Math 300 History of Mathematics Jt Smith Bibliography Spring 2009

MATH 300 HISTORY OF MATHEMATICS JT SMITH BIBLIOGRAPHY SPRING 2009

I’ll accumulate in this file detailed references to all items that I cite during this course. Thus its content will change often and without notice. I’m using the style used in the Marchisotto and Smith 2007 bibliography, which was patterned on the Documentation two style of Chicago 1993.

A notation [Internet] signifies that the item is available on the Internet via our library. A notation of the form MSN: * indicates that a review by * is available on MathSciNet [Internet].

Barbagli, Marzio. [1974] 1982. Educating for Unemployment: Politics, Labor Markets, and the School System—Italy, 1859–1973. Translated by Robert H. Ross. New York: Columbia University Press. First published in Italian as Disoccupazione intellectuale e sistema scolastico in Italia, Bologna: Società Editrice Il Mulino, 1974. Bell, Eric Temple. 1937. Men of Mathematics. New York: Simon and Schuster. A collection of entertaining but sometimes misleading biographies. A copy should be on reserve in our library. Boyce, William E., and Richard C. Diprima. 1997. Elementary differential equations and boundary value problems. Sixth edition. New York: John Wiley & Sons, Inc. Boyer, Carl B. 1949. Review of Struik [1948] 1987. Isis 40: 287–289. [Internet] Boyer, Carl B., and Uta Merzbach. 1989. A History of Mathematics. New York: John Wiley & Sons, Inc. MSN: C. R. Fletcher. A comprehensive textbook on history of mathematics. A copy should be on reserve in our library. Bronowsky, Jacob. 1973. The Ascent of Man. Boston: Little, Brown, & Company. This text was developed to accompany an outstanding TV series on the history of science. Chapter 5, on mathematics, is particularly compelling. Burton, David M. 2007. The History of Mathematics: An Introduction. Sixth edition. Boston: McGraw-Hill Higher Education. MSN: E. J. Barbeau. The current leading expensive comprehensive history of mathematics textbook. A copy should be on reserve in our library. Chicago Manual of Style, The. 1993. Fourteenth edition. Chicago: University of Chicago Press. This is my bible for writing technique. Dehn, Max. 1949. Review of Struik [1948] 1987. American Mathematical Monthly 56: 643–644. [Internet] Dehn will appear in several roles in this course. Descartes, René. [1637] 1954. The Geometry of René Descartes. Translated from the French and Latin by David Eugene Smith and Marcia L. Latham. New York: Dover Publications, Inc. The original and the translation are on facing pages. Dillingham, Rick. 1994. Fourteen Families in Pueblo Pottery. Foreword by J. J. Brody. Albuquerque: University of New Mexico Press. Dold-Simplicius, Yvonne. 1996. Problem of the two towers. In Franci, Pagli, and Toti Rigatelli 1996, 47–69. I have a copy of this.

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Dürer, Albrecht. [1525] 1977. The Painter’s Manual: A Manual of Measurement of Lines, Areas, and Solids by Means of Compass and Ruler Assembled for the Use of All Lovers of Art with Appropriate Illustrations. Translated, with a commentary, by Walter L. Strauss. New York: Abaris Books. Emmer, Michele, editor. 1993. The Visual Mind: Art and Mathematics. Cambridge, Massachusetts: MIT Press. Euclid. [1908] 1956. The Thirteen Books of Euclid’s Elements. Translated from the text of Heiberg, with introduction and commentary by Sir Thomas L. Heath. Second edition. Three volumes. New York: Dover Publications. Available on the Internet: click here for a *.pdf file and there for an elaborately hyperlinked file . Eves, Howard W. 1990. Introduction to the History of Mathematics with Cultural Connections by Jamie H. Eves. Philadelphia: Saunders College Publishers. MSN: E. J. Barbeau. A comprehensive history of mathematics textbook. A copy should be on reserve in our library. Franci, Raffaella, Paoli Pagli, and Laura Toti Rigatelli, editors. 1996. Itinera mathema- tica: Studî in onore di Gino Arrighi per il suo 90E compleanno. Siena: Centro Studi Sulla Matematica Medioevale Università di Siena. Frank, Larry, and Francis J. Harlow. 1974. Historic Pottery of the Pueblo Indians 1600–1800. Photographs by Bernard Lopez. Boston: New York Graphic Society. Freudenthal, Hans. 1953. Zur Geschichte der vollständigen Induktion. Archives interna- tionales d’histoire des sciences 6:17–37. ———. 1962. Review: Science Awakening. Bulletin of the American Mathematical Society 68: 543–545. [Internet] Review of Van der Waerden 1963. Gauss, Carl Friedrich. 1799. Omnem Functionem Algebraicam Rationalem Integram Unius Variabilis in Factores Reales Primi vel Secundi Gradus Resolvi Posse. Doctoral dissertation, University of Helmstedt. In Gauss 1876, volume 3, 11–41. [Internet] ———. 1876. Werke. Volume 3. Second edition. Göttingen: Königlichen Gesellschaft der Wissenschaften. [Internet] Genocchi, Angelo. 1884. Calcolo differenziale e principii di calcolo integrale, edited by Giuseppe Peano. Turin: Fratelli Bocca Editore. Included in Peano 2002 as file 1884c.pdf. Partially translated in Peano 1973, 44–50. Gillispie, Charles C., editor. 1970–. Dictionary of Scientific Biography. Eighteen volumes. New York: Charles Scribner’s Sons. Later volumes have a different editor. This is a wonderful source of detailed biographical articles, usually by world-known experts. It is available in the reference department of our library. Grassmann, Hermann Günter. [1844] 1994. A new branch of mathematics: The Aus- dehnungslehre of 1844. Included in Grassmann 1994, 1–314. ———. 1894–1911. Gesammelte mathematische und physikalische Werke. Edited by Friedrich Engel. Three volumes, each in two parts. Leipzig: Druck und Verlag von B. G. Teubner. ———. 1994. A New Branch of Mathematics: The Ausdehnungslehre of 1844 and Other Works. Translated by Lloyd C. Kannenberg. Peru, Illinois: Open Court Publishing Company. MSN: Pambuccian. Translation of part of Grassmann 1894–1911.

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Grattan-Guinness, Ivor. 1997. The Norton History of the Mathematical Sciences: The Rainbow of Mathematics. New York: W. W. Norton & Company. MSN: V. J. Katz. This most recent comprehensive history of mathematics is a reference book, not a textbook. A copy should be on reserve in our library. Hilbert, David. [1899] 1971. Foundations of Geometry (Grundlagen der Geometrie). Second edition. Translated by Leo Unger from the tenth German edition. Revised and enlarged by Paul Bernays. LaSalle, Illinois: Open Court. The original work was announced in June 1899 at the celebration of the Gauss–Weber monument in Göt- tingen, and published by B. G. Teubner. ———. [1900] 2000. Mathematical problems. Translated by Mary Winston Newson. Bulletin of the American Mathematical Society (new series) 37: 407–436. [Internet] Reprinted from Bulletin of the American Mathematical Society, 8 (1902): 437–479. Originally published as “Mathematische Probleme,” Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse 1900: 253–297. [Internet] ———. 1930. Hilbert’s 1930 radio address. Delivered on 8 September in Königsberg at the Congress of the Association of German Natural Scientists and Medical Doctors. Audio mp3 file with an English translation by James T. Smith. On the Internet at http:// math.sfsu.edu/smith/Documents/HilbertRadio/HilbertRadio.pdf. Johnson, Warren P. 2002. The curious history of Faà di Bruno’s formula. American Mathematical Monthly 109, 217–234. [Internet] MSN: Muldoon. Kennedy, Hubert C. [1980] 2006. Peano: Life and Works of Giuseppe Peano. Definitive edition. Concord, California: Peremptory Publications. The original edition was Studies in the History of Modern Science, 4, Dordrecht: D. Reidel Publishing Company. This edition has footnotes omitted from the original. A free electronic or inexpensive paperback version is available via http://www.lulu.com/content/ 413765. MSN: I. Grattan-Guinness; also reviewed in Richards 1982. This is an official text for the course. Klein, Felix. 1892–1893. A comparative review of recent researches in geometry. Translated by Mellea W. Haskell, with additional footnotes by the author. Bulletin of the New York Mathematical Society 2: 215–249. [ Internet] Translation of Ver- gleichende Betrachtungen über neuere geometrische Forschungen, Erlangen: Andreas Deichert, 1872. Klein’s Erlanger program. ———. 1939. Elementary Mathematics from an Advanced Standpoint. Two volumes. Translated from the third German edition by Earle R. Hedrick and Charles A. Noble. New York: Dover Publications, Inc. The original handwritten edition, edited by Ernst Hellinger, was published in 1909 by B. G. Teubner. Kuhn, Thomas S. [1962] 1970. The Structure of Scientific Revolutions. Second edition, enlarged. Chicago: University of Chicago Press. The first edition was part of the International Encyclopedia of Unified Science. Lejeune Dirichlet, Peter Gustav. 1837. Ueber die Darstellung ganz willkürlicher Func- tionen durch Sinus- und Cosinusreihen. Repertorium der Physik I:152–174. Reprinted in Lejeune Dirichlet 1889–1897, volume 1, 133–160.

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———. 1889–1897. G. Lejeune Dirichlet’s Werke. Two volumes. Edited by Leopold Kronecker and Lazarus E. Fuchs. Berlin: Druck und Verlag von Georg Reimer. [Internet]. Livio, Mario. 2005. The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. New York: Simon & Schuster. MSN: Carlip. Luciano, Erika, Clara Silvio Roero, Stefania Chiavero, and Dora Damiano. 2008. Lo spirito creativo è leggero: Giuseppe Peano (1858–1932) matematico e maestro. In occasione delle Celebrazioni dei 150 anni della nascita di Giuseppe Peano e dei 100 anni della pubblicazione del Formulario Mathematico. Cuneo, Italy: Città di Cuneo. Marchisotto, Elena Anne, and James T. Smith. 2007. The Legacy of Mario Pieri in Geometry and Arithmetic. Boston: Birkhäuser. MSN: A. C. Lewis. [Internet] Click http://math.sfsu.edu/smith/Documents/PieriBook/PieriBookIndex.htm; ask me for a password if necessary. Michaelides, Tefcros. 2008. Pythagorean Crimes. Las Vegas: Parmenides Fiction. Moise, Edwin E. [1963] 1990. Elementary Geometry from an Advanced Viewpoint. Third Edition. Reading, Massachusetts: Addison-Wesley Publishing Company. MSN: Coxeter. The first edition stemmed from a School Mathematics Study Group project. Mueller, Ian. 1981. Philosophy of Mathematics and Deductive Structure in Euclid’s Elements. Cambridge, Massachusetts: MIT Press. MSN: Dipert. O’Connor, John J., and Edmund F. Robertson. [no date]. The MacTutor History of Mathematics Archive. On the Internet at http://www-gap.dcs.st-and.ac.uk/ ~history/. This is rather comprehensive but imbalanced and often inaccurate. Peano, Giuseppe. 1881. Costruzione dei connessi (1,2) e (2,2). Atti della Reale Acca- demia delle Scienze di Torino 16 (1880–1881), 497–503. Included in Peano 2002 as file 1880a.pdf. Peano’s first published work, completed in 1880 and presented to the Academy by Enrico D’Ovidio in 1881. ———. [1888] 2000. Geometric Calculus According to the Ausdehnungslehre of H. Grassmann. Translated by Lloyd C. Kannenberg. Boston: Birkhäuser. Translation of Calcolo geometrico secondo l’Ausdehnungslehre di H. Grassmann, preceduto dalle operazioni della logica deduttiva, Torino: Fratelli Bocca Editori, which is included in Peano 2002 as file 1888a.pdf. The title refers to Grassmann [1844] 1994. ———. [1889] 1973. The Principles of Arithmetic, Presented by a New Method. Trans- lated by Hubert C. Kennedy. In Peano 1973, 101–134. Translation of Arithmetices Principia, Nova Methodo Exposita, Rome: Augustae Taurinorum, Fratres Bocca, included in Peano 2002 as file 1889a.pdf. ———. [1890] 1973a. A space-filling curve. In Peano 1973, 143–148. Translation of “Sur une courbe, qui remplit toute une aire plane,” Mathematische Annalen 36: 157–160. [Internet] Included in Peano 2002 as file 1890b.pdf. ———. 1973. Selected works of Giuseppe Peano. Translated and edited, with a biographical sketch and bibliography, by Hubert C. Kennedy. Toronto: University of Toronto Press. ———. 2002. L’opera omnia di Giuseppe Peano. Edited by Clara S. Roero. Turin: Dipartimento di Matematica, Università di Torino. CD-ROM.

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Playfair, John. [1795] 1860. Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids, to Which Are Added, Elements of Plane and Sphericale Trigonometry. Philadelphia: J. D. Lippincott & Company. [Internet]. The source of the form of the parallel axiom used in Smith 2000. Playfair is more noted as geologist than mathematician. Rashed, Roshdi. 1972. L’induction mathématique: al-Karaji, as-Samaw’al. Archive for History of Exact Sciences 9:1–21. [Internet] Ray, Joseph. 1880. Ray’s New Higher Arithmetic. Cincinnati: Van Antwerp, Bragg & Co. [Internet]. The original edition was published around 1860. Richards, Joan L. 1982. Review of Kennedy [1980] 2006. Isis 73: 118–119. [Internet] Riemann, Bernhard. 1854. Über die Darstellbarkeit einer Function durch eine trigono- metrische Reihe, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 13. Reprinted in Riemann 1892, article 12, 227–264. The title means “On the representation of a function by a trigonometric series.” [Internet] ———. 1892. Gesammelte mathematische Werke und wissenschaftlicher Nachlass. Edited by Heinrich Weber, with collaboration by Richard Dedekind. Second edition, with a supplement edited by Max Noether and Wilhelm Wirtinger. Leipzig: Druck und Verlag von B. G. Teubner. [Internet] Rowe, David E. 1989. Review of Struik [1948] 1987. Isis 80: 156–157. [Internet] ———. 2001. Looking back on a bestseller: Dirk Struik’s A Concise History of Mathe- matics. Notices of the American Mathematical Society 48(6):590–592. [Internet] Segre, Michael. 1994. Peano’s axioms in their historical context. Archive for the History of Exact Sciences 48: 201–342. MSN: J. R. Dauben. [Internet] Smith, Fenny K. C. 1996. The circumnavigation of the earth and a 15th Century solution to a quartic equation. In Franci, Pagli, and Toti Rigatelli 1996, 124–130. I have a copy of this. Smith, James T. 1973. Orthogonal geometries I. Geometriæ dedicata 1: 221–235. MSN: I. Pieper. [Internet] Smith, James T. 2000. Methods of Geometry. New York: John Wiley & Sons, Inc. Sec- tion 2.3 is online: http://math.sfsu.edu/smith/Math300/Bibliography/02_03.pdf. Struik, Dirk J. [1948] 1987. A Concise History of Mathematics. Fourth revised edition. New York: Dover Publications, Inc. MSN: E. J. Dijksterhuis. Also reviewed in Boyer 1949, Dehn 1949, Rowe 1989, and Rowe 2001. Copies of the first and fourth editions should be on reserve in our library. This is an official text for the course. ———. 1986. The sociology of mathematics revisited: A personal note. Science & Society 50: 280–299. This has many good references. Tarski, Alfred, Zygmunt Chwia³kowski, and Wac³aw Schayer. [1935] 1946. Geometrja dla trzeciej klasy gimnazjalnej. Second edition, reprinted. Hanover: Polski Zwi¹zek WychodŸctwa Przymusowego w Hanowerze. The title means “Geometry for the third gymnasium class.” The 1935 edition was published in Lwów by Pañstwowe Wydaw- nictwo Ksi¹¿ek i Pomocy Szkolnych. This edition was originally published in Jerusa- lem in 1944. Toeplitz, Otto. [1949] 1963. The Calculus: A Genetic Approach. Edited by Gottfried Köthe, translated by Luise Lange. Chicago: University of Chicago Press. Originally

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published as Die Entwicklung der Infinitesimalrechnung: Eine Einleitung in die Infinitesimalrechnung nach der genetischen Methode, erster Band. Grundlehren der mathematischen Wissenschaften, 56, Berlin: Springer-Verlag, 1949, MSN: Bochner. Van der Waerden, B. L. van der. 1963. Science Awakening. Third edition. Translated by Arnold Dresden. New York: John Wiley & Sons. A fascinating history of ancient mathematics by one of the founders of modern algebra, who turned historian later in his career. Reviewed in Freudenthal 1962.

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