Research Interests

Michael Filaseta works in the general area of Number theory, including analytic, classical algebraic, combinatorial, computational, elementary, and transcendence topics.  His specific research interests include lattice points close to (or on) a curve or surface, the distribution of special sequences of integers in short intervals, applications of Pade approximations to Number Theory, the irreducibility of polynomials over the rationals, computations with sparse or lacunary polynomials, and covering systems of the integers.  His most recent work has focused largely on polynomials over the rationals and, in particular, on their factorization.

Education

• B.A. in Mathematics, University of Arizona (1980)
• Ph.D. in Mathematics, University of Illinois at Urbana-Champaign (1984)

Honors and Awards

• Carolina Trustees Professorship (2017)
• Faculty Fellow of the South Carolina Honors College (2014-2017)
• Mungo Graduate Teaching Award (2010)
• The Distinguished Award of the Hardy-Ramanujan Society (with Ognian Trifonov) (1991)

Experience

• Professor, University of South Carolina (1995 – present)
• Assistant Chair, University of South Carolina (2012 – 2017)
• Associate Professor, University of South Carolina (1989 – 1995)
• Assistant Professor, University of South Carolina (1984 – 1989)

Courses Taught

• MATH 122: Calculus for Business Administration and Social Sciences
• MATH 141: Calculus I
• MATH 142: Calculus II
• MATH 174: Discrete Mathematics for Computer Science
• MATH 221: Basic Concepts of Elementary Mathematics I
• MATH 241: Calculus III
• MATH 511: Probability
• MATH 531: Foundations of Geometry
• MATH 532: Modern Geometry
• MATH 541: Algebraic Coding Theory
• MATH 544: Linear Algebra
• MATH 552: Applied Complex Variables
• MATH 554: Analysis I
• MATH 555: Analysis II
• MATH 574: Discrete Mathematics I
• MATH 580: Elementary Number Theory
• MATH 599F: The Theory of Equations
• MATH 780: Elementary Number Theory
• MATH 782: Analytic Number Theory I
• MATH 783: Analytic Number Theory II
• MATH 784: Algebraic Number Theory
• MATH 785: Transcendental Number Theory
• MATH 788F: The Theory of Irreducible Polynomials
• MATH 788G: The Theory of Irreducible Polynomials II
• MATH 788M: Computational Number Theory

Selected Publications

• Michael Filaseta and Robert Wilcox. An explicit dense universal Hilbert set, Mathematical Proceedings of the Cambridge Philosophical Society  167 (2019), 531-547.
• Michael Filaseta and Sam Gross. 49598666989151226098104244512918, Journal of Number Theory 137 (2014), 16--49.
• Michael A. Bennett, Michael Filaseta and Ognian Trifonov. On the factorization of consecutive integers, J. Reine Angew. Math. (Crelle's Journal) 629 (2009), 171--200.
• Michael Filaseta, Andrew Granville and Andrzej Schinzel. Irreducibility and greatest common divisor algorithms for sparse polynomials, Number Theory and Polynomials (ed. James McKee and Chris Smyth), LMS Lecture Note Series 352, Cambridge Univ. Press, 2008, pp. 155--176.
• Michael Filaseta, Kevin Ford, Sergei Konyagin, Carl Pomerance and Gang Yu. Sieving by large integers and covering systems of congruences, Journal of the AMS 20 (2007), 495-517.
• Michael Filaseta and Ognian Trifonov. The irreducibility of the Bessel polynomials,
  J. Reine Angew. Math. 550 (2002), 125--140.
• Michael Filaseta, Kevin Ford, and Sergei Konyagin. On an irreducibility theorem of A. Schinzel associated with coverings of the integers, Illinois J. Math. 44 (2000), 633--643.
• Michael Filaseta and Ognian Trifonov. The distribution of fractional parts with applications to gap results in number theory, Proc. London Math. Soc. 73 (1996), 241--278.
• Michael Filaseta. The irreducibility of all but finitely many Bessel polynomials, Acta Math. 174 (1995), 383--397.
• Michael Filaseta and Ognian Trifonov. On gaps between squarefree numbers, II, J. London Math. Soc. 45 (1992), 215--221.
• Michael Filaseta. An elementary approach to short interval results for k-free numbers, J. Number Theory 30 (1988), 208--225.