Office Hours

T:  1-2:20pm
R: 10-10:50am
(and as posted in my
google calendar)

 

interests

  • Matrix analysis (numerical ranges)
  • Number Theory
 

Patrick Rault

Associate Professor of

Mathematics

South 326C
1 College Circle
Geneseo, NY 14454
585-245-5392
rault@geneseo.edu

Patrick X. Rault has been a member of the Geneseo faculty since 2008.

Faculty Information

Education

  • Ph.D, University of Wisconsin at Madison; 2008
  • Delta Certificate in Research, Teaching, and Learning, University of Wisconsin at Madison; 2008
  • B.S, College of William and Mary; 2003
  • Math In Moscow, Independent University of Moscow, Spring 2003
  • Budapest Semesters in Mathematics, Fall 2002
  • Mathematics Advanced Study Semesters, The Pennsylvania State University, Fall 2001

Employment

  • Associate Professor, SUNY College at Geneseo: 2014-current
  • Assistant Professor, SUNY College at Geneseo: 2008-2014
  • Teaching Assistant, University of Wisconsin at Madison, 2003-2008
  • VIGRE Fellow, University of Wisconsin at Madison, 2004-2005

Research Interests

Matrix Analysis (numerical ranges) and Number Theory (counting functions).

Publications and Professional Activities

  • Taylor, Ron; Rault, Patrick X. A TeXas Style Introduction to Proof. Mathematical Association of America (MAA) Textbook Series (to appear).
  • Rault, Patrick X. Teaching proofs via Inquiry-Based Learning. MAA Notes Volume on “Innovative Techniques for Teaching Proof-writing.” to appear. Mathematics Association of America (MAA) Notes volume (to appear).
  • Coons, Jane I; Knowles, Doug; Jenkins, Jack; Luke, Rayanne; Rault, Patrick X. Numerical Ranges over Finite Fields. Linear Algebra and its Applications. 501, 2016, 37-47.
  • Camenga, Kristin; Rault, Patrick X; Sendova, Tsvetanka; Spitkovsky, Ilya. On the Gau–Wu number for some classes of matrices. Linear Algebra and its Applications. 444 (2014), 254-262.
  • Camenga, Kristin; Rault, Patrick X; Rossi, Dan; Sendova, Tsvetanka; Spitkovsky, Ilya. Numerical range of some doubly stochastic matrices. Applied Mathematics and Computation. 221, September 2013, 40 – 47.
  • Rault, Patrick X. On uniform bounds for rational points on rational curves and thin sets of arbitrary degree. Journal of Number Theory. 133 (9), 2013, 3112-3118.
  • Rault, Patrick X; Sendova, Tsvetanka; Spitkovsky, Ilya. 3-by-3 matrices with elliptical numerical range revisited. Electron. J. Linear Algebra 26, 2013, 158-167.
  • Bennett, Mike; Lazebnik, Kirill Y; Rault, Patrick X; Singer, Jeffrey A. On invariant area formulas and lattice point bounds for the intersection of hyperbolic and elliptic regions. Journal of Combinatorics and Number Theory 4 (3), 2012.
  • Cheung, Wilson; Rault, Patrick X. On uniform bounds for rational points on quadratic rational curves and thin sets. Journal of Algebra and Number Theory Academia, August 2012, 37-62.
  • Rault, Patrick X. On uniform bounds for rational points on rational curves and thin sets. JP Journal of Algebra, Number Theory and Applications, 23 (2), 2011, 171—185.
  • Rault, Patrick X. On uniform bounds for lattice points in intersections of hyperbolic plane regions. Journal of Combinatorics and Number Theory. 2 (3), 2010, 209--215
  • Rault, Patrick X. On uniform bounds for rational points on rational curves and thin sets. Ph.D. Thesis, 2008
  • Johnson, Charles R.; Harel, Yonatan; Hillar, Christopher J.; Groves, Jonathan M.; Rault, Patrick X. Absolutely flat idempotents. Electron. J. Linear Algebra 10, 2003, 190—200

Affiliations

  • Henry L. Alder Award, presented by the Mathematics Association of America (MAA), 2015
  • Center for Undergraduate Research in Mathematics (CURM) $22,000 mini-grant for a 2014-15 student research group.
  • Elected to the Council on Undergraduate Research (CUR) for 2014-17
  • Educational Advancement Foundation (EAF) grant to support training initiatives in Inquiry-Based Learning (IBL). $60,000 for first year. 2014. Joint with St. John Fischer College, Nazareth College, SUNY Plattsburgh, and Buffalo State.
  • Council on Undergraduate Research (CUR) Mathematics and Computer Sciences Division 2013 Faculty Mentoring (National) Award for Outstanding Mentoring of Undergraduate Students in Research.
  • “Honoring Teachers” Award, by the Teaching and Learning Center and the SA Academic Affairs Committee, for “positively impacting students’ experience.” 2013-2014.
  • Project NExT Fellow (New Experiences in Teaching), 2008-2009
  • NSF VIGRE Fellow, 2004-2005
  • Barry M. Goldwater Scholar, 2002-2004
Spring 2016 Classes

MATH 233:
Linear Algebra I

    Study of matrices, matrix operations, and systems of linear equations, with an introduction to vector spaces and linear transformations. Elementary applications of linear algebra are included. Prerequ
    isites: MATH 213 or MATH 221 or permission of instructor. Offered every semester
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MATH 330:
Abstract Algebra

    A study of the basic properties of groups, rings, and integral domains, including the fundamental theorem of group homomorphisms. The concepts basic to the development of algebraic systems are studied
    initially. Prerequisites: MATH 222, MATH 233, and MATH 239. Offered every semester
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MATH 348:
Oral Presentation &Res Seminar

    In this course, the student will research a mathematical topic and prepare for an oral presentation based on that research. The student will learn about research resources such as journals and electr
    onic databases. Students will learn mathematical writing conventions and presentation techniques. Students will prepare a talk of at least one half hour in length to be presented in a public forum. Prerequisites: MATH 239 and permission of the instructor. Co-requisite: Student must be a mathematics major who is simultaneously enrolled in a 300 level mathematics course. Offered every spring or more often if demand in sufficient
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