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Crista Arangala

Associate Professor of Mathematics
Duke 307F
2320 Campus Box
Elon, NC 27244
ccoles@elon.edu (336) 278-6249

Professional Expertise

Teacher Scholar

Brief Biography

Dr. Crista Arangala is an Associate Professor of Mathematics at Elon University.

She received degrees from Allegheny College, PA, and the University of Cincinnati. She is a numerical analyst with interests in partial differential equations and inverse problems but currently focuses much of her energy on undergraduate research. Upon coming to Elon in 2000, she mentored over 25 students in undergraduate research projects, many of which are related to applied linear algebra. Dr. Arangala is very interested in inquiry learning both in and outside of the classroom.  She is the co-director (and co-founder) of the Elon Traveling Science Center, where Elon undergraduate students develop science and math exhibits for both local and international exhibitions.

 

 

 

Education

 

Undergraduate Institution:        Allegheny College, Bachelor of Science in Mathematics, 1993

Graduate Institution:                   University of Cincinnati, Masters of Science in Mathematics, 1995

                                                         University of Cincinnati, Ph.D. in Mathematics, Numerical Analysis, 2000

Employment History

 

Appointments:                2006-Present  Elon University, Associate Professor of Mathematics                                                         

                                           2000-2006         Elon University, Assistant Professor of Mathematics       

                                           1995-1997       Wittenberg University, Visiting Instructor

                                           1993-1995, 1997-2000            University of Cincinnati, Graduate Assistant

Courses Taught

MTH 110: General Statistics

MTH 151: Calculus I

MTH 220: Statistics in Application

MTH 239: Linear Algebra

MTH 251: Calculus II

MTH 252: Multivariate Calculus

MTH 329: Probability Theory and Statistics

MTH 330: Math Reasoning

MTH 349: Applied Matrix Theory

MTH 359: Differential Equations

MTH 460/461: Senior Seminar

MTH 445: Numerical Analysis

Other Courses: Nature of Mathematics, GST 110: Global Experience, STA 236 Preparatory Course for India Education and Development, GST 236: India Education and Development, STA 238 Post Course for India Education and Development

Periclean Courses: PER 351, PER 352, 

 

Leadership Positions

 

Elon Committees and Leadership Roles:

·         Periclean Scholars

  • ·         Fall 2011-- present Associate Director of Periclean Scholars

Organize events such as Celebrate (fall recruiting) and Induction Week (a week of reflection around a significant global issue), write internal and external grants for Periclean initiatives, mentor current Periclean class mentors, recruit new Periclean class mentor, and attend all Project Pericles director and steering committee meetings.

  • ·         Spring 2008--present Periclean Scholars Mentor for the class of 2011

Developed 6 courses focusing on global issues and how they relate to the country of Sri Lanka integrating service learning. The focus of this program is in environmental education, Sri Lanka, and using media as a form of communication.  This role also included guiding and staying involved in student service projects both locally and internationally, organizing and participating in Pan-periclean events, helping students in fund raising efforts, and guiding students toward leaving a legacy. This role also includes mentoring students as alumni of the Periclean program.

  • ·         Fall 2008—present Periclean Scholars Steering Committee 

This committee meets approximately twice a week to discuss Periclean initiatives and to move forward on the mission of the Periclean program.

  • ·         Fall 2011—present Board for Elon Fellowship at CRHP

The Periclean class of 2012 have started an Elon Fellowship at CRHP in India to send one or two graduating seniors to CRHP for a year to intern. The Board reads all applications for this appoint and recommends candidates to CRHP for this position.

  • ·         Spring 2012—present Board for Periclean Foundation

 

  • ·         Fall 2011 -- present  Academic Council
  • ·         Spring 2012 Director of Domestic Programs Search Committee
  • ·         Spring 2012 – present Global Village Planning Committee
  • ·         Fall 2009 -- Spring 2011 Promotion and Tenure Committee
  • ·         Fall 2009 -- Spring 2012  Study Abroad Committee  
  • ·         Spring 2003 -- present Distinguished University Professor Committee
  • ·         Fall 2009 -- Spring 2011 Honorary Degree Advisory Committee
  • ·         Spring 2010 -- Associate Dean Search Committee

Research

I predominantely  work on Inverse Problems and other problems related to applied linear algebra.

Grants Awarded

 

External Grants

  1.    Fulbright Teaching Award for 2013-2014

This teaching award will support my ongoing commitment to inquiry learning .  The support of this award would offer me a semester long teaching position in Sri Lanka where I would teach using inquiry in the classroom and would continue partnerships related to the Elon Traveling Science Museum.      

2.    August 2011 American Embassy Grant, with T. Arcaro, $4,500

This grant was to support two Periclean Scholars attendance in the Training for Trusteeship hosted by the Weeramantry Center for Peace and Education Research in Colombo, Sri Lanka. Forty students from around South Asia participated in this workshop. The two Periclean Scholars involved were the only United States students invited to participate in this workshop. These two students also gave a talk at the American Center in Colombo about the work.

3.  December 2010 Park Foundation Grant, with T. Arcaro, J. Lee, C. Smith, J. Dodson, $12,000.

This grant was to support a documentary focusing on the environment in Sri Lanka called the Elephant in the Room, http://vimeo.com/groups/doteco/videos/30460629.

4.   December 2010 American Embassy Grant, with T. Arcaro, $5,000.  This grant was to support the Leaders in Environmental Advocacy Forum, January 2011.

Internal Grants

  1. Spring 2013 Funds for Excellence, Moving Calculus to the Edge:  Infusion of Interdisciplinary Perspective and World-class Technology, $2800
  2. Summer 2013 Faculty Research and Development, Summer Fellowship and Financial Support ($4400)
  3.  Fall 2012 Funds for Excellence, A Week of Discussion Around Corporate Responsibility, with T. Arcaro and C. Benson, $1500
  4. Fall 2011 Funds for Excellence, SOLVE Consultant Center, with K. Yokley, A. Russell, and H. Walton, $1310
  5.  Fall 2011 Funds for Excellence, Human Trafficking Symposium, with T. Arcaro, $2500
  6.  Fall 2008 Funds for Excellence,  Elon Periclean Scholars Class of 2011 Presents: Sri Lanka at Elon(A Week of Cultural Exposure), $2850
  7.  Fall 2008 Community Partnership Initiative Grant, Partnership with Graham Middle School to develop on outdoor garden classroom, $2200
  8. Spring 2008 Faculty Research and Development Sabbatical and Funding, Spring 2008, A Comparative International Study: Interest and Understanding in Math and Science Exhibits, funding for $2250,  to present science museum exhibits in Sri Lanka and to study how cultural differences affect how students interact for inquiry learning exhibits. Co-founder of the Elon Traveling Science Museum.
  9.  Winter 2008 CATL Grant, Periclean 2011: Meaningful Connections with Sri Lankan Partners, $1918
  10.  Fall 2006 Funds for Excellence, The Inquiry Process Using Mathematics and Science Center Exhibits and the Development Needs of Sri Lanka, $5500
  11.  Fall 2006 CATL Grant, Students to create science exhibits they will then share with students in Sri Lanka, $3500
  12.  Fall 2005 Community Partnership Initiative Grant, Elon Traveling Science Museum, $300

Publications

 

  1.  September 2012 The 4xn Multistate Lights Out Game, Mathematical Sciences International Research Journal, Vol 1, N      Number 1, Pages 10-13.

This paper includes a discussion of solutions for 4xn Lights Out games in which buttons can take on more than two states. Games with buttons states which are a power of 3 are explored in detail.

2.   May 2012 Developing Curiosity in Science with Service, accepted to The Journal for Civic Commitment, accepted December 28, 2012

In 2008, my sabbatical focused on analyzing the impact of the Elon Traveling Science Center.  This paper discusses the experience and how it impacts those involved.  This paper follows several presentations on the subject and has led to several consulting opportunities.

3.   May 2012 Multistate Lights Out, with Rachel Wilson, submitted to Mathematics Magazine.

The two state Lights Out game has been studied in detail. In this paper we explore the multistate Lights Out, in which rectangular Lights Out games have buttons that can take on more than two states.  A linear algebra approach is discussed and several classes of games that have solutions are explored.

4.  February 2012 Pascal’s Triangle in Higher Dimensions, with Amanda Coe, accepted with revisions to Involve, revisions submitted November 2012.

This paper is in the field of number theory and is an extension of results of interest in the field including an extension of Pascal’s Tetrahedron and Star of David Theorem to multinomial coefficients.

5.  December 2011 Seriation Algorithms for Determining the Evolution of the Star Husband Talewith J. Todd Lee and Cheryl Borden, accepted to Involve.

The Star Husband Tale is an American Indian tale shared by over 80 tribes across North America. As the tale traveled from one tribe to the next it was altered and morphed but still each version shared some characteristics of commonality.  This paper looks at the characteristic present, or lacking, in each of the versions of the tale and uses applied linear algebra techniques to determine the path through which the tale evolved. It is interesting to note that the mathematical results of this paper match up nicely with historians’ views of where the tale began.

6.   Turning Lights Out, UMAP/ILAP/BioMath Modules 2010: Tools for Teaching, with J. Todd Lee and Brianna Yoho, edited by Paul J. Campbell. Bedford, MA: COMAP, Inc., Pages 1-26.

This is a reprint of Turning all Lights Out. Editor Campbell chooses a few modules to highlight in his Tools for Teaching.  The editor recognized the thoroughness and impact of this article and asked the authors to reprint the results.  The UMAP Modules presents new results in applied mathematics to an audience with a style toward teaching the audience about the result, including suggested exercises for the reader.

7.   Turning all Lights Out, with J. Todd Lee and Brianna Yoho,  The UMAP Journal, Vol 31.1.

Lights Out is a hand-held game of electric buttons and adjacent connections. The goal of the game is, given a random initial condition of on and off buttons, to press buttons in a sequence that will turn all of the lights off. In this paper, we explore a general grid of buttons and connections where all of the lights start on. Several approaches are taken to prove that one can always turn the lights out.

8.   Notes on Leximorphic Spaces, with J. Todd Lee, and Ellen Mir, The Rocky Mountain Journal of Mathematics, Volume 40, Number 4, Pages 1257-1274.

There are many ways to order objects or numbers. Lexicographic ordering is similar to dictionary ordering in that if (a,b) < (a’,b’) then a<a’ and if a=a’ then b <b’. Leximorphic spaces are spaces related to these orderings and in this paper the leximorphic spaces and their properties are further explored.

9.  Collecting Cardswith J. Todd Lee and Ellen Mir, UMAP Journal, Vol 28.4.

There are so many collector cards set out there today for kids to try to collect so in this paper we explore the mathematical theory of collecting all of the cards in a set through the collection process. This paper the probability of collecting all of the cards in a set is discussed as well as an estimation to the number of cards that would have to be collected in order to collect an entire set of cards.

10. Parameter estimation for a drying system in a porous medium, with Diego Murio, Computers & Mathematics with ApplicationsVolume 51, Issues 9-10Pages 1519-1528.

This paper introduces a numerical solution to the Luikov model for drying a porous medium. This model is an application of heat and mass transfer. Initial conditions are known on a boundary of the medium and the behavior of the medium is estimated under the introduced model.

11.   Numerical solutions of inverse spatial Lotka-Volterra systems, with Diego Murio, Mathematical and Computer ModellingVolume 42, Issue 13Pages 1411-1420.

Lotka-Volterra systems are used to model predator prey biological systems.  These are well know models however this paper looks at inverse systems were predator and prey density populations are known, within a window of error, in a particular location of a habitat and these initial densities are used to predict the population densities throughout a habitat over time.

12.  August 2004  Parameter Identification Using Mollification for Predator-Prey Models in Spatially Heterogeneous EnvironmentsComputers & Mathematics with Applications, Volume 48, Issues 3-4, Pages 505-515.

This paper concentrates on a Lotka-Volterra model in which spatially dependent diffusion effects and bias dispersal are added. Bias dispersal allows the species to use their perception to move toward favorable regions. The numerical algorithm described in this paper allows for the recovery of population densities and diffusion coefficients in the model.

13.  December  2002  Parameter Estimation in the 1-D Transport Equation with Advection  Computers & Mathematics with Applications, Volume 44, Issue 12, Pages 1493-1502.

This paper looks at an ecological model in which the habitat is spatially non-uniform and which random and non-random dispersion are present.  The dispersion coefficient and population density are recovered.  I was informed by the editor of this journal that this paper was among the most downloaded from January 2003 to March 2003.

14.  December 2001  Simultaneous Space Diffusivity and Source Term Reconstruction in 2D IHCPwith Diego Murio, Computers & Mathematics with Applications, Volume 42, Issue 12, Pages 1549-1564.

This paper focuses on a two dimensional inverse heat conduction problem in which an external source term is present.  In this model, the external source term is dependent on both space parameters as well as time.  It is assumed that this term can be written as two independent functions, one as a function of space, the spatially dependent source, and the other as a function of time, the temporal dependent source.  The diffusivity coefficient and the spatially dependent source are estimated simultaneously.

15.  Automatic Numerical Solution of the Generalized 2-D IHCP by Discrete Mollification, with S. Zhan and D.A. Murio, Computers and Mathematics with Applications, Volume 41, Issues 1-2, Pages 15-38.

16.  Identification of Parameters in the Two Dimensional Inverse Heat Conduction Problem, with D. A. Murio, Computers and Mathematics with Applications, Volume 40, Issues 8-9, Pages 939-956.

Presentations

 

Recent Presentations :

·         October 2012 An International Perspective: Running a student driven international traveling science center, Association of Science – Technology Centers (ASTC) Annual Conference, 13-16 October 2012, Colombus, OH.

·         September 2012 The 4xn Multistate Lights Out Game, International Conference on Mathematics, 13-14 September, Hyderabad, India.

·         August 2010  All Lights Out, International Conference on Mathematical Applications in Engineering (ICMAE’10), 3-5 August 2010, Kuala Lumpur, Malaysia.

·         August 2009  Turning Lights Out, Mathematical Association of America MathFest, Portland, Oregon.

Professional Activities

 

Conference Organization and Leadership 

 

  • January 2011 (Organizer) Leaders in Environmental Advocacy Forum (LEAF), University of Colombo, Sri Lanka.

The Periclean Scholars class of 2011 decided to organize and host LEAF in their junior year and I along with these scholars started planning this conference. This entailed finding speakers, funding sources, location, catering, advertising, and all other details. As this conference was in Sri Lanka, this proved to be exceptionally challenging. The LEAF program was partially funded through a grant from the U.S. Embassy American Center, and was sponsored by the University of Colombo, the National Science Foundation of Sri Lanka, and Rainforest Rescue International. The conference was opened by United States Ambassador to Sri Lanka and the Maldives, Patricia Butenis.

 

  • March 2010 (Co-organizer) The 89th Annual Meeting of the Southeastern Section of MAA, Elon University, NC.

The Elon Mathematics and Statistics Department values the annual southeastern section meeting of the MAA sending many majors and faculty to the meeting to participate.  In March 2010, Elon hosted this conference. I assisted Dr. Jim Beuerle in all organizational matters related to making this event success.