Curriculum Vitae
Richard H. Elderkin
Department of Mathematics
(909) 621-8409
relderkin@pomona.edu
http://pages.pomona.edu/~relderkin
Education
(N.D.E.A. Fellow, 1967-1970)
Fields of
Specialization and Interest
Differential Equations, Mathematical Modeling (especially environmental)
Teaching Positions
Associate Professor 1980-1988
Assistant Professor 1974-1980
Graduate
Research Fellowships
and Appointments
NSF Research Experience for Undergraduates, Claremont Mathematics
Project, Director of the Dynamical Systems group. 2005,
summer
Mellon Foundation grant for Math
Modeling in Calculus II, with Prof.
Mellon Foundation grant as
principal investigator with co-investigators John Molinder
(Engineering, HMC) and Bob Borrelli and Courtney Coleman (Math, HMC).
Visiting Scientist
Howard Hughes Medical Program 1990, summer
Undergraduate Research Grant
High School Teacher Fellowship Co-Investigator
Sloan New Liberal Arts Appropriate Technology Program Curricular Grant 1989, summer
Mathematical modeling of shape-memory alloys
Claremont Colleges Mellon Curricular Grant 1986, summer
Discrete mathematical modeling of sudden infant death syndrome
University of
Senior Fellow
NSF Research
Sloan New Liberal Arts Fellowship 1985, May
Rensselaer Polytechnic Institute
Oxford University Mathematics Institute 1979-1980
(NSF Science Faculty Professional Development Grant)
NSF Summer Research Grants 1976-1980
Co-investigator
NSF Undergraduate Research Participation Grant 1976
Project Director
Research Assistant Professor
Assistant Professor
Professional Societies
American Mathematical Society
Mathematical
Association of
Resource Modeling Association
Mathematical Modeling for Environmental Analysis (book ms.)
Modeling grain-legume-pest interactions.
Publications
“Predator-prey
interactions with delays due to juvenile maturation,” coauthored with K.L.
Cooke, W. Huang,
"Algorithms," in The Encyclopedia of Science, Technology and Society. 1998
"Populations structured by vector-borne disease", in Differential Equations and Applications to Biology and Industry, M. Martelli, K. Cooke, E. Cumberbatch, B. Tang, and H. Thieme, eds., World Scientific Pub., Singapore, 1996.
"Pitch, Yaw and Roll," with David Boyd, in ATLAST, Computer Exercises for Linear Algebra, S. Leon, E. Herman, and R. Faulkerberry, eds., Prentice Hall, 1996.
"Orthogonal Projections for Approximating Discretely Sampled Functions by Discrete Special Functions," with Tom Cairns, in ATLAST, Computer Exercises for Linear Algebra, S. Leon, E. Herman, and R. Faulkerberry, eds., Prentice Hall, 1996.
"Structured Populations with Nonlinear, Nonlocally Dependent Dynamics: Basic Theory," Journal of Mathematical Analysis and Applications, 192, 392-412 (1995).
"Dynamics of prevalence of disease in populations
structured by disease density," in Mathematical
Population Dynamics: Analysis of Heterogeneity, Volume One: Theory of Epidemics,
O. Arino, D Axelrod, M. Kimmel and M. Langlais, eds., Wuerz Pub. Ltd,
"Lessons from Cognitive theory for teaching mathematical modeling to freshmen", Humanistic Mathematics Network Newsletter, Dec. 1989
"Harvesting procedures with management policy in iterative density-dependent population models," (with M. Witten, K.L. Cooke), J. Natural Resources Modeling, Vol. 2, No. 3(1988), 383-420.
"Contour interpolation of random data," as adviser to Chris Jacobs, John Keltner, and Brian Vant-Hull, Mathematical Modelling, 7(1986), 577-583, and in the UMAP Journal, 7(1986), 289-296.
"Nonlinear, globally age-dependent population models: some basic theory," J. Math. Analy. & Appl., Vol. 108(1985), 546-562.
"Population models with globally age-dependent dynamics: on computing the steady state," in Hyperbolic Partial Differential Equations, Vol. 1, M. Witten (ed.), Pergamon, 1983, 371-376.
"Spatial patterning of the spruce budworm after
spraying," Math. Models of Renewable Resources, R. Lamberson
(ed.),
"On an age-dependent model of seed dispersal in a patchy environment," J. Math. Biol. 13(1982), 283-303.
"Summary analysis of an age-dependent, nonlinear model of seed dispersal," Integral & Functional Differential Equations, T.L. Herdman, S.M. Rankin, H.W. Stech (eds.,), Dekker, 1981, 165-172.
"On the steady state of an age dependent model for Malaria," (with D. Berkowitz, F. Farris, C. Gunn, F. Hickernell, S. Kass, F.I. Mansfield, R. Taranto), Nonlinear Systems and Their Applications, Academic Press, 1977, 491-512.
"Separatrices in solitude," Rocky Mountain J. Math., 7(1977), 479-440.
"Separatrices and solitary periodic solutions," J. Differential Equations, 25(1977), 325-341.
"Solitary invariant sets," (with F.W. Wilson, Jr.), Dynamical Systems, Vol. 2, An International Symposium, 1976.
"Separatrix structure for regions attracted to solitary periodic solutions," Dynamical Systems, Vol. 2, An International Symposium, 1976.
"Separatrix Structure for
Elliptic Flows," Ph.D. Thesis, University of
Lectures, Workshops
and Posters
Invited lecture: “Maturation Delays and Oscillation in Predator-Prey Models,” American Mathematical Society, Western Section meeting at Claremont, CA, May 3-4, 2008, Special Session on Applications of Delay-Differential Equations to Models of Disease.
Invited seminar: “Oscillation in Predator-Prey Models: Chaotic Teacups, Tori, and Delayed Dynamics wit Hangovers,” University of Southern California, Department of Mathematics, Dynamical Systems Seminar, March 3, 2008.
Participant: Short Course: Environmental Modeling, Annual Joint Meetings of the American Mathematical Society, the Mathematical Association of America (etc.), San Antonio, Texas, January, 2006.
Participant: Joint mathematics meetings,
Participant:
“Modeling Indirect Competition Between Two Predators with a Shared Resource,” with student Robert Gerrity, poster at conference on Natural Resource Modeling, Humboldt State University, June 14-17, 2005. Won “Best Student Poster”.
Participant: Joint meeting of the Southern California Section of the Society for Industrial and Applied Mathematics and the Southern California Applied Mathematics Symposium, April 24, 2004.
Participant: “Workshop on Mathematical Modeling Courses”
Participant:
Participant:
Participant: “Conversations on Mathematics and the Environment” at the Annual Summer Meeting of the Mathematical Association of America, Boulder, Colorado, July 31-August 3, 2003.
Contributed lecture:
“Environmental Decision Making as a Path to Quantitative Literacy”
delivered at the Annual Summer Meeting of the Mathematical Association of
America,
Contributed lecture:
“Understanding Model through Dimensional Analysis: the Example of
Predator-prey Interactions” delivered at the Joint Annual Meetings of the
American Mathematical Society and the Mathematical Association of America,
Participant: “Conversations on Mathematics and the Environment” at the Annual Summer Meeting of the Mathematical Association of America, Boulder, Colorado, July 31-August 3, 2003.
“Predator-prey Interactions with Delays due to Juvenile
Maturation”, invited talk in the Special Session for Functional Differential
Equations,
Howard Hughes Outreach Program: With
students Dan Stoebel (math and biology double major, '00), Sarah
Williams (math and econ double major, '99) and Larry Wong (math and physics
double major, '98), I gave two workshops on curricular use of the mathematical
modeling software, Stella, to 60 high
school and junior college faculty in March of 1998 and 1999.
“Paradigms of Interacting Populations”, for Mathematical Modeling in the Undergraduate Curriculum, at the University of Wisconsin at LaCrosse, June 12, 13, 1998.
“Chaos, Dissipation and Predation”, invited colloquium at
the
“Modeling Prevalence of Disease in Populations Structured by
Disease Density”, invited talk to mathematics students at the
“Steady States of Populations Structured by Disease Characteristics in Individuals,” at an NSF Conference Board of Mathematical Sciences meeting on Structured Populations, North Carolina State University, Raleigh, NC, June 1997.
“Singular Value Decomposition as a Last Lecture for Linear
Algebra Classes”, jointly authored with Colm Mulcahy (
"Highlights and Pitfalls in O.D.E. Reform," Panel
discussant at the Ninth Annual International Conference on Technology in
Collegiate Mathematics, Reno, NV, November 9, 1996.
ATLAST Developers Workshop,
"Populations Structured by Disease Characteristics in Individuals," Joint Meeting of the Northern California and Southern California Sections of the Mathematical Association of America, in San Luis Obispo, October, 1995.
"Pitch, Yaw and Roll," co-authored with David Boyd, and presented by
Boyd at the annual national meeting of the American Mathematical Society in
"Steady state of structured populations," poster
with Jeff Bradley, presented at undergraduate poster sessions at
"Mathematical visualization," poster with Doug Fidaleo, presented
at undergraduate poster sessions at
"Steady population distributions of structured poulations", Annual Meeting of the Society for
Mathematical Biology,
"The genesis of some differential equations of population biology," Claremont Weekly Biomath Seminar, September, 1994
"Structured population models of vector borne
disease," International Conference on Differential Equations and
Applications to Biology,
ATLAST Developers Workshop,
"On models
for prevalence of disease structured by density of the disease", Regional
meeting of the American Mathematical Society,
"Matlab exercises to enable geometric intuition for linear
transformations" Annual Joint Meetings of the American Mathematical
Society and the Mathematical Association of America,
"Modeling prevalence of disease in poulations structured by disease density," Claremont College Mathematics Colloquium, February 1993.
"Dynamics of
prevalence of disease in populations structured by disease density," Third
International Conference on Mathematical Population Dynamics,
"Ways of knowing", Phi Beta Kappa President's Lecture at the annual initiation of members to Gamma Chapter of California, 1990
Demonstrations of Phaser and Phasplan (differential equations software) at a Pew Trust Western Liberal Arts Colleges Cluster curricular workshop, 1989
"Mathematics in liberal education," in the Liberal
Arts and Liberal Education series at
"Insect population dynamics with apportioned diffusion and recruitment for sterile and fertile subdivisions," at the Southeastern Mathematical Ecology Conference, 1986.
"Modeling the big stretch: finite elasticity and von Karman," for the Claremont Mathematics Colloquium, 1985.
"Ciarlet theory of von Karman equations," at Rensselaer Polytechnic Institute, 1985.
"Plugging a bottle with sterile insect release," (two lectures) for the Claremont Applied Math Seminar, 1984.
"Nonlinear hyperbolic equilibria and trajectory equivalence," Claremont Mathematics Colloquium, January 1981.
"Some age-dependent models in biology," for the Claremont Mathematical Biology Seminar, 1979.
"A rogue's gallery of phase portraits," for the undergraduate mathematics club at UCLA, November 1976.
"Separatrix structure near solitary invariant sets," Southern California Ordinary Differential Equations Seminar, April 1975.
Book Reviews
ATLAST, Computer
Exercises for
Theory of Nonlinear Age-Dependent Population Dynamics, by Glenn F. Webb, in Comput. Math. Applic., Vol. 13(1987), 913-915.
Population Biology of Infectious Diseases, Life Sciences Research Reports, R.M. Anderson and R.M. May (eds.), in Mathematical Modeling, 7(1986), 1654-1656.
Senior Thesis
Advising
Yavor Kostov,
’10 (Math), Bifurcation in
Delay-Differential Equations with Two Delays.
Paige Maas, ’09 (Math), A Model of Coral Dynamics.
Louis Russell, ’09 (Environmental Analysis), Solar-Thermal Energy at Pomona College.
Michael Baumstein, ’09 (Math), Modeling Colony Collapse Disorder.
Emi Oakamoto, ’08 (Math), Modeling the Sspread of Tuberculosis in a Population.
Brittany Biebl, ’07 (Environmental Analysis), Need and cost-benefit analyses of solar hot-water heating for Haldeman Pool.
Will Leer, ‘07, (Math) Optimal strategy for medium distance running events.
Meg McCarter, ’07, (Math) Mathematical Modeling of Residence Times for
Lead Poisoning.
Brandon Routman, ‘07, (Math), Agricultural Modeling.
Talley Starbird, ‘07 (Environmental Analysis), Forests’ Role in the Carbon Cycle.
Robert Gerrity, ’06, Searching for a Neimark-Sacker Bifurcation in a System of Delay Differential Equations.
William Jeck, ’05, Lagrangian Data
Assimilation in Geophysical Flows and an Assessment of Data Gathering
Strategies for Submerged Ocean Drifters
Warren Davidson, ’05, Predator
Prey Growth Model with a Genetic Variant
Kim Knapp, ’03, A Mathematical Model of a Juvenile Justice System, (second reader for honors)
Jeff Fesenmaier, ’02, A Model for Pricing Financial Derivatives with Applications
for European Options
Dan Morgan, ’02, Constructing Three Dimensional Topographic Models from Limited Data Sets Using Bessel Functions
Audrey Hill, ’02, Local Action, Local Change:
Community-based Sustainability Programs in Hunguillla
and EcoVillage
Van Dang,
Celia Chan, ’99, Derivation
of the Black-Scholes Equation
Erica Chinn, ‘98, A Two Age, Two Sex, Two Culture Demographic Model.
Woon (Larry) Wong, ‘98, The Mystery of the Population Outbreak of
the Crown of Thorns Starfish in the
Peter Leth, ’97, Discrete Dynamics of Population Harvesting.
Douglas Martin, ’97, Aspherical Inflation of Balloons.
Alden Romney, '96, The Diffusion Equation and Black Scholes Analysis,
Abagail Brown,
Mellon Foundation grant for
“Mathematical Modeling with Stella
for Alternative Calculus”, with
Group leader at an NSF supported Atlast Developers' Workshop,
June, 1997 at the
Mellon grant for “Simulating and Visualizing Dynamical Systems”, as principal investigator with co-investigators John Molinder (Engineering, HMC) and Bob Borrelli and Courtney Coleman (Math, HMC). Summer 1996.
Group leader at an NSF supported Atlast Developers' Workshop,
August, 1996, at the
Pew Foundation support for development of modules of Economics and Chemistry for Calculus III. Spring 1996.
Howard Hughes Medical Program, Summer 1990, High School Teaching Co-Investigator
Sloan New Liberal Arts Appropriate Technology Program Curricular Grant, Summer 1989,
Mathematical
modeling of shape-memory alloys
Claremont Colleges Mellon Curricular Grant, Summer 1986,
Discrete mathematical modeling of sudden infant death syndrome
Courses taught recently:
Mathematical Modeling (Pomona College Math 183): models using Markov chains, ordinary and partial differential equations; dimensional analysis and scaling; compartment models and residence times; student projects. Prerequisite: linear algebra and differential equations. Based on personal notes, reprints and excerpts.
Dynamical Systems (Pomona College Math 181): primarily oriented toward continuous systems with some attention to discrete; strong emphasis on nonlinear systems; Hartman-Grobman and Poincare’-Bendixson theorems; long time limits of solutions and their stability; bifurcation; Floquet theory; recently used Glendinning’s Stability, Instability and Chas and personal notes. Prerequisite: topology of Euclidean space, differential equations, linear algebra.
Numerical Analysis (Pomona College Math 165); numerical linear algebra; numerical differentiation and integration; splines; solution of o.d.e. initial and boundary value problems; both theory and practicum using Matlab; recently used Burden and Faires, Numerical Analysis.
Differential Equations and Modeling (Pomona College Math 102); theory and solution of o.d.e.’s; scalar equations and systems; motivated by models from physical, biological and social sciences; relies heavily on linear algebra; some numerical solution, including systems of more than two equations; recently used Differential Equations: A Modeling Approach, by Glenn Ledder.
Linear Algebra (Pomona College Math 60); emphasis on vector spaces and linear transformations but includes matrices and similarity transformations; eigens; recently used Robert Messer’s Linear Algebra. Prerequisite: Calc III.
Calculus I, II, III (Pomona College Math 30, 31, 32): Standard courses from a variety of standard texts. Frequently I use the “Harvard” reformed texts for a conceptual basis and supplement with somewhat more traditional exercises.
Real and Functional Analysis, I,II (Claremont Graduate University Math 331,332): a first course in abstract measure and integration, beginning with Lebesgue theory in Euclidean spaces; recently based on Gerald Folland’s Measure and Integration. Prerequisite: undergrad real analysis and metric spaces.
Service to the
Professional Community
Referee/Reviewer for:
J. of Theoretical Biology (’05)
Mathematics Magazine (‘00, ’01, ’02, ’03, ’04, ‘05)
McGraw Hill (differential equations text, ‘03)
Prentice Hall (differential equations text, ‘03)
Natural Resource Modeling (’02)
Computers & Mathematics with
Applications (’01, ‘04)
Journal of
Mathematical Biology (’99,’00)
American Mathematical Monthly
Numerical Methods for Partial Differential Equations
Steering Committee; Program in Environmental Analysis, Pomona College, 2002-2004
Coordinator, Program in Environmental Analysis, Pomona College, 2001-2002
Coordinator of faculty organizing a program in Environmental
Studies at
1996-2001. Program recognized in April, 2001.
Chair, Department of Mathematics, Pomona College, 1993-1996
Organizing committee for an International Conference on
Differential Equations and Applications to Biology and
Population
Dynamics (to honor Ken Cooke),
Adviser for the
Mathematical Modeling, 1986-1991, 1996-1998. They did well.
Service as a citizen
Various local political campaigns and organizations
(Linda Elderkin for City Council, Yes on S, Yes on Parks and Pasture)
Boy Scouts Assistant Scoutmaster, Troop 407, 1995-2004
Coordinator of Walk for the Hungry, 2000-2002
Curricular liaison with CHS Mathematics Department
Various local political campaigns and organizations.
Girl Scouts volunteer, 1985-1996
City of
four years as chair