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Patrick Rault

Patrick Rault, PhD

Patrick Rault, PhD

  • Associate Professor
  • Dr. George Haddix Community Chair of Mathematics
  • DSC 227 / 402.554.3437
email:
prault@unomaha.edu
personal website:
https://sites.google.com/view/prault
area of focus:
  • Number Theory, Matrix Analysis, Mathematics Education, Undergraduate Research

Additional Information

Education

Ph.D., Mathematics, University of Wisconsin, 2008
B.S., Mathematics (with minor in Physics), College of William and Mary, 2003

Research Interests
I completed my Ph.D. at UW Madison in 2008, in the area of number theory (specifically, arithmetic geometry).  More recently I have branched out into linear algebra (specifically the study of numerical ranges in matrix analysis).  I also have interest in Mathematics Education, and more generally STEM (Science, Technology, Engineering, and Mathematics) Education.  In particular, I am interested in Inquiry-Based Learning,Undergraduate Research, and other High Impact Practices.
Selected Publications (with student co-authors underlined)

Cushman, Jane R; Gantner, Ryan; George, C. Yousuf; Morrow, Margaret L; Rault, Patrick X.  A Model for Expanding Active Learning Regionally: The Greater Upstate New York Inquiry-Based Learning Consortium, PRIMUS, July 2018.  DOI: 10.1080/10511970.2018.1424743.

Taylor, Ron; Rault, Patrick X.  A TeXas Style Introduction to Proof.  Mathematical Association of America (MAA) Textbook Series.  2017.  ISBN:  9781939512130.

Rault, Patrick X.  Teaching proofs via Inquiry-Based Learning.  Mathematical Association of America (MAA) Notes volume on “Beyond Lecture: Techniques to Improve Student Proof-Writing Across the Curriculum.”  2016, 177-184. 

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 M.  3-by-3 matrices with elliptical numerical range revisited.  Electronic Journal of 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, 161-175.

Cheung, Wilson; Rault, Patrick X.  On uniform bounds for rational points on quadratic rational curves and thin sets.  Journal for Algebra and Number Theory Academia. August 2012, 37-62.