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Mark Kac’s First Publication: A Translation of "O nowym sposobie rozwiązywania równań stopnia trzeciego" – Bibliography

David Derbes (University of Chicago Laboratory School, retired)

Alekseev, V. B. 2004. Abel’s Theorem in Problems and Solutions, based on the lectures of Professor V. I. Arnold. Translated by Francesca Aicardi. Dordrecht: Kluwer Academic Publishers (Springer).

Artin, E. 2007. Algebra with Galois Theory. Notes by Albert A. Blank. Courant Lecture Notes in Mathematics, vol. 15. Providence, RI: American Mathematical Society. (Note: This is not the same as Artin’s 1942 Notre Dame lecture series, Galois Theory, with notes by Arthur N. Milgram, published by Dover Publications, 2012.)

Bewersdorff, J. 2006. Galois Theory for Beginners: A Historical Perspective. Translated by D. Kramer. Student Mathematical Library, vol. 35. Providence, RI: American Mathematical Society.

Boole, G. 1842. Exposition of a general theory of linear transformations, Part II. Cambridge Mathematical Journal 3:106–119.

Boyer, C. B. 1985. A History of Mathematics. Princeton, NJ: Princeton University Press. (Orig. pub. 1968.)

Cardano, G. 1545. Artis magnae, sive de regulis algebraicis. Nuremberg: Ioh Petreius. English translation by T. Richard Witmer, The Rules of Algebra (Ars Magna), Cambridge, MA: MIT Press, 1968; reprinted as G. Cardano, Ars Magna or The Rules of Algebra, Garden City, NY: Dover Publications, 1993.

Cohen, J. E. 1986, October. A Life of the Immeasurable Mind. The Annals of Probability 14(4): 1139–1148.  

Dabkowska, E. 2019. Polish Mathematical Education Periodicals from 1930 to 1950. PhD diss., Columbia University.

Erdös, P., and M. Kac. 1940. The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions. American Journal of Mathematics 62(1/4): 738–742.

Fauvel, J., and J. Gray, eds. 1987. The History of Mathematics: A Reader. London and Milton Keynes: Macmillan Education association with the Open University (UK).

Feynman, R. 2006. Don’t You Have Time To Think? Edited by Michelle Feynman. London: Penguin Books. (Note: This is the same book as R. Feynman, Perfectly Reasonable Deviations from the Beaten Path; the title was changed for the British edition.)

Isaacs, I. M. 1985, October. Solution of Polynomials by Real Radicals. The American Mathematical Monthly 92(8): 571–575.

Kac, M. 1947. Random Walk and the Theory of Brownian Motion. The American Mathematical Monthly 54: 369–391. (Note: Awarded MAA Chauvenet Prize in 1950.)

Kac, M. 1949. On Distributions of Certain Wiener Functionals. Transactions of the American Mathematical Society 65: 1–13.

Kac, M. 1959a. Statistical Independence in Probability, Analysis and Number Theory. Carus Mathematical Monograph, vol. 12. Washington, DC: Mathematical Association of America. Reprinted by Dover Publications, Garden City, NY, 2018.

Kac, M. 1959b. Probability and Related Topics in Physical Sciences (Proceedings of the Summer Seminar, Boulder, Colorado, 1957), with special lectures by G. E. Uhlenbeck, A. R. Hibbs and B. van der Pol. New York: Interscience Publishers, Inc.

Kac, M., G. E. Uhlenbeck, and P. C. Hemmer. 1963. On the van der Waals Theory of the Vapor-Liquid Equilibrium, Parts I and II. Journal of Mathematical Physics 4: 216–228, 229–247.

Kac, M. 1966, April. Can one hear the shape of a drum? The American Mathematics Monthly 73(4/2): 1–23. (Note: Awarded MAA Chauvenet Prize in 1968.)

Kac, M., and S. M. Ulam. 1968. Mathematics and Logic: Retrospect and Prospects. Philadelphia: Frederick A. Praeger. Reprinted by Dover Publications, Garden City, NY, 1992.

Kac, M. 1979. Probability, Number Theory, and Statistical Physics: Selected papers. Edited by K. Baclawski and M. D. Donsker. Cambridge, MA: MIT Press.

Kac, M. 1985. Enigmas of Chance: An Autobiography. New York: Harper & Row.

Kalman, D. 2009. Uncommon Mathematical Excursions: Polynomia and Related Realms. Dolciani Mathematical Exposition, vol. 35, 79–82. Washington, DC: Mathematical Association of America.

Kline, M. 1972. Mathematical Thought from Ancient to Modern Times. Vol. 1. New York: Oxford University Press.

Livio, M. 2005. The Equation that Couldn’t Be Solved. New York: Simon & Schuster.

McFarland, A., J. McFarland, and J. T. Smith, eds. 2014. Alfred Tarski: Early Work in Poland—Geometry and Teaching. Berlin: Birkhaüser.

McKean, H. P. 1990. Mark Kac 1914–1984. Biographical Memoirs of the National Academy of Science. Vol. 59, 214–235. Washington, DC: The National Academies Press.

Mollame, V. 1890. Sul casus irreducibilis del’equazione cubicaRendiconto dell’Accademia delle Scienze Fisiche e Matematiche (Sezione della Società Reale di Napoli), ser. 2. 4:167–171.

Nahin, P. 1998. An Imaginary Tale: The Story of \(\sqrt{-1}\). Princeton, NJ: Princeton University Press.

Niss, M. 2018. A Mathematician Doing Physics: Mark Kac’s Work on the Modeling of Phase Transitions. Perspectives on Science 26(2): 185–212.

Pesic, P. 2003. Abel’s Proof. Cambridge, MA: MIT Press.

Roy, R. n.d. Mark Kac and the cubic, unpublished paper.

Roy, R. 2011. Sources in the Development of Mathematics. Cambridge: Cambridge University Press.

Stewart, I. 2015. Galois Theory. 4th ed. Boca Raton, FL: CRC Press.

Stroock, D. W. 2015. A Simple Pole in Ithaca, NY. Antiquitates Mathematicae 9(1): 93–104.

Struik, D. J., ed. 1969. A Source Book in Mathematics, 1200–1800. Cambridge, MA: Harvard University Press. Reprinted by Princeton University Press, Princeton, NJ, 2014.

Tignol, J.-P. 2001. Galois’ Theory of Algebraic Equations. Singapore: World Scientific.

Ulam, S. M. 1991. Adventures of a Mathematician. Berkeley and Los Angeles: University of California Press.

van der Waerden, B. L. 1970. Algebra. 3rd English ed. Translated by F. Blum and J. R. Schulenberger. Vol. 1. New York: Frederick Ungar Publishing Co.

Viète, F. 1615. De Aequationum Recognitione et Emendatione Tractatus Duo (Two Tracts on the Revision and Amendment of Equations). In F. Viète, The Analytic Art. Nine Studies in Algebra, Geometry and Trigonometry from the 'Opus Restitutæ Mathematicæ Analyseos, seu Algebra Nova,'  translated by T. Richard Witmer. Kent, OH: Kent State University Press, 1983; reprinted by Dover Publications, Garden City, NY, 1993.

Wolfson, P. R. 2008. George Boole and the origins of invariant theory. Historia Mathematica 35: 37–46.

David Derbes (University of Chicago Laboratory School, retired), "Mark Kac’s First Publication: A Translation of "O nowym sposobie rozwiązywania równań stopnia trzeciego" – Bibliography," Convergence (April 2021)