# Dr. Patrick X. Rault

Dr. George Haddix Community Chair of Mathematics

Assistant Director, STEM TRAIL Center

Director, COMMIT Network

Co-Director, Center for Undergraduate Research in Mathematics

Associate Professor of Mathematics

University of Nebraska Omaha

Dr. Patrick X. Rault has been a member of the University of Nebraska Omaha faculty since August, 2018. Before joining UNO, Dr. Rault spent eight years at the State University of New York at Geneseo and two years as Program Director of Mathematics for the distance college at the University of Arizona.

As the *Dr. George Haddix Community Chair of Mathematics*, Dr. Rault strives to meet the objectives of the Haddix endowment:

*Established in 2010 by George Haddix to provide leadership and resources for the UNO Mathematics Department, in coordination with the College of Education, to address the critical need for STEM majors, and to place UNO at the forefront of innovation in preparation of mathematics teachers.*

For more information on Dr. Rault, you're encouraged to see one of his projects:

STEM TRAIL Center: https://www.unomaha.edu/academic-affairs/stem-trail-center/index.php

COMMIT: https://www.comathinquiry.org/

SINE COMMIT: https://sites.google.com/view/iblinc

CURM: http://urmath.org/curm/

CUR Math-CS: http://www.mathcscur.org/

Twitter: @Patrick_Rault

Below are a few resources from old projects, for faculty and students, posted here 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-present

o UNO STEM TRAIL Center Teaching Practices Workshop Series, organizer, 2019-present

o IBL Iowa-Nebraska Community (IBLINC) co-leader, 2019-present

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

### Need to run into Dr. Rault in the hallway but canâ€™t due to university closure? Sign up for a quick hallway meeting:

## Instructor Resource: Priority sorting program for Inquiry Based Learning Courses

(Program by Brian Knapp, Fall 2011 Teaching Assistant for Math 239, Introduction to Mathematical Proof, at SUNY Geneseo).

This program has three pieces, and one "ReadMe" file with directions for use. There are two packages available here, one from 2011 and one from 2012. Each contains the following files:

* PrioritySystem.jar - the program, written in java (you may need to find and download java separately), for imputting grades, sorting students, and displaying the sorted list.

* ClassList.csv - a classlist template in the "commas separated value" format, readable by MS Excel.

* Options.txt - a file which lists parameters for changing the sorting algorithm based on frequency of class meetings and frequencey of presentations.

* ReadMe.rtf - a file which gives instructions for use of the program.

While this program is now being used at several other colleges (including Nazareth College in Rochester, NY and University of Toronto at Mississauga), the original version of this program was used in a 25 student sophomore-junior level Introduction to Mathematical Proof (Math 239) course at the State University of New York, College of Geneseo, using a textbook by Ron Taylor and me. This 3-credit class met for three 50-minute sessions per week, for 15 weeks.

Students were awarded 0-4 points for presenting proofs in class, and 0-3 points for presenting a calculation (see my article in the MAA Notes for more detail). These points were inputted into the computer program, which then displayed the re-sorted list on a smart-board screen; note that this Smartboard was not a primary board, but rather an "overflow" board for when the class ran out of space on the various blackboards in the room, and for when the instructor had something to present. The program also includes a "recentness" feature - in this version of the program students are given 125 temporary points on the day which they present, which is reduced to 25 the next day, 5 points the next, 1 point the next, and then 0 thereafter. This prioritizes students who have not presented recently, and prevents students from presenting on consecutive class meetings.

By popular request of students, the program was initially designed to quickly and efficiently display to students "who was up next" in the order of presentations; now, at the end of each class, I press the spacebar to reorder the list to the next day's recentness values. The program has also had the effect of giving a more transparent and fluid grading scheme, where students can quickly understand why they are or are not being chosen for a presentation.

More details about every facet of this program can be found in the ReadMe.rtf file (enclosed in either package), written by Brian Knapp.

Here are the files to download:

New package, with priority queue at the top of the screen. This is perfectly suited for rooms where the projector screen covers the blackboard or whiteboard, but one may pull down the screen just a few feet to allow for blackboard use "in the spotlight."

The original package, with the queue on the left side of the screen. This was designed for use on a Smartboard, where the left side is cannot be written on because of the presence of page tabs.

Note: if you are having trouble opening these zipped folders, please look into getting an unzipping program like Winzip.

## Student Resources

Here are some resources which may be useful to mathematics students.

**Student resources:**

LaTeX starter file, with many examples which you can edit and see the effect of.

## Publications

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