Appendix B

Chapter 1: References and Further Readings

Bennet, Deborah, Randomness, Cambridge, MA: Harvard University Press, 1998.

Bernstein, Peter, Against the Gods: The Remarkable Story of Risk, New York: John Wiley & Sons, 1996.

David, Florence Nightingale, Games, Gods, and Gambling, New York: Dover Publications, 1998.

Everitt, Brian S., Chance Rules: An Informal Guide to Probability, Risk, and Statistics, New York: Springer-Verlag, 1999.

Feller, William, An Introduction to Probability Theory and its Applications, 2 vols, New York: John Wiley & Sons, 1968.

Galilei, Galileo, Sopra le Scoperte dei Dadi, Opere, Firenze, Barbera, 8 (1898), pp. 591–594.

Hald, Anders, A History of Probability and Statistics and Their Applications before 1750, New York: John Wiley & Sons, 1990.

_____, A History of Mathematical Statistics From 1750 to 1930, New York: John Wiley & Sons, 1998.

Keynes, John M., A Treatise on Probability, New York: Harper and Row, 1992.

McGervey, John d., Probabilities in Everyday Life. New York: Ivy Books, 1992.

Packel, Edward, The Mathematics of Games and Gambling, Washington, DC: Mathematical Association of America, 1981.

Ross, Ken, A Mathematician at the Ballpark: Odds and Probabilities for Baseball Fans, New York: Pearson Education, 2004.

Chapter 2: References and Further Readings

Albert, James, Teaching Statistics Using Baseball, Washington, DC: Mathematical Association of America, 2003.

Gould, Stephen J., The Mismeasure of Man, New York: W. W. Norton, 1996.

Hald, Anders, A History of Probability and Statistics and Their Applications before 1750, New York: John Wiley & Sons, 1990.

_____, A History of Mathematical Statistics From 1750 to 1930, New York: John Wiley & Sons, 1998.

Jacoby, Russell, and Naomi Glauberman (eds), The Bell Curve Debate: History, Documents, Opinions, New York: Times Books, 1995.

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

Quetelet, Adolphe, Letters addressed to H. R. H. the grand duke ofSaxe Coburg and Gotha, on the Theory of Probabilities as Applied to the Moral and Political Sciences, trans. O. G. Downes, London: Layton, 1849.

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

____, Statistics on the Table, Cambridge: Harvard University Press, 1999.

Walpole Ronald E., Myers, Raymond H., Myers, Sharon L., Ye, Keying, and Yee, Keying, Probability and Statistics for Engineers and Scientists, (7th Edition), New Jersey: Prentice Hall, 2002.

Chapter 3: References and Further Readings

Arrow, Kenneth, Social Choice and Individual Values, 2nd ed. New Haven: Yale University Press, 1963.

Barry, Brian W. and Russell Hardin, Rational Man and Irrational Society? An Introduction and Sourcebook. Beverly Hills: Sage Publications, 1982.

Bauer, Alissa, “Rank System Strips Teams of Postseason Opportunities.” University Daily Kansan, p. 2, December 8, 2004.

Black, Duncan, The Theory of Committees and Elections. Cambridge: Cambridge University Press, 1958.

Borda, Jean-Charles de, Memoire sur les Elections au Scrutin’. Paris: His 1’Academie Royale des Sciences, 1781.

Condorcet, Marquis de, Essai sur L’ application L’ analyse a la probabilite des Decisions Rendues a la Pluralite des Voix (trans. Essay on the Application of Mathematics to the Theory of Decision-Making). Paris: L’Imprimerie Royale, 1785.

Devlin, Keith, “Election Math.” Devlin’s Angle, MAA, 2004. Online. devlin/devlin_114_04.html.

Fishburn, Peter C, “Paradoxes of Voting.” American Political Science Review 68(1974), No. 2, 537–556.

Harsanyi, John C, “Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility.” Journal of Political Economy 61(1955), 309–321.

Hilburn, Robert, “It’s Time to Nominate a New System.” Los Angeles Times, February 28, 2002.

Johnson, Paul E., Social Choice: Theory and Research. Thousand Oaks, CA: Sage, 1998.

Jones, Bradford, Benjamin Radcliffe, Charles Taber, and Richard Timpone, “Condorcet Winners and the Paradox of Voting.” American Political Science Review 89(1995), No. 1, 137–144.

Mackenzie, Dana, “Making Sense Out of Consensus: How Did That Guy Win?” SIAM News 33, 2000a.

Mackenzie, Dana, “May the Best Man Lose.” Discover 21(2000b), No. 11, 85–91.

May, Kenneth O, “A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision.” Econometrica 20(1952), 680–784.

Nash, John F, “The Bargaining Problem.” Econometrica 18(1950), 155–162.

Nelson, Randy A., Michael R. Donihue, Donald M. Waldman, and Calbraith Wheaton, “What’s An Oscar Worth?” Economic Inquiry 39(2001), No. 1, 1–16.

Novaselic, Krist, “Instant Runoff Voting Used for First Time in San Francisco Elections” 2004. http://www.fixour.us/editorials/l1.08.04.html.

Novoselic, Krist, Of Grunge & Government: Let’s Fix This Broken Democracy! New York: Akashic Books, 2004.

Reilly, Benjamin, “Social Choice in the South Seas: Electoral Innovation and the Borda Count in the Pacific Island Countries.” International Political Science Review 23 (2002), No. 4, 355–372.

Riker, William H, Liberalism Against Populism: A Confrontation Between the Theory of Democracy and the Theory of Social Choice. San Francisco, CA: W. H. Freeman, 1982. Riker, William H, The Art of Political Manipulation. New Haven, CT: Yale University Press, 1986.

Saari, Donald G, Geometry of Voting. Berlin: Springer-Verlag, 1994.

Schulze, Markus, “A New Monotonic and Clone-Independent Single-Winner Election Method.” Voting Matters 17(2003), 9–19.

Woodling, Chuck, “Maybe It’s Time To Do Away with AP Poll.” Lawrence Journal World, p. 3C, December 24, 2004.

Chapter 4: References and Further Readings

Coleman, A., Game Theory and Experimental Games, Pergamon Press, Oxford, 1982.

Davenport, W. C, Jamaican Fishing Village, Papers in Carribean Anthropology, 59, (I. Rouse ed.) Yale University Press, 1960.

Davis, M. D., Game Theory, Basic Books, New York, 1983.

Dixit, A. and Nalebuff B., Thinking Strategically, W. W. Norton & Company, New York, 1991.

Dresher, M., The Mathematics of Games and Strategy, Theory and Applications, Dover, New York, 1981.

Gale, D., The Theory of Linear Economic Models, McGraw Hill, New York, 1960.

Haywood O. G. Junior, Military Decision and Game Theory. J. of the Operations Research Society of America, 2(1954), 365–385.

Heckathorn, D. D., The Dynamics and Dilemmas of Collective action, American Sociological Review, 61(1996) No. 2, 250–277.

Jones, A. J., Game Theory: Mathematical Models of Conflict, Halstead Press, Chichester, England.

Luce, R. D., and Raiffa, H., Games and Decision: Introduction and Critical Survey, John Wiley and Sons, London 1957.

Maynard Smith, J. and Parker, G. A., The Logic of Animal Conflict, Nature, 246(1973), 15–18.

Maynard Smith, J., Evolution and the Theory of Games, Cambridge University Press, London 1982.

Montgomery J. D., Equilibrium Wage Dispersion and Interindustry Wage Differentials, Quarterly Journal of Economics 1991, 163—179.

Morris, P., Introduction to Game Theory, Springer-Verlag, New York, 1994.

Nash, J., Non-cooperative games, Annals of Mathematics, 54(1950), 286–295.

Packel E., The Mathematics of Games and Gambling, The Mathematical Association of America, Washington D. C, 1981.

Poundstone, W., Prisoner’s Dilemma, Doubleday: New York, 1992.

Rapoport A., Guyer, M. J., and Gordon, D. G., The 2 x 2 Game, The University of Michigan Press: Ann Arbor, 1976.

Sinervo, B., and Lively, C. M., The Rock-Paper-Scissors game and the evolution of alternative male strategies, Nature, 380(1996), 240–243.

Straffin P. D., Game Theory and Strategy, The Mathematical Association of America: Washington, D. C, 1993.

Thomas L. C, Games, Theory and Applications, Ellis Horwood Limited: Chichester, England, 1984.

Ventsel, Y. S., Elements of Game Theory, Mir Publishers: Moscow, 1980.

von Neumann, J., Zur Theorie der Geselltschaftsspiele, Mathematische Annalen, 100(1928), 295–300.

von Neumann, J. and Morgenstern O., Theory of Games and Economic Behavior, Princeton University Press: Princeton 1947.

Williams, J. D., The Compleat Strategyst, Dover, New York, 1986.

Zagare, F. C, Game Theory: Concepts and Applications, Sage Publications: Beverly Hills, 1984.

Chapter 5: References and Further Readings

Dorfman, Robert, Samuelson, Paul A., and Solow, Robert M., Linear Programming and Economic Analysis, New York: Dover Publications, 1987.

Gass, Saul I., An Illustrated Guide to Linear Programming, New York: McGraw-Hill, 1970.

____, Decision Making, Models, and Algorithms, Florida: Krieger, 1991.

Kolman, Bernard and Beck, Robert E., Elementary Linear Programming with Applications, (2nd Edition), New York: Academic Press, 1995.

Chapter 6: References and Further Readings

Ausdley, W. and G., Designs and Patterns from Historic Ornaments, Dover Publications: New York, 1989.

Budden, F. J., Fascination of Groups, Cambridge University Press, Cambridge, 1972.

Farmer, D. W., Groups and Symmetry: A Guide to Discovering Mathematics, American Mathematical Society: Washington DC, 1996.

Grünbaum, B., and Shepard, G. C, Tilings and Patterns, W. H. Freeman and Co., 1987.

Jones, O., The Grammar of Chinese Ornament, Studio Editions: London, 1987.

Martin, G. E., Transformation Geometry: An Introduction to Symmetry, Springer-Veralg: New York, 1982.

Schattschneider, D., The Plane Symmetry Groups, Their Recognition and Notation, Amer. Math. Monthly, 85(1978) no. 6, 439–50.

Weyl, H., Symmetry, Princeton University Press: Princeton, 1952.

Chapter 7: References and Further Readings

Coxeter, H. S. M., Regular Polytopes, Dover Publications: New York, 1973.

Hilton, P., and Pedersen, Jean, Build Your Own Polyhedra, Addison Wesley: Reading, MA, 1994.

Weyl, H., Symmetry, Princeton University Press: Princeton, 1952.

Chapter 8: References and Further Readings

[1]R. Adrain, Research concerning the probabilities of the errors which happen in making observations, Analyst 1(1808), 93–109. Reprinted in Stigler 1980.

[2]D. Bernoulli, Dijudicatio maxime probabilis plurium observationam discrepantium atque versimillima inductio inde formanda. Ada Acad. Set Imp. Petrop., 1(1777) 3–23. Reprinted in Werke 2(1982), 361–375. Translated into English by C. G. Allen as “The most probable choice between several discrepant observations and the formation therefrom of the most likely induction,” Biometrica, 48(1961) 1–18; reprinted in Pearson and Kendall (1970).

[3]______, Specimen philosophicum de compensationibus horologicis, et veriorimensura temporis. Ada Acad. Set Imp. Petrop. 2(1777), 109–128. Reprinted in Werke 2(1982), 376–390.

[4]F. W. Bessel, Untersuchungen über die Wahrscheinlichkeit der Beobachtungsfehler, Astron. Nadir. 15(1838), 369–04. Reprinted in Abhandlungen 2.

[5]R. Cotes, Aestimatio Errorum in Mixta Mathesi, per Variationes Partium Trianguli Plani et Sphaerici. In Opera Miscellanea Cambridge, 1722.

[6]F. N. David, Games, Gods, and Gambling, New York: Hafner Pub. Co., 1962.

[7]C. Eisenhart, The background and evolution of the method of least squares. Unpublished. Distributed to participants of the ISI meeting, 1963. Revised 1974.

[8]W. Feller, An Introduction to Probability Theory and its Applications, 2 vols, John Wiley & Sons: New York, 1968.

[9]G. Galilei, Dialogue Concerning the Two Chief World Systems – Ptolemaic & Copernican (S. Drake translator), 2nd ed., Berkeley, Univ. California Press, 1967.

[10]F. Galton, Hereditary Genius: An Inquiry into its Laws and Consequences. London: Macmillan, first ed. 1863, 2nd ed. 1892.

[11]_____, Statistics by intercomparison, with remarks on the law of frequency of error. Philosophical Magazine, 4th series, 49(1875), 33–6.

[12]C. F. Gauss, Theoria Motus Corporum Celestium. Hamburg: Perthes et Besser, 1809. Translated as Theory of Motion of the Heavenly Bodies Moving about the Sun in Conic Sections (trans. C. H. Davis), Boston, Little, Brown 1857. Reprinted: New York: Dover 1963.

[13]C. C. Gillispie, Mémoires inedits ou anonymes de Laplace sur la théorie des erreurs, les polyômes de Legendre, et la philosophie des probabilités. Révue d’histoire des sciences 32(1979), 223–279.

[14]G. J. ’sGravesande, Démonstration mathématique de la direction de la providence divine. Oeuvres 2(1774), 221–236.

[15]G. Hagen, Grundzüge der Wahrscheinlichskeit-Rechnung, Dummler: Berlin, 1837.

[16]A. Hald, A History of Probability and Statistics and Their Applications before 1750. New York: John Wiley & Sons, 1990.

[17]_____, A History of Mathematical Statistics From 1750 to 1930. New York: John Wiley & Sons, 1998.

[18]J. F. W. Herschel, Quetelet on probabilities, Edinburgh Rev. 92(1850) 1–57.

[19]J. Kepler, New Astronomy (W. H. Donahue, translator) Cambrdige: Cambridge University Press, 1992.

[20]J. Lancaster, private communication, 2004.

[21]P. S. Laplace, Mémoire sur la probabilité des causes par les évènements. Mémoires de l’Academie royale des sciences presentés par divers savan 6(1774), 621–656. reprinted in Laplace, 1878–1912, Vol. 8, pp 27–65. Translated in [38].

[22]____, Mémoire sur les approximations des formules qui sont fonctions de très grand nombres et sur leur applications aux probabilités. Mémoires de l’Academie des sciences de Paris, 1809, pp. 353–415, 559–565. Reprinted in Oeuvres complètes de Laplace, Paris: Gauthier-Villars, vol. 12, pp. 301–353.

[23]____, Recherches sur le milieu qu’il faut choisir entre les résultat de plusieurs obervations. In [13] pp. 228–256.

[24]J. C. Maxwell, Illustrations of the dynamical theory of gases. Phil. Mag. 19(1860), 19–32. Reprinted in The Scientific papers of James Clerk Maxwell. Cambridge, UK: Cambridge University Press, 1890, and New York, Dover, 1952.

[25]A. de Moivre, Approximatio ad Summam Terminorum Binomii in Seriem Expansi. Printed for private circulation, 1733.

[26]A. de Morgan, Least Squares, Penny Cyclopaedia. London: Charles Knight, 1833–1843.

[27]E. S. Pearson, and M. Kendall (eds.), Studies in the history of statistics and probability. Vol. 1, London: Griffin, 1970.

[28]K. Pearson, Notes on the History of Correlation. Biometrika 13(1920) 25–5. Reprinted in [27].

[29]R. L. Placket, The principle of the arithmetic mean, Biometrika 45(1958), 130–135. Reprinted in [27].

[30]____, Data Analysis Before 1750, International Statistical Review, 56(1988), No. 2, 181–195.

[31]T. M. Porter, The Rise of statistical Thinking 1820–1900, Princeton: Princeton University Press, 1986.

[32]A. Quetelet, Lettres à S. A. R. Le Due Régnant de Saxe Cobourg et Gotha, sur la théorie des probabilités, appliquée aux sciences morales et politique. Brussels: Hayez, 1846.

[33]____, Letters addressed to H. R. H. the grand duke of Saxe Coburg and Gotha, on the Theory of Probabilities as Applied to the Moral and Political Sciences, trans. O. G. Downes. London: Layton, 1849. Translation of [32].

[34]____, A Treatise on Man and the Development of his Faculties, New York: Burt Franklin, 1968.

[35]O. B. Sheynin, The history of the theory of errors. Deutsche Hochschulschriften [German University Publications], 1118. Hänsel-Hohenhausen, Egelsbach, 1996, 180 pp.

[36]T. Simpson, A Letter to the Right Honourable George Macclesfield, President of the Royal Society, on the Advantage of taking the Mean, of a Number of Observations, in practical Astronomy, Phil. Trans. 49(1756), 82–93.

[37]____, Miscellaneous Tracts on Some Curious, and Very Interesting Subjects in Mechanics, Physical-Astronomy, and Speculative Mathematics. London: Nourse, 1757. [38] S. M. Stigler, Memoir on the probability of the causes of events. Statistical Science 1(1986) 364–378.

[39]____, The History of Statistics: The Measurement of Uncertainty before 1900. Cambridge: The Belknap Press of the Harvard University Press, 1986.

[40]____, American Contributions to Mathematical Statistics in the Nineteenth Century. 2 vols., New York: Arno Press, 1980.

[41]____, Statistics on the Table, Cambridge: Harvard University Press, 1999.

Chapter 9: References and Further Readings

[1]K. Appel and W. Haken, The four color problem, Mathematics Today, ed. L. A. Steen, Springer-Verlag. 1978, pp. 153–180.

[2]N. L. Biggs, E. K. Lloyd, and R. J. Wilson, Coloring maps on surfaces, Graph Theory, 1736–1936, Oxford University Press, 1976, pp. 109–130.

[3]R. C. Bose, On the construction of balanced incomplete block designs, Ann. of Eugenics, 9 (1939) 353–399.

[4]H. Cohn, Conformal Mapping on Riemann Surfaces, Dover, 1967.

[5]R. Courant and H. Robbins, What is Mathematics?, Oxford, 1941.

[6]H. S. M. Coxeter, The map-coloring ofunorientable surfaces, Duke Math. J., 10 (1943) 293–304.

[7]G. A. Dirac, Map colour theorems, Can. J. Math., 4 (1952) 480–90.

[8]P. Franklin, A six color problem, J. Math. Physics, 13 (1934) 363–369.

[9]W. Gustin, Orientable embeddings of Cayley graphs, Bull. Amer. Math. Soc, 69 (1963) 272–275.

[10]P. J. Heawood. Map color theorem, Quart. J. Math., 24 (1890) 332–338.

[11]L. Heffter, Uber das Problem der Nachbargebiete, Math. Ann. 38 (1891) 477–508. An English translation of much of this is in reference [2].

[12]D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination, Chelsea, 1952.

[13]I. N. Kagno, A note on the Heawood color formula, J. Math. Physics, 14 (1935) 228–231.

[14]A. B. Kempe, On the geographical problem of the four colors, Amer. J. Math., 2 (1879) 193–200.

[15]W. S. Massey, Algebraic Topology: An Introduction, Harcourt, Brace & World, 1967.

[16]J. Mayer, he Probléme des Regions Voisines sur les Surfaces Closes Orientables. J. Comb. Th, 6 (1969) 177–195.

[17]A. F. Möbius, Uber die Bestimmung des Inhaltes eines Polyeders, Ber. K. Sachs. Ges. Wiss. Leipzig Math-Phys Cl., 17 (1865) 31–68, also Werke, vol. 2, pp. 473–512.

[18]B. Riemann. Grundlagen fur eine allgemeine Theorie desFunktionen einer verandliche Grosse, Collected Works, Dover. 1953.

[19]G. Ringel, Bestimmung der Maximalzahl der Nachbargebiete auf nichtorientierbaren Flachen, Math. Ann., 127 (1954) 181–214.

[20]____. Map Color Theorem, Springer-Verlag, 1974.

[21]H. Tietze, Eine Bemerkungen uber das Problem der Kartenfarbens auf dnseitigen Flachen, Jahrsber. Deutsch. Math. Vereinigung, 19 (1910), pp. 155–159. An English translation of much of this is in reference [2].

[22]J. W. T. Youngs, The Heawood map-coloring conjecture. Graph Theory and Theoretical Physics, Academic Press, 1967, pp. 313–354.