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* Axt, P. (1959) On a Subrecursive Hierarchy and Primitive Recursive Degrees, ''Transactions of the American Mathematical Society'' 92, pp. 85-105
* Axt, P. (1959) On a Subrecursive Hierarchy and Primitive Recursive Degrees, ''Transactions of the American Mathematical Society'' 92, pp. 85-105
*[http://research.microsoft.com/~gurevich/Opera/164.pdf|title=Algorithms: A Quest for Absolute Definitions|journal= Bulletin of European Association for Theoretical Computer Science|volume= 81]. Includes an excellent bibliography of 56 references.
*[https://research.microsoft.com/~gurevich/Opera/164.pdf|title=Algorithms: A Quest for Absolute Definitions|journal= Bulletin of European Association for Theoretical Computer Science|volume= 81]. Includes an excellent bibliography of 56 references.
*0-521-20402-X: cf. Chapter 3 ''Turing machines'' where they discuss "certain enumerable sets not effectively (mechanically) enumerable".
*0-521-20402-X: cf. Chapter 3 ''Turing machines'' where they discuss "certain enumerable sets not effectively (mechanically) enumerable".
* Burgin, M. ''Super-recursive algorithms'', Monographs in computer science, Springer, 2005. ISBN 0387955690
* Burgin, M. ''Super-recursive algorithms'', Monographs in computer science, Springer, 2005. ISBN 0387955690
*Engines of Logic: Mathematicians and the Origin of the Compute. Davis offers concise biographies of [[Leibniz]], [[Boole]], [[Frege]], [[Georg Cantor|Cantor]], [[Hilbert]], [[Gödel]] and [[Alan Turing|Turing]] with [[von Neumann]] as the show-stealing villain. Very brief bios of [[Joseph-Marie Jacquard]], [[Babbage]], [[Ada Lovelace]], [[Claude Shannon]], [[Howard Aiken]], etc.
*Engines of Logic: Mathematicians and the Origin of the Compute. Davis offers concise biographies of [[Leibniz]], [[Boole]], [[Frege]], [[Georg Cantor|Cantor]], [[Hilbert]], [[Gödel]] and [[Alan Turing|Turing]] with [[von Neumann]] as the show-stealing villain. Very brief bios of [[Joseph-Marie Jacquard]], [[Babbage]], [[Ada Lovelace]], [[Claude Shannon]], [[Howard Aiken]], etc.
*Darwin's Dangerous Idea
*Darwin's Dangerous Idea
*[[Yuri Gurevich]], [http://research.microsoft.com/~gurevich/Opera/141.pdf] ''Sequential Abstract State Machines Capture Sequential Algorithms''], ACM Transactions on Computational Logic, Vol 1, no 1 (July 2000), pages 77–111. Includes bibliography of 33 sources.
*[[Yuri Gurevich]], [https://research.microsoft.com/~gurevich/Opera/141.pdf] ''Sequential Abstract State Machines Capture Sequential Algorithms''], ACM Transactions on Computational Logic, Vol 1, no 1 (July 2000), pages 77–111. Includes bibliography of 33 sources.
*Recursive Predicates and Quantifiers, Reprinted in ''The Undecidable'', p. 255ff. Kleene refined his definition of "general recursion" and proceeded in his chapter "12. Algorithmic theories" to posit "Thesis I" (p. 274); he would later repeat this thesis (in Kleene 1952:300) and name it "Church's Thesis"(Kleene 1952:317) (i.e., the [[Church Thesis]]).
*Recursive Predicates and Quantifiers, Reprinted in ''The Undecidable'', p. 255ff. Kleene refined his definition of "general recursion" and proceeded in his chapter "12. Algorithmic theories" to posit "Thesis I" (p. 274); he would later repeat this thesis (in Kleene 1952:300) and name it "Church's Thesis"(Kleene 1952:317) (i.e., the [[Church Thesis]]).
*Introduction to Metamathematics|edition=Tenth Edition 1991
*Introduction to Metamathematics|edition=Tenth Edition 1991
*On Computable Numbers, With An Application to the Entscheidungsproblem|journal=Proceedings of the London Mathematical Society Corrections, ibid, vol. 43(1937) pp.544-546. Reprinted in ''The Undecidable'', p. 116ff. Turing's famous paper completed as a Master's dissertation while at King's College Cambridge UK.
*On Computable Numbers, With An Application to the Entscheidungsproblem|journal=Proceedings of the London Mathematical Society Corrections, ibid, vol. 43(1937) pp.544-546. Reprinted in ''The Undecidable'', p. 116ff. Turing's famous paper completed as a Master's dissertation while at King's College Cambridge UK.
*Systems of Logic Based on Ordinals, Proceedings of the London Mathematical Society Reprinted in ''The Undecidable'', p. 155ff. Turing's paper that defined "the oracle" was his PhD thesis while at Princeton USA.
*Systems of Logic Based on Ordinals, Proceedings of the London Mathematical Society Reprinted in ''The Undecidable'', p. 155ff. Turing's paper that defined "the oracle" was his PhD thesis while at Princeton USA.
*[http://www.uspto.gov/web/offices/pac/mpep/documents/2100_2106_02.htm] Mathematical Algorithms Patentability''], Manual of Patent Examining Procedure (MPEP). Latest revision August 2006
*[https://www.uspto.gov/web/offices/pac/mpep/documents/2100_2106_02.htm] Mathematical Algorithms Patentability''], Manual of Patent Examining Procedure (MPEP). Latest revision August 2006
=== Secondary references ===
=== Secondary references ===
*Turing's Man: Western Culture in the Computer Age, ISBN 0-8078-4108-0 pbk.
*Turing's Man: Western Culture in the Computer Age, ISBN 0-8078-4108-0 pbk.
== External links ==
== External links ==
* [http://everydaymath.uchicago.edu/educators/Algorithms_final.pdf Algorithms in Everyday Mathematics]
* [https://everydaymath.uchicago.edu/educators/Algorithms_final.pdf Algorithms in Everyday Mathematics]
* [http://sortieralgorithmen.de/ Sortier- und Suchalgorithmen (German)]
* [https://sortieralgorithmen.de/ Sortier- und Suchalgorithmen (German)]
[[Category: Mathematics]]
[[Category: Mathematics]]
[[Category: Computer Science]]
[[Category: Computer Science]]
