Research Areas of the Mathematics Faculty

Wayne Aitken
David Chien
Ricardo Fierro
Linda Holt
André Kündgen
Tejinder Neelon
Amber L. Puha
Radhika Ramamurthi
K. Brooks Reid
Marshall Whittlesey
 

Wayne Aitken’s main area of research is arithmetic algebraic geometry, i.e., that part of algebraic geometry which interacts with number theory.  His specialty is the Arakelov theory of arithmetic surfaces, but he is also conducts research in permutation polynomials over finite fields.  He is also interested in classical algebraic geometry (i.e., algebraic geometry over the field of real or complex numbers), other branches of number theory including algebraic, analytic, and computational number theory, the theory of modular forms and its relation to the theory of elliptic curves, cryptography, commutative algebra, group representation theory, and the geometric side of mathematical physics. In addition, he is  interested in general education mathematics, especially courses designed to give non-math majors a deeper understanding and appreciation for mathematics and its history.  He has also become interested in ways of teaching critical thinking.  He assisted the Department Chair with scheduling; and is the Graduate Program Coordinator.

David Chien’s research is concerned mainly with the numerical solution of integral equations. Presently, most of his work deals with the solution of potential theory problems using integral equation formulations in three dimensions. He is also working to extend the ideas imbedded in integral equations into some related problems in computer graphics, radiosity.  He is interested in issues of technology in the mathematics curriculum, in particular the use of the computer in collegiate mathematics classes, whenever it is appropriate. He also is interested in all of the peripheral issues and problems that surround the use of computers in higher education (e.g., serves as the unofficial computer consultant to the Department of Mathematics). He was one of three CSUSM researchers in a three-campus, NSF funded, mathematics education project entitled Quality Indicators for Undergraduate Mathematics Education.  Dr. Chien is currently serving as the Mathematics Department Chair, and serves on the CAPI (Collaborative Academic Preparation Initiative) program as the CSUSM team member for Carlsbad High School.

Ricardo Fierro’s research specialty is in numerical linear algebra and scientific computing.  His research involves the analysis and development of numerical algorithms and is motivated by the need for fast and reliable algorithms in applications such as information retrieval and spectroscopy in signal processing  After receiving his Ph.D. from the University of California, San Diego, he was a postdoctoral fellow at the University of California, Los Angeles.  He is interested in technology in the classroom and frequently teaches courses with the computer lab components, such as Numerical Analysis and Computing, Probability Modeling and Statistical Inference, and Introduction to Mathematical Programming. He is also active in the teaching of mathematics for the preparation of future K-8 teachers.  Currently, he advises the Math Club, maintains the department website,  serves as the Assessment Coordinator for the department, and serves as the coordinator for the business calculus and mathematics for elementary teaching courses.

Linda Holt’s research specialty is in the study of nonlinear hyperbolic partial differential equations, in particular, the behavior of singularities of solutions to such equations compared to the linear theory.  She also is interested in the preparation of future teachers, and improving mathematics education at all levels, K-16.  She currently serves as the Department of Mathematics Single Subject Preparation Program Coordinator. She has played an active role in the development of the general education curriculum in both mathematics and critical thinking. She was one of three CSUSM researchers in a three-campus, NSF funded, mathematics education project entitled Quality Indicators for Undergraduate Mathematics Education.  She was the Program Director during 1994-1997; and currently serves as the (course) Scheduling Coordinator for the Department.    Linda Holt is currently the Director of the Collaborative Academic Preparation Initiative (CAPI), funded by the CSU Chancellor's Office, which has the purpose of promoting greater collaboration with local high schools to increase academic performance of high school students in Math and English, and to reduce the need for remediation at CSUSM.  She is also serving as the CSUSM CAPI team member for Vista High School and Rancho Buena Vista High School.

André Kündgen's research is in discrete mathematics with an emphasis on graph theoretical questions.  He studies graph colorings, graphs on surfaces and extremal questions, as well as algorithmic aspects and applications of probabilistic methods to discrete mathematics.  After receiving his Ph.D. from the University of Illinois, where he won a departmental teaching award, he was a postdoctoral fellow at the Fields Institute in Toronto.  He joined the department in February of 2001 and has since then been involved in the teaching of Discrete Mathematics and Graph Theory.

Tejinder Neelon wrote his thesis in the area of Multi-dimensional Complex Analysis but has branched out into other areas.  He is currently working in the area of Local Real Analytic Geometry.  He is also learning computational/algorithmic  aspects of algebra, and, in future, he hopes to make some  contributions to it.  He is interested in a wide range of topics in mathematics e.g., Commutative Algebra, Linear Partial Differential Equations,  Complex Analytic Geometry. He has taught a variety of service courses and majors courses and variety of graduate courses.  He has attended many pedagogy workshops and has incorporated new ideas into his classroom environment, and has led the department discussion around calculus reform.  He has also developed classroom units to supplement the course texts.  He currently serves on the CAPI (Collaborative Academic Preparation Initiative) project as the CSUSM team member for Temecula Valley High School. 

Amber L. Puha’s research focus is in Probability Theory, and her work is primarily in the area of stochastic processes.  For her thesis project she studied a particular class of stochastic processes, interacting particle systems.  These processes can be used to model physical and/or biological systems in such a way as to determine how randomness together with an underlying spacial structure can impact the behavior of the system.  While at UCLA she studied with one of the world’s leading experts in the area, Professor Thomas M. Liggett.  Upon completing her thesis project, she expanded her research interests to include other types of stochastic processes, stochastic networks which have applications to the modeling of manufacturing processes and communications and computer networks.  For this purpose, she spent a year at UCSD as a postdoctoral fellow collaborating with Professor Ruth J. Williams. This work is ongoing, and she plans to continue with this project through the academic year 2000-2001 when she will take leave to focus on research.  Amber is a native of North County San Diego.  Upon arriving to CSUSM she took over articulation responsibilities and is using her contacts at the local area community colleges to bridge communication between CSUSM mathematics faculty and community college faculty.  Moreover, she also has interest in developing curriculum and degree programs at CSUSM, particularly in the area of probability and statistics.  She is also involved in the curriculum for general education mathematics courses and remediation.

Radhika Ramamurthi's research is in the area of graph theory and combinatorics. She is specially interested in coloring problems of graphs and hyerpgraphs and problems relating to topological graph theory. She did her Masters in Operations Research with a special emphasis on Queueing Theory from the University of
Delhi, and then completed her Ph.D. from the University of Illinois. She was a postdoctoral visitor at the University of California at San Diego before she joined CSUSM.

K. Brooks Reid's research is in the discrete mathematics of combinatorics and graph theory, particularly in the study of the combinatorial structure of complete, asymmetric digraphs (commonly called tournaments). He also studies combinatorial problems arising from voting theory, location of facility theory, population ecology, some issues on dominance in animal societies, and from other areas of mathematics and theoretical computer science. He has written over 60 research papers (several jointly) in these areas and serves as an active referee and reviewer for journals in these areas. He is a frequent reviewer for Math Reviews. He held external research support from the Office of Naval research during 1992-1998. He has lectured widely throughout the U.S. as well as abroad. During summers 1999, 2000, 2001 he participated in an integrative program between researchers and high school mathematics teachers at DIMACS at Rutgers University (he was Chair of the research component in 1999). He was active in curriculum reform at LSU, where he was on the mathematics faculty for 21 years, by designing and teaching a sequence of courses in discrete mathematics, combinatorics, graph theory, and modeling, for the major and for the graduate program. He supervised 4 Ph.D. students there, and was Chairman of the Department when he moved to CSUSM. As one of the Founding Faculty at CSUSM he designed the initial undergraduate program in Mathematics at CSUSM. He also co-authored the M.S. program, and he remains active in the refining of these curricula. He has had 3 M.S. thesis students. He was one of the designers of upper-division G.E at CSUSM, led the designing and launching of the University Honors Program, and served as Honors Director for three years. He is interested in current national issues of collegiate mathematics education and frequently participates in regional meetings on these issues. He regularly infuses considerable writing of mathematics in his courses, and he has experimented with technology in the teaching of the beginning calculus and linear algebra course. He is committed to high quality general education in mathematics, the training of future teachers, a top notch undergraduate program, and a fine M.S. program. He also served for several years on the CAPI (Collaborative Academic Preparation Initiative) project as the CSUSM team member for San Marcos High School.

Marshall Whittlesey's general area of research is the study of functions and domains in one and several complex variables.  In particular, he has studied extensively the existence of analytic structure.  He has also worked on applications of this area to frequency domain design of components of certain machines, which are important in linear control theory.  He has been a visiting faculty member at Texas A&M University and at the University of California, San Diego, where he was an S.E. Warschawski Assistant Professor.  An aficionado of the art of public speaking (e.g., he gave the graduate student address at his Ph.D. commencement), he is interested in helping students learn to present themselves in a constructive and inspiring manner in public presentations.  He currently serves as the professor in charge of the department's Precalculus course.