I teach across the mathematics curriculum, including Calculus I, II, and III, Linear Algebra, Foundations of Mathematics, Abstract Algebra I (Group Theory) and II (Ring and Field Theory), and Number Theory. I also enjoy creating courses that cut across disciplines and schools such as "Vienna: The Biography of a City," a travel course to Vienna.
My research lies in the history of mathematics, particularly in the fields of algebra and number theory. When Mark Warner was governor of Virginia he asked "what do historians of mathematics study?" That is a great question. We study mathematics, the people who create mathematics, the institutions that support mathematics, the false starts in particular areas of mathematics, the politics that influence the development of mathematics and how the larger cultural context impinges on the development of mathematics. This discipline combines technical questions in mathematics with appropriate historical questions to yield a rich perspective on both mathematics and history. If you are interested in pursuing research in this area, please contact me.
State Council of Higher Education for Virginia's Outstanding Faculty Award
Dumbaugh, Della and Joachim Schwermer, Emil Artin and Beyond: Class Field Theory and L-Functions, Zürich: European Mathematical Publishing House, ~250 pages, ISBN: 978-3-03719-146-0, expected 2014.
Dumbaugh, Della and Joachim Schwermer, “Creating a Life: Emil Artin in America,” Bulletin of the American Mathematical Society 50 (2013): 321-330.
Dumbaugh, Della and Joachim Schwermer, “The collaboration of Emil Artin and George Whaples: Artin’s mathematical circle extends to America,” Archive for History of Exact Sciences 66 (2012): 465-484. DOI 10.1007/s00407-012-0100-2.
Dumbaugh, Della D. and Hannah Fenster. Review of Professor Mommy: Finding Work-Family Balance in Academia, Association for Women in Mathematics Newsletter 42 (4) July-August, 2012.
Fenster, Della D. "Emil Artin," in The Princeton Companion to Mathematics, pp. 812-813, edited by W. T. Gowers and J. Barrow-Green, Princeton: Princeton University Press, 2008.
Fenster, Della D. "Research in Algebra at the University of Chicago: Leonard Eugene Dickson and A. Adrian Albert," History of Algebra in the 19th and 20th Centuries, pp. 179-197, edited by Jeremy J. Gray and Karen Hunger Parshall, Providence, R.I., and London, England: The American Mathematical Society and the London Mathematical Society, 2007.
Fenster, Della D. and Joachim Schwermer, "Beyond Class Field Theory: Helmut Hasse's Arithmetic in the Theory of Algebras in Early 1931," Archive for History of Exact Sciences 61 (2007): 425-456.
Fenster, Della D. and Joachim Schwermer, "A Delicate Collaboration: A. Adrian Albert and Helmut Hasse and the Principal Theorem in Division Algebras in the Early 1930's," Archive for History of Exact Sciences 59 (2005): 349-379.
Fenster, Della D. "Artin in America (1937-1958): A Time of Transition," Emil Artin: Leben und Werk, pp. 99-118, edited by Karin Reich and Alexander Kreuzer, Augsburg, Dr. Erwin Rauner Verlag, 2007.
Fenster, Della D. "Gauss Goes West: The Reception of the Disquisitiones Arithmeticae in the USA," in The Shaping of Arithmetic: after Carl-Friedrich Gauss's Disquisitiones Arithmeticae, pp. 463-479, edited by Catherine Goldstein, Norbert Schappacher, and Joachim Schwermer, Heidelberg: Springer-Verlag, 2007.
Fenster, Della D. and Joachim Schwermer "Composition of Quadratic Forms: An Algebraic Perspective," in The Shaping of Arithmetic: after Carl-Friedrich Gauss's Disquisitiones Arithmeticae, pp. 145-158, edited by Catherine Goldstein, Norbert Schappacher, and Joachim Schwermer, Heidelberg: Springer-Verlag, 2007.
Fenster, Della D. "Leonard Dickson, History of the Theory of Numbers," in Landmark Writings in Western Mathematics, 1640-1940, pp. 833-843, edited by Ivor Grattan-Guinness, Amsterdam: Elsevier Press, 2005.