Sources for the Math Symbols and Words Pages

Abbreviations: OED2 refers to the Oxford English Dictionary, Second Edition; MWCD10 is Merriam-Webster’s Collegiate Dictionary, Tenth Edition; RHUD2 refers to the Random House Dictionary of the English Language, Second Edition Unabridged. If the earliest use of a word known to Webster is its appearance in a dictionary, the date is preceded by "ca."; in those cases, it can be assumed earlier uses of those words exist. JSTOR refers to the web site

The following written sources have been used.

Abbott, David, general editor. The Biographical Dictionary of Scientists: Mathematicians. New York: Peter Bedrick Books, 1985.

Aldrich, J. Doing least squares: perspectives from Gauss and Yule. International. Statistical Review, 66 (1), 61-81 (1998).

Aldrich, J. (1995) "Correlations Genuine and Spurious in Pearson and Yule," Statistical Science, 10, 364-376.

Aldrich, J. The Language of the English Biometric School, International Statistical Review, Vol. 71(1), pp. 109-131, (2003).

Asimov, Isaac. Asimov’s Biographical Encyclopedia of Science and Technology.

Ball, W. W. Rouse. A Short Account of the History of Mathematics. New York: Dover Publications, 1960.

Ball, W. W. Rouse, and H. S. M. Coxeter. Mathematical Recreations and Essays, Thirteenth Edition. New York: Dover Publications, Inc., 1987.

Bell, E. T. The Development of Mathematics. 1945.

Bell, E. T. The Development of Mathematics. Dover. New York, 1972.

Borowski, E. J., and J. M. Borwein The Collins Dictionary of Mathematics, 2nd edition 2002. HarperCollins Glasgow.

Boyer, Carl B. A History of Mathematics. Revised by Uta C. Merzbach. John Wiley & Sons, 1989.

Burn, R. P. "Irrational Numbers in English Language Textbooks, 1890-1915: Constructions and Postulates for the Completeness of the Real Numbers," Historia Mathematica 19 (1992).

Burton, David M. The History of Mathematics - An Introduction. Dubuque, Iowa: William C. Brown, 1988.

Cabillón, Julio González (1959- ) is the author of numerous mathematics textbooks. He currently teaches Real Analysis at the German Institute DSM (Deutsche Schule Montevideo) in Uruguay. His main subject in mathematics is "q-Gaussian coefficients."

Cajori, Florian. A History of Mathematics. New York: The Macmillan Co., 1893.

Cajori, Florian. A History of Mathematics. New York: The Macmillan Co., 1906.

Cajori, Florian. A History of Mathematics. New York: The Macmillan Co., 1919.

Cajori, Florian. A History of Mathematical Notations. 2 volumes. Lasalle, Illinois: The Open Court Publishing Co., 1928-1929.

Chabert, Jean-Luc, Évelyne Barbin, Michel Guillemot, Anne Michel-Pajus, Jacques Borowczyk, Ahmed Djebbar, Jean-Claude Martzloff. Histoire D'Algorithmes. Éditions Belin, 1994.

Clawson, Calvin C. Mathematical Mysteries: The Beauty and Magic of Numbers. New York: Plenum Press, 1996.

David, H. A. "First (?) Occurrence of Common Terms in Mathematical Statistics," The American Statistician 49:2, May 1995.

David, H. A. "First (?) Occurrence of Common Terms in Probability and Statistics -- A Second List, with Corrections," The American Statistician 52:1, February 1998.

David, H. A. (2001) First (?) Occurrence of Common Terms in Statistics and Probability, Appendix B and pp. 219-228 in H. A. David & A. W. F. Edwards (eds). Annotated Readings in the History of Statistics, Springer New York.

Davies, Charles, and William G. Peck. Mathematical Dictionary and Cyclopedia of Mathematical Sciences comprising definitions of all the terms employed in mathematics -- an analysis of each branch, and of the whole, as forming a single science. New York: A. S. Barnes and Co., 1857. [The preface of this book is dated June, 1855.]

Dickson, Leonard Eugene. History of the Theory of Numbers. Three volumes, 1919, 1920, 1923.

Dodge, Y. (ed.) Oxford Dictionary of Statistical Terms Oxford: Oxford University Press. 2003.

DSB. The Dictionary of Scientific Biography. C. C. Gillispie (editor in chief) New York : Charles Scribner’s Sons, 1970-1980.

Dunham, William. Euler: The Master of Us All. Mathematical Association of America, 1999.

Eisenhart, C. "On the Transition from Student’s z to Student’s t, American Statistician, 33, 6-10, 1979.

Eves, Howard. An Introduction to the History of Mathematics. Fifth edition. CBS College Publishing, 1983.

Finney, Ross L., and George B. Thomas, Jr. Calculus. Addison-Wesley Publishing Co., 1992.

Franceschetti, Donald R. Biographical Encyclopedia of Mathematicians. Marshall Cavendish Corporation, Tarrytown, N. Y., 1999.

Franci, Raffaella, and Laura Toti Rigatelli, "Maestro Benedetto de Firenze e la Storia dell'Algebra", Historia mathematica, x (1983), 297-317.

Francis, Richard L. "Jewel in the Crown: The Discover of the Law of Quadratic Reciprocity." Historical Notes: Mathematics Through the Ages. Lexington, Mass.: The Consortium for Mathematics and Its Applications, 1992.

Gardner, Martin. The 2nd Scientific American Book of Mathematical Puzzles & Diversions. New York: Simon & Schuster, 1961.

Grattan-Guinness, Ivor. The Fontana History of the Mathematical Sciences: The Rainbow of Mathematics, London: Harper-Collins, 1997.

Grattan-Guinness, Ivor. The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel, Princeton University Press, 2000.

Grinstein, Louise S. A note on the Greatest Integer Function. The Mathematics Teacher, January 1970.

Gullberg, Jan. Mathematics: From the Birth of Numbers. New York: W. W. Norton & Co., 1997.

Hacker, Sidney G. Identification of Napier’s Inequalities. The Mathematics Teacher, January 1970.

Hald, Anders. A History of Probability and Statistics and their applications before 1750, New York: Wiley, 1986.

Hald, Anders. A History of Mathematical Statistics From 1750 to 1930. New York: Wildey, 1998.

Halmos, Paul R. I Want to Be a Mathematician: An Automathography. Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1985.

Hawkins, T. W. (1975) Cauchy and the spectral theory of matrices, Historia Mathematica, 2, 1-29.

Hawkins, T. W. (1977) Weierstrass and the Theory of Matrices, Archive for the History of the Exact Sciences, 17, 119-163.

Heijenoort, Jean van, ed. From Frege to Gödel: a source book in mathematical logic 1879-1931. Cambridge, MA: Harvard University Press, 1967.

Huntley, H. E. The Divine Proportion. New York: Dover Publications, Inc., 1970.

Hutton, Charles. A Mathematical and Philosophical Dictionary. 1795-96.

James, Glenn and Robert C., editors. Mathematics Dictionary. Van Nostrand Co., Inc. 1949.

Johnson, Art. "History of Mathematical Symbols." Classic Math: History Topics for the Classroom. Dale Seymour Publications, 1994.

Johnson, Art. "History of Mathematical Terms," Classic Math: History Topics for the Classroom. Dale Seymour Publications, 1994.

Katz, Kaila. "The Notation for Inverse Trigonometric Functions: From Whence Did It Come?" Historical Notes: Mathematics Through the Ages. Lexington, Mass.: The Consortium for Mathematics and Its Applications, 1992.

Katz, Victor J. A History of Mathematics: An Introduction. Harper Collins, 1993, or Addison Wesley, 1998.

Kendall, Maurice G., and Alan Stuart. The Advanced Theory of Statistics, 3rd edition (in three volumes). New York: Hafner Publishing Company, 1969.

Kline, Morris. Mathematical Thought From Ancient to Modern Times. Oxford University Press, 1972.

Kramer, Edna E. The Nature and Growth of Modern Mathematics. Hawthorn Books, Inc., New York, 1970.

Lambert, Johann Heinrich. Histoire de l'Academie Royale des sciences et des belles-lettres de Berlin, vol. XXIV, p. 327, 1768.

Lucas, D'après Édouard. Théorie des nombres, tome premier. Paris, 1901.

Manning, Kenneth R. "A History of Extraneous Solutions." The Mathematics Teacher. February 1970.

Maor, Eli. e: The Story of a Number. Princeton, N. J.: Princeton University Press, 1994. ISBN: 0-691-03390-0.

Mascheroni, Lorenzo. "Adnotationes ad calculum integralem Euleri: In quibus nonnulla problemata ab Eulero proposita resolvuntur - Auctore Laurentio Mascheronio", Petri Galeatii, 72 pages, Ticini, MDCCXC (1790).

McCarthy, Paul J. Introduction to Arithmetical Functions. Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1986.

Menninger, Karl. Number Words and Number Symbols: A Cultural History of Numbers. The M.I.T. Press, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1969.

Moore, Eliakim Hastings. "A Doubly Infinite System of Simple Groups," Mathematical Papers read at the International Mathematical Congress Held in Connection with the World’s Columbian Exposition Chicago 1893, 1896.

Moore, Sir Jonas Moore. A mathematical compendium: or, useful practices in arithmetick, geometry, and astronomy, geography and navigation ... explaining the logarithms, with new indices; Nepair’s rods or bones; making of movements, and the application of pendulums: with the projection of the sphere for an universal dyal, &c. Collected out of the notes and papers of Sir Jonas Moore by Nicholas Stephenson. London, Printed and sold by Nathanael Brooke, 1674.

MWCD10. Merriam-Webster’s Collegiate Dictionary, Tenth Edition. Springfield, Mass.: Merriam-Webster, Inc., 1993.

OED2. The Oxford English Dictionary, Second Edition.

OED Online. Oxford English Dictionary Online.

Pier, J.-P. Historique de la Notion de Compacité. Historia Mathematica, 7, 425-443. (1980)

Porter, Theodore M. The Rise of Statistical Thinking 1820-1900. Princeton University Press, 1986.

Proctor, Richard Anthony. A treatise on the cycloid and all forms of cycloidal curves, and on the use of such curves in dealing with the motions of planets, comets, &c., and of matter projected from the sun. Longmans, Green, and Co., London, 1878.

Reye, Karl Theodor. Die Geometrie der Lage, Ruempler, Hannover. Bd. 1 (1866), Bd. 2 (1868).

Riccati, Vincenzo. Vincentii Riccati Soc. Jesu Opusculorum ad res physicas, & mathematicas pertinentium tomus primus, Apud Laelium a Vulpe Instituti Scientiarum Typographum, Bononiae, 1757.

Schwartzman, Steven. The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English. The Mathematical Association of America, 1994.

Scott, J. F. A History of Mathematics. London: Taylor & Francis Ltd., 1960.

Seltman, Muriel, and Eddie Mizzi. "Thomas Harriot: Father of English Algebra?" The Mathematical Intelligencer, vol 19, number 1, 1997.

Shapiro, Harold N. Introduction to the Theory of Numbers. John Wiley & Sons, Inc., 1983.

Singh, Simon. Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Puzzle. Walker Publishing Co., Inc., 1997.

Smart, James R. Modern Geometries, Third Edition. Pacific Grove, California: Brooks/Cole Publishing Co., 1988.

Smith, David Eugene. History of Modern Mathematics. Fourth edition, 1906.

Smith, David Eugene (1860-1944). History of Mathematics, vol. I. New York: Dover Publications, Inc., 1958.

Smith, David Eugene. History of Mathematics, vol. II. Boston: Ginn and Co., 1925.

Sommerville, D. M. Y. The Elements of Non-Euclidean Geometry. Chicago: The Open Court Publishing Co., 1919.

Stein, Sherman K., and Anthony Barcellos. Calculus and Analytic Geometry. McGraw Hill, Inc., 1992.

Stigler, Stephen M. (ed) (1980), American Contributions to Mathematical Statistics in the Nineteenth Century,  2 volumes. New York: Arno Press.

Stigler, Stephen M. The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press of Harvard University Press, Cambridge, Mass., 1986.

Stigler, Stephen M. Statistics on the Table. Belknap Press of Harvard University Press, Cambridge, Mass., 1999

Struik, Dirk Jan. A source book in mathematics, 1200-1800. Princeton University Press.

Tankard, James W., Jr. The Statistical Pioneers. Cambridge, Mass.: Schenkman Publishing Co., Inc., 1984.

Taylor, A. A Study of Maurice Frechet: I. His Early Work on Point Set Theory and the Theory of Functionals. Archive for History of Exact Sciences, 27 (3), 233-295. (1982)

Taylor, Charles. An Introduction to the Ancient and Modern Geometry of Conics. 1881.

Thompson, D'Arcy Wentworth Thompson. On Growth and Form (The Complete Revised Edition). Dover Books, 1992.

Todhunter, Isaac. A History of the Mathematical Theories of Attraction and the Figure of the Earth: From the Time of Newton to that of Laplace. London: Macmillam and Co., 1873.

v. Baravalle, H. The Geometry of the Pentagon and the Golden Section. The Mathematics Teacher, January 1948.

von Plato, Jan. Creating Modern Probability, Cambridge: Cambridge University Press, 1994.

Walker, Helen M. Studies in the History of Statistical Method, with a special reference to certain educational problems. Baltimore: Williams & Williams, 1929.

Youschkevitch, A. P. The Concept of Function up to the Middle of the 19th Century, Archive for History of Exact Science, 16 (1976).

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