# Dr. Patrick X. Rault

Department Chair & Professor of Mathematics, Idaho State University

President, COMMIT Network

Co-Director, Center for Undergraduate Research in Mathematics

Schedule a meeting (Zoom or in person): https://app.reclaim.ai/m/patrick-isu/quick-meeting

Dr. Patrick X. Rault joined the faculty at Idaho State University in 2022. Before joining ISU, Dr. Rault spent eight years at the State University of New York at Geneseo, two years as Program Director of Mathematics for the distance college at the University of Arizona, and four years as the Haddix Community Chair at the University of Nebraska at Omaha where he was the Assistant Director and co-founder of the STEM Teaching, Research, And Inquiry-based Learning (TRAIL) Center.

Students are encouraged to take a look at the Student Research link at the top of the page, to see whether they might be interested in getting involved in a collaborative project.

The second link at the top of the page includes a few resources from old projects, for faculty and students, posted for general use.

For an up-to-date CV, with updated publication and award lists, contact Dr. Rault directly. The following CV was updated in January 2022: curriculum vitae.

## Selected Leadership Roles

o COMmunities for Mathematics Inquiry in Teaching (COMMIT) Network, Director, 2019-2022; President 2022-2023

o UNO STEM TRAIL Center Teaching Practices Workshop Series, organizer & center Assistant Director, 2019-22

o South (D)akota, Iowa, NEbraska (SINE) COMMIT co-leader, 2019-22

o MAA Committee on the Teaching of Undergraduate Mathematics, chair, 2021-23

o MAA SIGMAA on Undergraduate Research, chair, 2018-20

o Center for Undergraduate Research in Mathematics, co-director, 2017-22

o Council of Undergraduate Research, Mathematics and Computer Science Division, chair, 2017-2019

## Publications

Camenga, Kristin; Rault, Patrick X; Spitkovsky, Ilya; Yates, Rebekah. The Gau-Wu Number for 4-by-4 and Select Arrowhead Matrices. Linear Algebra and its Applications. 644, 1 July 2022, 192-218. DOI: 10.1016/j.laa.2022.02.026

Camenga, Kristin; Collins, Brandon; Hoefer, Gage; Rault, Patrick X; Quezada, Jonny; Willson, James; Yates, Rebekah B. Johnson. On the Geometry of Numerical Ranges over Finite Fields. Linear Algebra and its Applications. 628, July 2021, 182-201. DOI: 10.1016/j.laa.2021.07.008.

Gantner, Ryan; Gomez Johnson, Kelly; Jakopovic, Paula; Ksir, Amy E; Rault, Patrick X. The COMmunities for Mathematics Inquiry In Teaching (COMMIT) Network. MAA Focus. 40 (6), 2020, 25-27. http://digitaleditions.walsworthprintgroup.com/display_article.php?id=3840598&view=687574

Camenga, Kristin; Deaett, Louis; Rault, Patrick X; Sendova, Tsvetanka; Spitkovsky, Ilya; Johnson Yates, Rebekah. Singularities of Base Polynomials and Gau-Wu Numbers Linear Algebra and Its Applications. Linear Algebra and Its Applications. 581, November 2019, 112-127. DOI: 10.1016/j.laa.2019.07.005.

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 (July 2017).

Rault, Patrick X. Teaching proofs via Inquiry-Based Learning. MAA Notes Volume on "Innovative Techniques for Teaching Proof-writing." Mathematics Association of America (MAA) Notes volume, 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. 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

## Awards

Inquiry-Based Learning Communities project. PI. NSF-DUE, Supplemental Funding Award for Award Number 1925188. $59,998. 2020-22.

Inquiry-Based Learning Communities project. PI. NSF-DUE, Award Number 1925188. $299,999 for 2019-22.

NebraskaMATH Omaha Noyce Partnership: Phase2, a Track 1 Noyce Teacher Scholarship Program. CoPI. NSF-DUE, Award Number 1852908. $1,177,299 for 2019-2024.

National Science Foundation grant to support the Center for Undergraduate Research in Mathematics (CURM). As Co-PI and CURM Co-Director, I am aiding in training national faculty applicants to work with undergraduates on research. NSF-DMS. $1,387,000 for 2017-2022.

Council on Undergraduate Research Transformations Project, to support implementation of new curricula to include scaffolded undergraduate research experiences in two science departments. Principal Investigator; project includes over 15 colleagues & administrators.

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). PI for $102,210. 2014-17. 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