Mathematical induction (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Mathematical induction" in English language version.

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Acerbi 2000. Acerbi, Fabio (August 2000). "Plato: Parmenides 149a7-c3. A Proof by Complete Induction?". Archive for History of Exact Sciences. 55 (1): 57–76. doi:10.1007/s004070000020. JSTOR 41134098. S2CID 123045154.

ams.org

mathscinet.ams.org

Rabinovitch 1970. Rabinovitch, Nachum L. (1970). "Rabbi Levi Ben Gershon and the origins of mathematical induction". Archive for History of Exact Sciences. 6 (3): 237–248. doi:10.1007/BF00327237. MR 1554128. S2CID 119948133.
Peirce 1881. Peirce, Charles Sanders (1881). "On the Logic of Number". American Journal of Mathematics. 4 (1–4): 85–95. doi:10.2307/2369151. JSTOR 2369151. MR 1507856. Reprinted (CP 3.252–288), (W 4:299–309)
Shields 1997. Shields, Paul (1997). "Peirce's Axiomatization of Arithmetic". In Houser, Nathan; Roberts, Don D.; Evra, James Van (eds.). Studies in the Logic of Charles S. Peirce. Indiana University Press. pp. 43–52. ISBN 0-253-33020-3. MR 1720827.

archive.org

Anderson, Robert B. (1979). Proving Programs Correct. New York: John Wiley & Sons. p. 1. ISBN 978-0471033950.
Shields 1997. Shields, Paul (1997). "Peirce's Axiomatization of Arithmetic". In Houser, Nathan; Roberts, Don D.; Evra, James Van (eds.). Studies in the Logic of Charles S. Peirce. Indiana University Press. pp. 43–52. ISBN 0-253-33020-3. MR 1720827.

bnf.fr

visualiseur.bnf.fr

Cauchy, Augustin-Louis (1821). Cours d'analyse de l'École Royale Polytechnique, première partie, Analyse algébrique, Archived 14 October 2017 at the Wayback Machine Paris. The proof of the inequality of arithmetic and geometric means can be found on pages 457ff.

books.google.com

Rashed 1994, pp. 62–84. Rashed, R. (1994). "Mathematical induction: al-Karajī and al-Samawʾal". The Development of Arabic Mathematics: Between Arithmetic and Algebra. Boston Studies in the Philosophy of Science. Vol. 156. Springer Science & Business Media. ISBN 9780792325659.
Mathematical Knowledge and the Interplay of Practices "The earliest implicit proof by mathematical induction was given around 1000 in a work by the Persian mathematician Al-Karaji"
Rashed 1994, p. 62. Rashed, R. (1994). "Mathematical induction: al-Karajī and al-Samawʾal". The Development of Arabic Mathematics: Between Arithmetic and Algebra. Boston Studies in the Philosophy of Science. Vol. 156. Springer Science & Business Media. ISBN 9780792325659.
Peirce 1881. Peirce, Charles Sanders (1881). "On the Logic of Number". American Journal of Mathematics. 4 (1–4): 85–95. doi:10.2307/2369151. JSTOR 2369151. MR 1507856. Reprinted (CP 3.252–288), (W 4:299–309)

brilliant.org

"Forward-Backward Induction | Brilliant Math & Science Wiki". brilliant.org. Retrieved 23 October 2019.

cornell.edu

courses.cs.cornell.edu

"Proof:Strong induction is equivalent to weak induction". Cornell University. Retrieved 4 May 2023.

doi.org

Acerbi 2000. Acerbi, Fabio (August 2000). "Plato: Parmenides 149a7-c3. A Proof by Complete Induction?". Archive for History of Exact Sciences. 55 (1): 57–76. doi:10.1007/s004070000020. JSTOR 41134098. S2CID 123045154.
Cajori (1918), p. 197: 'The process of reasoning called "Mathematical Induction" has had several independent origins. It has been traced back to the Swiss Jakob (James) Bernoulli, the Frenchman B. Pascal and P. Fermat, and the Italian F. Maurolycus. [...] By reading a little between the lines one can find traces of mathematical induction still earlier, in the writings of the Hindus and the Greeks, as, for instance, in the "cyclic method" of Bhaskara, and in Euclid's proof that the number of primes is infinite.' Cajori, Florian (1918). "Origin of the Name "Mathematical Induction"". The American Mathematical Monthly. 25 (5): 197–201. doi:10.2307/2972638. JSTOR 2972638.
Rabinovitch 1970. Rabinovitch, Nachum L. (1970). "Rabbi Levi Ben Gershon and the origins of mathematical induction". Archive for History of Exact Sciences. 6 (3): 237–248. doi:10.1007/BF00327237. MR 1554128. S2CID 119948133.
Peirce 1881. Peirce, Charles Sanders (1881). "On the Logic of Number". American Journal of Mathematics. 4 (1–4): 85–95. doi:10.2307/2369151. JSTOR 2369151. MR 1507856. Reprinted (CP 3.252–288), (W 4:299–309)
Öhman, Lars–Daniel (6 May 2019). "Are Induction and Well-Ordering Equivalent?". The Mathematical Intelligencer. 41 (3): 33–40. doi:10.1007/s00283-019-09898-4.

earlham.edu

Suber, Peter. "Mathematical Induction". Earlham College. Archived from the original on 24 May 2011. Retrieved 26 March 2011.

emory.edu

mathcenter.oxford.emory.edu

"The Binomial Theorem". mathcenter.oxford.emory.edu. Retrieved 2 December 2024. That said, he was not the first person to study it. The Persian mathematician and engineer Al-Karaji, who lived from 935 to 1029 is currently credited with its discovery. (Interesting tidbit: Al-Karaji also introduced the powerful idea of arguing by mathematical induction.)

harvard.edu

math.harvard.edu

Gerardo con Diaz, Mathematical Induction Archived 2 May 2013 at the Wayback Machine, Harvard University

jstor.org

Acerbi 2000. Acerbi, Fabio (August 2000). "Plato: Parmenides 149a7-c3. A Proof by Complete Induction?". Archive for History of Exact Sciences. 55 (1): 57–76. doi:10.1007/s004070000020. JSTOR 41134098. S2CID 123045154.
Cajori (1918), p. 197: 'The process of reasoning called "Mathematical Induction" has had several independent origins. It has been traced back to the Swiss Jakob (James) Bernoulli, the Frenchman B. Pascal and P. Fermat, and the Italian F. Maurolycus. [...] By reading a little between the lines one can find traces of mathematical induction still earlier, in the writings of the Hindus and the Greeks, as, for instance, in the "cyclic method" of Bhaskara, and in Euclid's proof that the number of primes is infinite.' Cajori, Florian (1918). "Origin of the Name "Mathematical Induction"". The American Mathematical Monthly. 25 (5): 197–201. doi:10.2307/2972638. JSTOR 2972638.
Peirce 1881. Peirce, Charles Sanders (1881). "On the Logic of Number". American Journal of Mathematics. 4 (1–4): 85–95. doi:10.2307/2369151. JSTOR 2369151. MR 1507856. Reprinted (CP 3.252–288), (W 4:299–309)

semanticscholar.org

api.semanticscholar.org

Acerbi 2000. Acerbi, Fabio (August 2000). "Plato: Parmenides 149a7-c3. A Proof by Complete Induction?". Archive for History of Exact Sciences. 55 (1): 57–76. doi:10.1007/s004070000020. JSTOR 41134098. S2CID 123045154.
Rabinovitch 1970. Rabinovitch, Nachum L. (1970). "Rabbi Levi Ben Gershon and the origins of mathematical induction". Archive for History of Exact Sciences. 6 (3): 237–248. doi:10.1007/BF00327237. MR 1554128. S2CID 119948133.

sfu.ca

Matt DeVos, Mathematical Induction, Simon Fraser University

stonehill.edu

web.stonehill.edu

Simonson 2000. Simonson, Charles G. (Winter 2000). "The Mathematics of Levi ben Gershon, the Ralbag" (PDF). Bekhol Derakhekha Daehu. 10. Bar-Ilan University Press: 5–21.

web.archive.org

Gerardo con Diaz, Mathematical Induction Archived 2 May 2013 at the Wayback Machine, Harvard University
Suber, Peter. "Mathematical Induction". Earlham College. Archived from the original on 24 May 2011. Retrieved 26 March 2011.
Cauchy, Augustin-Louis (1821). Cours d'analyse de l'École Royale Polytechnique, première partie, Analyse algébrique, Archived 14 October 2017 at the Wayback Machine Paris. The proof of the inequality of arithmetic and geometric means can be found on pages 457ff.

yorku.ca

eecs.yorku.ca

.Shafiei, Niloufar. "Strong Induction and Well-Ordering" (PDF). York University. Retrieved 28 May 2023.