Linked bibliography for the SEP article " Dedekind's Contributions to the Foundations of Mathematics" by Erich Reck

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Primary Literature (German Editions and English Translations)

Works listed in this section are by Richard Dedekind, unless otherwise specified.

1854 “Über die Einführung neuer Funktionen in der Mathematik; Habilitationsvortrag”; in Dedekind (1930–32), Vol. 3, pp. 428–438.
1857 “Abriß einer Theorie der höheren Kongruenzen in bezug auf einen reellen Primzahl-Modulus”; reprinted in Dedekind (1930–32), Vol. 1, pp. 40–67.
1872 Stetigkeit und irrationale Zahlen, Vieweg: Braunschweig (originally published as a separate booklet); reprinted in Dedekind (1930–32), Vol. 3, pp. 315–334, and in Dedekind (1965), pp. 1–22; English trans., Dedekind (1901b).
1876a “Bernhard Riemanns Lebenslauf”, in Riemann (1876), pp. 539–558.
1876b “Briefe an Lipschitz (1–2)”, in Dedekind (1930–32), Vol. 3, pp. 468–479.
1876 Riemann, Bernard, Gesammelte Mathematische Werke und Wissenschaftlicher Nachlass, H. Weber, ed., with assistance by R. Dedekind; second edition (revised) 1892, with a supplement added in 1902; reprinted by Dover: New York, 1953.
1877 Sur la Théorie des Nombres Entiers Algébrique, Gauthier-Villars: Paris; reprinted in Dedekind (1930–32), Vol. 3, pp. 262–296; English trans. Dedekind (1996b).
1882 “Theorie der algebraischen Funktionen einer Veränderlichen”, with H. Weber; reprinted in Dedekind (1930–32), Vol. 1, pp. 238–350.
1888a Was sind und was sollen die Zahlen?, Vieweg: Braunschweig (originally published as a separate booklet); reprinted in Dedekind (1930–32), Vol. 3, pp. 335–91, and in Dedekind (1965), pp. III–XI and 1–47; English trans., (Dedekind 1901c) and (revised) Dedekind (1995).
1888b “Brief an Weber”, in Dedekind (1930–32), Vol. 3, pp. 488–490.
1890 “Letter to Keferstein”, in Van Heijenoort (1967), pp. 98–103.
1893 Lejeune-Dirichlet, P.G., Vorlesungen über Zahlentheorie, fourth edition, edited and with supplements by R. Dedekind; Vieweg: Braunschweig; reprinted by Chelsea: New York, 1968.
1897 “Über Zerlegungen von Zahlen durch ihre größten gemeinsamen Teiler”; reprinted in Dedekind (1930–32), Vol. 2, pp. 103–147.
1900 “Über die von drei Moduln erzeugte Dualgruppe”; reprinted in Dedekind (1930–32), Vol. II, pp. 236–271.
1901a Essays on the Theory of Numbers, W.W. Beman, ed. and trans., Open Court Publishing Company: Chicago, 1901; reprinted by Dover: New York, 1963; English version of Dedekind (1965); essays also included in Ewald (1996a), pp. 756–779 and 787–833, and in Hawking (2005a), pp. 901–964.
1901b “Continuity and Irrational Numbers”, in (Dedekind 1901a), pp. 1–27; English trans. of Dedekind (1872).
1901c “The Nature and Meaning of Numbers”, in (Dedekind 1901a), pp. 29–115; English trans. of Dedekind (1888a).
1930–32 Gesammelte Mathematische Werke, Vols. 1–3, R. Fricke, E. Noether & Ö. Ore, eds., Vieweg: Braunschweig; reprinted (except for the separately published Dedekind 1964) by Chelsea Publishing Company: New York, 1969.
1937 Noether, E. & Cavaillès, J., eds., Briefwechsel Cantor-Dedekind, Hermann, Paris.
1964 Über die Theorie der ganzen algebraischen Zahlen. Nachdruck des elften Supplements (from Lejeune-Dirichlet 1893), with a preface by B. L. van der Waerden, Vieweg: Braunschweig.
1965 Was sind und was sollen die Zahlen?/Stetigkeit und irrationale Zahlen. Studienausgabe, G. Asser, ed., Vieweg: Braunschweig; later German version of Dedekind (1901a).
1981 “Eine Vorlesung über Algebra”, in Scharlau (1981a), pp. 59–100.
1982 “Unveröffentlichte algebraische Arbeiten Richard Dedekinds aus seiner Göttinger Zeit, 1855–1858”, Archive for History of Exact Sciences 27:4, 335–367.
1985 Vorlesungen über Diffential- und Integralrechnung 1861/62, based on notes by H. Bechtold, M.-A. Knus & W. Scharlau, eds., Vieweg: Braunschweig.
1986 Lipschitz, Rudolf, Briefwechsel mit Cantor, Dedekind, Helmholtz, Kronecker, Weierstrass und anderen, W. Scharlau, ed., Vieweg: Braunschweig.
1991 Meschkowski, H. & Nilson, W., eds., Georg Cantor. Briefe, Berlin: Springer; especially “Die Periode des Briefwechsels mit Dedekind — die Entstehung der Mengenlehre”, pp. 29–66.
1995 What Are Numbers and What Should They Be? H. Pogorzelski, W. Ryan & W. Snyder, eds. and trans., Research Institute for Mathematics: Orono, ME; revised English trans. of Dedekind (1888).
1996a “Julius Wilhelm Richard Dedekind (1831–1916)”, in Ewald (1996a), Vol. 2, pp. 753–837; English trans. of various texts by Dedekind.
1996b Theory of Algebraic Integers, J. Stillwell, ed. and trans., Cambridge University Press; English trans. of Dedekind (1877).
1999 Dirichlet, P.G.L., Lectures on Number Theory, with supplements by Richard Dedekind, J. Stillwell, ed. and trans., American Mathematical Society: Providence; English trans. of Lejeune-Dirichlet (1893).
2008 Richard Dedekind: La création des nombres, H.B. Sinaceur, ed. and trans., Vrin: Paris; French trans. of various texts by Dedekind.

Secondary Literature (in English, French, and German)

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