What Is Mathematics? An Elementary Approach to Ideas and Methods, 2nd Edition (1996)

GENERAL REFERENCES

W. Ahrens. Mathematische Unterhaltungen und Spiele, 2nd edition, 2 vols. Leipzig: Teubner, 1910.

W. W. Rouse Ball. Mathematical Recreations and Essays, 11th edition, revised by H. S. M. Coxeter. New York: Macmillan, 1939.

E. T. Bell. The Development of Mathematics. New York: McGraw-Hill, 1940.

———. Men of Mathematics. New York: Simon and Schuster, 1937.

T. Dantzig. Aspects of Science. New York: Macmillan, 1937.

A. Dresden. An Invitation to Mathematics. New York: Holt, 1936.

F. Enriques. Questioni riguardanti le matematiche elementari, 3rd edition, 2 vols. Bologna: Zanichelli, 1924 and 1926.

E. Kasner and J. Newman. Mathematics and the Imagination. New York: Simon and Schuster, 1940.

F. Klein. Elementary Mathematics from an Advanced Standpoint, translated by E. R. Hedrick and C. A. Noble, 2 vols. New York: Macmillan, 1932 and 1939.

M. Kraitchik. La Mathematique des Jeux. Brussels: Stevens, 1930.

O. Neugebauer. Vorlesungen über Geschichte der antiken mathematischen Wissenschaften. Erster Band: Vorgriechische Mathematik. Berlin: Springer, 1934.

H. Poincaré. The Foundations of Science. Lancaster, Pa.: Science Press, 1913.

H. Rademacher und 0. Toeplitz. Von Zahlen und Figuren, 2nd edition. Berlin: Springer, 1933.

B. Russell. Introduction to Mathematical Philosophy. London: Allen and Unwin, 1924.

———. The Principles of Mathematics, 2nd edition. New York: Norton, 1938.

D. E. Smith. A Source Book in Mathematics. New York: McGraw-Hill, 1929.

H. Steinhaus. Mathematical Snapshots. New York: Stechert, 1938.

H. Weyl. “The Mathematical Way of Thinking,” Science, XCII (1940), p. 437 ff.

H. Weyl. Philosophie der Mathematik und Naturwissenschaft, Handbuch der Philosophie, Bd. II. Munich: Oldenbourg, 1926, pp. 3-162.

CHAPTER I

L. E. Dickson. Introduction to the Theory of Numbers. Chicago: University of Chicago Press, 1931.

———. Modern Elementary Theory of Numbers. Chicago: University of Chicago Press, 1939.

G. H. Hardy. “An Introduction to the Theory of Numbers,” Bulletin of the American Mathematical Society, XXXV (1929), p. 789 ff.

G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers. Oxford: Clarendon Press, 1938.

J. V. Uspensky and M. H. Heaslet. Elementary Number Theory. New York: McGraw-Hill, 1939.

CHAPTER II

G. Birkhoff and S. MacLane. A Survey of Modern Algebra. New York: Macmillan, 1941.

M. Black. The Nature of Mathematics. New York: Harcourt, Brace, 1935.

T. Dantzig. Number, the Language of Science, 3rd edition. New York: Macmillan, 1939.

G. H. Hardy. A Course of Pure Mathematics, 7th edition. Cambridge: University Press, 1938.

K. Knopp. Theory and Application of Infinite Series, translated by Miss R. C. Young. London: Blackie, 1928.

A. Tarski. Introduction to Logic. New York: Oxford University Press, 1939.

F. Enriques. The Historic Development of Logic, translated by J. Rosenthal. New York: Holt, 1929.

CHAPTER III

J. L. Coolidge. A History of Geometrical Methods. Oxford: Clarendon Press, 1940.

A. De Morgan. A Budget of Paradoxes, 2 vols. Chicago: Open Court, 1915.

L. E. Dickson. New First Course in the Theory of Equations. New York: Wiley, 1939.

F. Enriques (editor). Fragen der Elcmentargeometrie, 2nd edition, 2 vols. Leipzig: Teubner, 1923.

E. W. Hobson. “Squaring the Circle,” a History of the Problem. Cambridge: University Press, 1913.

A. B. Kempe. How to Draw a Straight Line. London: Macmillan, 1877.

F. Klein. Famous Problems of Geometry, translated by W. W. Beman and D. E. Smith, 2nd edition. New York: Stechert, 1930.

L. Mascheroni. La geometria del compasso. Palermo: Reber, 1901.;

G. Mohr. Euclides Danicus. Copenhagen: Hølst, 1928.

J. M. Thomas. Theory of Equations. New York: McGraw-Hill, 1938.

L. Weisner. Introduction to the Theory of Equations. New York: Wiley, 1939.

CHAPTER IV

W. C. Graustein. Introduction to Higher Geometry. New York: Macmillan, 1930.

D. Hilbert. The Foundations of Geometry, translated by E. J. Townsend, 3rd edition. La Salle, III.: Open Court, 1938.

C. W. O’Hara and D. R. Ward. An Introduction to Projective Geometry. Oxford: Clarendon Press, 1937.

G. de B. Robinson. The Foundations of Geometry. Toronto: University of Toronto Press, 1940.

Girolamo Saccheri. Euclides ab omni naevo vindicatus, translated by G. B. Halsted. Chicago: Open Court, 1920.

R. G. Sanger. Synthetic Projective Geometry. New York: McGraw-Hill, 1939.

O. Veblen and J. W. Young. Projective Geometry, 2 vols. Boston: Ginn, 1910 and 1918.

J. W. Young. Projective Geometry. Chicago: Open Court, 1930.

CHAPTER V

P. Alexandroff. Einfachste Grundbegriffe der Topologie. Berlin: Springer, 1932.

D. Hilbert und S. Cohn-Vossen. Anschauliche Geometrie. Berlin: Springer, 1932.

M. H. A. Newman. Elements of the Topology of Plane Sets of Points. Cambridge: University Press, 1939.

H. Seifert und W. Threlfall. Lehrbuch der Topologie. Leipzig: Teubner, 1934.

CHAPTER VI

R. Courant. Differential and Integral Calculus, translated by E. J. McShane, revised edition, 2 vols. New York: Nordemann, 1940.

G. H. Hardy. A Course of Pure Mathematics, 7th edition. Cambridge: University Press, 1938.

W. L. Ferrar. A Text-book of Convergence. Oxford: Clarendon Press, 1938.

For the theory of continued fractions see, e.g.

S. Barnard and J. M. Child. Advanced Algebra. London: Macmillan, 1939.

CHAPTER VII

R. Courant. “Soap Film Experiments with Minimal Surfaces,” American Mathematical Monthly, XLVII (1940), pp. 167-174.

J. Plateau. “Sur les figures d’équilibre d’une masse liquide sans pésanteur,” Mémoires de l’Académie Royale de Belgique, nouvelle série, XXIII (1849).

———. Statique expérimentale et théoretique des Liquides. Paris: 1873.

CHAPTER VIII

C. B. Boyer. The Concepts of the Calculus. New York: Columbia University Press, 1939.

R. Courant. Differential and Integral Calculus, translated by E. J. Mc-Shane, revised edition, 2 vols. New York: Nordemann, 1940.

G. H. Hardy. A Course of Pure Mathematics, 7th edition. Cambridge: University Press, 1938.