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Sums of Powers of Positive Integers - References

Janet Beery (University of Redlands)

– Apostol, Tom M., 2008, “A Primer on Bernoulli Numbers and Polynomials,” Mathematics Magazine 81:3, 178-190.

– Baron, Margaret E., 1987, The Origins of the Infinitesimal Calculus, New York: Dover; first published by Pergamon Press, Oxford, 1969.

– Beery, Janet, and Jacqueline Stedall, 2009, Thomas Harriot’s Doctrine of Triangular Numbers: the “Magisteria Magna”, Zurich: European Mathematical Society.

– Bernoulli, Jakob, 1713, Ars Conjectandi, Basel.

– Boyer, Carl B., 1943, “Pascal’s Formula for the Sums of Powers of the Integers,” Scripta Mathematica 9, 237-244.

– Briggs, Henry, 1624, Arithmetica Logarithmica, London.

– Edwards, A.W.F., 1987, Pascal’s Arithmetical Triangle, London: Charles Griffin.

– Edwards, C. H., 1980, The Historical Development of the Calculus, New York: Springer.

– Faulhaber, Johannes, 1631, Academia Algebrae, Augsburg; accessed through University of Dresden Digital Library,

– Frisch, Christian (editor), 1858-1872, Joannis Kepleri Astronomi Opera Omnia, Vol. IV, Frankfurt.

– Hakewill, George, 1630, An Apologie of the Power and Providence of God in the Government of the World (2nd ed.), Oxford.

– Harriot, Thomas, “De Numeris Triangularibus et inde De Progressionibus Arithmeticis,” British Library Additional MS 6782, ff. 107-146v.

– Harriot, Thomas, “Ad aggregata [Squares], [Cubes], [Square-squares], et c. (For Sums of Squares, Cubes, Square-squares, Etc.),” British Library Additional MS 6782, ff. 239-240v.

– Harriot, Thomas, “Ad Progressiones,” British Library Additional MS 6782, ff. 234-236.

– Heath, Thomas L., 1981, A History of Greek Mathematics, Vol. II, New York: Dover; first published by Clarendon Press, Oxford, 1921.

– Hutton, Charles, 1812, Tracts on Mathematical and Philosophical Subjects, Vol. I, London.

– Katz, Victor, 1998, A History of Mathematics: An Introduction (2nd ed.), Reading, Mass.: Addison-Wesley.

– Knuth, Donald E., 1993, “Johann Faulhaber and Sums of Powers,” Mathematics of Computation 61:203, 277-294.

– Mahoney, Michael, 1994, The Mathematical Career of Pierre de Fermat (2nd ed.), Princeton University Press.

– Maurolico, Francisco, 1575, Arithmeticorum Libri Duo, Venice.

– Nelsen, Roger B., Proofs Without Words, 1993, Washington, DC: Mathematical Association of America.

– Pascal, Blaise, 1665, Traite du Triangle Arithmetique, Paris.

– Recorde, Robert, 1557, Whetstone of Witte, London; reprinted 1969, New York: Da Capo Press.

– Schneider, Ivo, 1993, Johannes Faulhaber (1580-1635): Rechenmeister in einer Welt des Umbruchs, Basel: Birkhauser.

– Smith, David Eugene (editor), 1964, A Source Book in Mathematics, New York: Dover; first published by McGraw-Hill, 1929.

– Stein, Sherman, 1999, Archimedes: What Did He Do Besides Cry Eureka?, Washington, DC: Mathematical Association of America.

– Struik, D. J. (editor), 1969, A Source Book in Mathematics (1200-1800), Cambridge, Mass.: Harvard University Press.

Janet Beery (University of Redlands), "Sums of Powers of Positive Integers - References," Convergence (July 2010), DOI:10.4169/loci003284

Sums of Powers of Positive Integers