Research

My research in functional analysis involves finding sufficient conditions under which mappings between function or operator algebras are isomorphisms and to this point has focused on norm-preserving and spectrum-preserving conditions.

I have recently begun considering numerical range problems as well, starting with exploring conditions under which the numerical range of an $n\times n$ matrix will have $n$-fold symmetry about the origin.

I am also interested in how undergraduates learn mathematics, in future teacher preparation, and in math enrichment for gifted K-12 students. I have worked with Kristin Camenga, a former Houghton colleague, on helping teachers make connections between Real Analysis and the 7-12 curriculum.

Publications

Deaett, L., Lafuente-Rodriguez, R., Marin, J., Martin, E., Patton, L., Rasmussen, K., and Yates, R. Trace conditions for symmetry of the numerical range, Electronic Journal of Linear Algebra, vol. 26, International Linear Algebra Society, September 2013, pp. 591-603.
Camenga, K., and Yates, R. Connecting the dots: rediscovering continuity, Mathematics Teacher, accepted.
Hatori, O., Lambert, S., Luttman, A., Miura, T., Tonev, T., and Yates, R. Spectral Preservers in Commutative Banach Algebras, in Function Spaces in Modern Analysis, Contemporary Mathematics, vol. 547, American Mathematical Society, Providence, RI, 2011, pp. 103-123.
Tonev, T. and Yates, R. Norm-Linear and Norm-Additive Operators Between Uniform Algebras, Journal of Mathematical Analysis and Applications, vol. 357, Issue 1, 1 September 2009, pages 45-53.
Yates, R. Classifying Quadratic Forms, Professional Project for M.A. degree, published in the University of Montana Department of Mathematical Sciences, 2006.
Hruska, S., Johnson, R., and Yates, R. An Alternating Series Expansion for $(\ln 2)^2$, Pi Mu Epsilon Journal, 11:10(2004), 545-548.

Talks

On Beyond Calculus (Slides and On Beyond Calculus poem)
Joint Mathematics Meetings, Seattle, January 9, 2016.
The Road Best Traveled: The Mathematics of Getting There and Back Again (Slides, Hamiltonian Circuits Group Activity, and TSP Algorithms Group Activity) Houghton Math and Science Day, Houghton College, February 3, 2015.
The Subspace Game
Joint Mathematics Meetings, San Antonio, January 10, 2015.
To Infinity and Beyond (Slides)
Houghton Math and Science Day, Houghton College, February 4, 2014.
Helping Students Overcome Discouragement in Real Analysis
Joint Mathematics Meetings, Baltimore, January 13, 2014
Integrating Faith through Writing in Calculus I
Association of Christian in the Mathematical Sciences Conference, Bethel University, St. Paul, MN, May 31, 2013.
Writing in Calculus I: Is It Derivative or Integral?
Joint Mathematics Meetings, San Diego, CA, January 12, 2013.
Numerical Range: Counting Necklaces and Searching for Symmetry
SUNY Geneseo Mathematics Colloquium, October 13, 2011.
An Infinity of Infinities
Houghton College Faculty Lecture Series, September 21, 2011.
Classical Results from a Functional Analysis Perspective
Mathematics and Computer Science Department faculty research seminar, Houghton College, September 5 & 19, 2011.
A Second Course in Linear Algebra: Teaching Students to Read and Speak Mathematics
Association of Christians in the Mathematical Sciences Conference, Westmont College, June 2, 2011.
How Big Is Infinity?
session for participants in the American Mathematics Competition, Houghton College, February 8, 2011.
Helping Pre-Service Teachers Recognize Continuity in the Secondary Curriculum
with Kristin Camenga, Joint Math Meetings, January 9, 2011.
Classical Results from a Functional Analysis Perspective
SUNY Potsdam/Clarkson University REU Colloquium, June 10, 2010.
Norm-Linear and Norm-Additive Operators Between Uniform Algebras

AMS Western Sectional Meeting, San Francisco State University, April 25, 2009.
Uniform Algebra Isomorphisms

Department of Mathematical Sciences Colloquium, University of Montana, April 10, 2009.
Uniform Algebra Isomorphisms

Analysis Seminar, University of Montana, March 25, 2009.
Norm-Linear and Norm-Additive Mappings Between Uniform Algebras

AMS Session on Functional Analysis and Operator Algebras at the Joint Mathematics Meetings, Washington, D.C., January 5, 2009.
Norm-Linear and Norm-Additive Operators Between Uniform Algebras (continued)

Analysis Seminar, University of Montana, October 15, 2008.
Norm-Linear and Norm-Additive Operators Between Uniform Algebras

Analysis Seminar, University of Montana, October 8, 2008.
General Additive Bishop's Lemma (continued)

Analysis Seminar, University of Montana, September 24, 2008.
General Additive Bishop's Lemma

Analysis Seminar, University of Montana, September 17, 2008.
Weakly Peripherally Linear Mappings Between Uniform Algebras

Annual Meeting of the Pacific Northwest Section of the MAA, Carroll College, June 20, 2008.
What's in a Name? Isomorphisms in Real Life and Pure Mathematics

Graduate Student and Faculty Research Conference, University of Montana, April 5, 2008.
On Singh's Proof of the Nonemptiness of the Spectrum

Analysis Seminar, University of Montana, December 6, 2006.
On Singh's Proof of the Nonemptiness of the Spectrum

Graduate Student Seminar, University of Montana, November 28, 2006.
Classifying Quadratic Forms Continued

Algebra Seminar, University of Montana, May 3, 2006.
Classifying Quadratic Forms

Algebra Seminar, University of Montana, April 19, 2006.
Classifying Quadratic Forms

Graduate Student Seminar, University of Montana, April 18, 2006.