Amphitheaters 3 and A. This colloquium was organised to celebrate the 60th birthday of Giuseppe Longo . Some photos of the meeting can be found here The main research area Giuseppe Longo has been interested in concerns syntactic and semantic properties of the "logical base" of functional languages: Combinatory Logic, Lambda-calculus and their extensions. However, he always investigated these topics in its broadest setting which relates them to Recursion Theory, Proof Theory and Category Theory. In this perspective, Longo worked at some aspects of Recursion Theory, Higher Type Recursion Theory, Domain Theory and Category Theory as part of a unified mathematical framework for the theory and the design of functional languages. In a sense, Longo has always been mostly interested in the "interconnecting results" or "bridges" and applications among different areas and to language design. He also worked at the applications of functional approaches to Object-Oriented programming. He is currently extending his interdisciplinary interests to Philosophy of Mathematics and Cognitive Sciences. A recent interdisciplinary project on Geometry and Cognition (started with the corresponding grant: "GÂ©omÂ©trie et Cognition", 1999 - 2002 with J. Petitot et B. Teissier), focused on the geometry of physical and biological spaces. The developements of this project lead to a new initiative at DI-ENS, in 2002, the setting up of the research team "ComplexitÂ© et information morphologiques" (CIM), centered on foundational problems in the interface between Mathematics, Physics and Biology.

 46. Intute: Science, Engineering And Technology - Search Results They discuss classical descriptive set theory, Borel sets, the influence of Recursion theory on descriptive set theory, analytic and coanalytic sets,http://www.intute.ac.uk/sciences/cgi-bin/search.pl?term1=recursion theory&limit=

47. 03Dxx
03D65 Highertype and set Recursion theory; 03D70 Inductive definability; 03D75 Abstract and axiomatic Recursion theory; 03D80 Applications of Recursion
http://www.ma.hw.ac.uk/~chris/MR/03Dxx.html
##### 03Dxx Recursion theory
• 03D03 Thue and Post systems, etc.
• 03D20 Recursive functions and relations, subrecursive hierarchies
• 03D25 Recursively enumerable sets and degrees
• 03D30 Other degrees; reducibilities
• 03D35 Undecidability and degrees of sets of sentences
• 03D50 Recursive equivalence types of sets and structures, isols
• 03D55 Hierarchies
• 03D60 Recursion theory on ordinals, admissible sets, etc.
• 03D65 Higher-type and set recursion theory
• 03D70 Inductive definability
• 03D75 Abstract and axiomatic recursion theory
• 03D80 Applications of recursion theory
• 03D99 None of the above but in this section
Top level of Index
Top level of this Section

48. Recursion Theory, Fall 2007
Recursion theory, fall 2007. Lecturer. AndrÃ©s Villaveces. Lectures. Weeks 3642 and 44-50, Monday 12Â14 and Thursday 12Â14 in room B322.
Department of Mathematics and Statistics
Faculty of Science

Faculty of Social Sciences

Departmental front page
News ... People
##### Lectures
Weeks 36-42 and 44-50, Monday 12Â14 and Thursday 12Â14 in room B322. 2 hours of exercise classes per week.
10 op, 5 ov
##### Exercises
Group Day Time Place Instructor ke Andres Villaveces

49. Introduction To Recursion Theory
H Rogers, theory of recursive functions and effective computability, McGrawHill, New York, 1967; P Odifreddi, Classical Recursion theory, North-Holland,
http://www1.cuni.cz/~svejdar/courses/recfn.html
##### Introduction to Recursion Theory
Syllabus of the course
(Faculty of Philosophy, Charles University)
##### Goal of the Course
This course roughly follows chapters 1-7 and partly chapter 11 of the book [Rogers]. The introductory part is much more detailed than in [Rogers] and makes use mainly of [Odi].
K zÃ­skÃ¡nÃ­ zÃ¡poÃ¨tu je tÃ¸eba vyÃ¸eÂit nejmÃ©nÃ¬ 21 cviÃ¨enÃ­ z prvnÃ­ho dÃ­lu cviÃ¨enÃ­, viz soubor cvlog1 dole, a pÃ¸edloÂit jejich seznam. PoÂadavky ke zkouÂce jsou dÃ¡ny nÃ¡sledujÃ­cÃ­m sylabem, navÃ­c je tÃ¸eba vyÃ¸eÂit rovnÃ¬Â nejmÃ©nÃ¬ 21 cviÃ¨enÃ­ z druhÃ©ho dÃ­lu cviÃ¨enÃ­, viz soubor cvlog2, a takÃ© pÃ¸edloÂit jejich seznam. Neschopnost vyÃ¸eÂit nÃ¬kterÃ© cviÃ¨enÃ­ mÃ¹Âe mÃ­t za nÃ¡sledek opakovÃ¡nÃ­ zÃ¡poÃ¨tu resp. zkouÂky. Soubor cvalg2 obsahuje sylabus stejnÃ½ jako ten, kterÃ½ nÃ¡sleduje, avÂak v Ã¨eÂtinÃ¬.
##### Recursive Functions and Sets
Recursive functions (primitive, general, partial) and (primitive) recursive sets and relations. Definitions of these are accepted as a mathematical basis that captures the informal notion of algorithm. Derived operations on functions and predicates: Boolean operations, bounded quantifiers, bounded minimisation, definitions of a function by cases, inverse image of a set. ([DKK]: 96-111) Coding of finite sequences of natural numbers. Generalisation of the operation of primitive recursion (ordinal recursion). ([DKK]: 112-126)
##### Further Computational Models

50. Recursion Theory - Definitions From Dictionary.com
Definitions of Recursion theory at Dictionary.com.
http://dictionary.reference.com/browse/recursion theory
var pid = 506373; var nid = 506415; var mid = 679788; var word = 'recursion%20theory'; SafeAddOnload(init_near);
##### 1 result for: recursion theory

51. Recursion
Instead they use a technique known as Recursion . This turns out to be a very powerful technique for some types of problem, so we ll take a look at it now.
http://www.freenetpages.co.uk/hp/alan.gauld/tutrecur.htm
##### Recursion
What will we cover?
• A definition of recursion
• How recursion works
• How recursion helps simplify some hard problems
Note: This is a fairly advanced topic and for most applications you don't need to know anything about it. Occasionally, it is so useful that it is invaluable, so I present it here for your study. Just don't panic if it doesn't make sense straight away.
##### What is it?
Despite what I said earlier about looping being one of the cornerstones of programming it is in fact possible to create programs without an explicit loop construct. Some languages, such as Scheme, do not in fact have an explicit loop construct like For, While, etc. Instead they use a technique known as recursion . This turns out to be a very powerful technique for some types of problem, so we'll take a look at it now. Recursion simply means applying a function as a part of the definition of that same function. Thus the definition of GNU (the source of much free software) is said to be recursive because GNU stands for 'GNU's Not Unix'. ie GNU is part of the definition of GNU! The key to making this work is that there must be a terminating condition such that the function branches to a non-recursive solution at some point. (The GNU definition fails this test and so gets stuck in an infinite loop).

52. Recursion: Index
Let s explore the concepts of Recursion and recurrences. Recursion often allows easily expressing complex procedure, with often impressive results.
http://www.cs.cmu.edu/~cburch/survey/recurse/index.html
Up:
##### Recursion
Let's explore the concepts of recursion and recurrences . Recursion often allows easily expressing complex procedure, with often impressive results. We examine recursion through two specific examples: the Towers of Hanoi puzzle and exponentiation. This tutorial begins with a description of the Towers of Hanoi puzzle
##### Contents
General
What is recursion?
What is a recurrence?

Aside: Avoiding circularity

Aside: Fibonacci numbers
...
Aside: Other recursion pages
Towers of Hanoi