# 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 http://www.jstor.org/.

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,*2

^{nd}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.

Conics.

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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