Research

1  Funded Research

• Source: National Science Foundation.

Program: Computational Mathematics.
Division of Mathematical Sciences (DMS).
Title: A Comprehensive Suite of Symbolic Tools for Integrability Testing of Nonlinear Differential and Differential-Difference Equations.
Proposal Number: DMS-0609600.
Submitted: November 30, 2005.
Amount: $280,742 (declined).
Period: 06/01/06-06/01/09.
Person-Months or % of Effort: Summ: 1 month in Summers `06, `07 & `08.
• Source: National Science Foundation.

Program: Applied Mathematics.
Division of Mathematical Sciences (DMS).
Title: Algorithms and Software for the Symbolic Computation of Conservatio nLaws of Continuous and Discrete Nonlinear Models .
Proposal Number: DMS-0605071.
Submitted: November 1, 2005.
Amount: $274,530 (declined).
Period: 06/01/06-06/01/09.
Person-Months or % of Effort: Summ: 1 month in Summers '06, '07 & '08.
• Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Design and Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
Proposal Number: 0327358.
Award Number: CCR-9901929.
Amount: $12,000
Period: 07/01/2003-07/31/2004.
Students involved: Adam Ringler.
• Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Design and Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
Proposal Number: 0218261.
Award Number: CCR-9901929.
Amount: $10,000
Period: 05/01/2002-08/31/2003.
Students involved: Douglas Baldwin and Jack Sayers.
• Source: National Science Foundation.

Program: DMS-Infrastructure Program:
Scientific Computing Research Environments for the Mathematical Sciences (SCREMS).
Title: Scientific Computing Research Environments for the Mathematical Sciences.
PI: G. Fairweather
Co-PIs: B. Bialecki, W. Hereman, A. Rockwood & J. Wang.
Proposal Number: 0215491.
Award Number: DMS-0215491.
Amount: $25,000 (excluding cost sharing by CSM with $25,092).
Period: 07/01/2002-07/01/2004.
• Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Design and Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
Award Number: 0107672.
Amount: $10,000.
Period: 05/01/2001-08/31/2001.
Students involved: D. Baldwin and B. Kowalski, undergraduate students.
• Source: National Science Foundation.

Program: Numeric, Symbolic and Geometric Computation Program.
Title: Symbolic Software for the Study of Integrability of Nonlinear Partial Differential and Differential-Difference Equations.
Award Number: 9901929.
Amount: $233,645.
Period: 08/15/99-07/31/02.
Students involved: Douglas Baldwin, undergraduate student, Paul Adams and Holly Eklund, master students.
• Source: Wolfram Research, Inc.

Program: Visiting Scholar Grants 2000.
Title: Exact Solutions of Nonlinear Partial Differential Equations.
Amount: air fare, lodging, free Mathematica software.
Period: 06/00/2000-03/01/01.
• Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines.
Co-PI: G. Fairweather and B. Bath
Senior Participants: W. Hereman et al.
Award Number: 9912293.
Amount: $129,799.
Period: 05/01/2000-05/01/2002.
Students involved: several undergraduate students.
• Source: Colorado School of Mines.

Program: Technology Fee Committee.
Title: Upgrading the Student PC Laboratory in Mathematical and Computer Sciences.
Co-PI: X. Wu.
Amount: $7,854
Period: AY 1999-2000.
Students involved: undergraduate students in MCS courses, all MCS majors.
• Source: National Science Foundation.

Program: Scientific Computing Research Environments for the Mathematical Sciences (SCREMS).
Title: Computing Environments for Mathematical Sciences Research.
Co-PIs: W. Navidi, B. Bialecki, L. Tenorio \& E. S. Van Vleck.
Award Number: 9872005.
Amount: $37,595 (excluding cost sharing by CSM with $37,110).
Period: 07/15/1998-06/30/2000.
• Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines.
Co-PI: E. Van Vleck et al.
Award Number: 9732069.
Amount: $40,000.
Period: 08/01/1998-10/31/1999.
Students involved: several undergraduate students.
• Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Design and Implementation of Integrability Tests in Mathematica for Systems of Nonlinear Differential Equations.
Award Number: 9625421.
Amount: $5,000.
Period: 05/01/1998-08/31/1999.
Student involved: Michael Colagrosso, undergraduate student.
• Source: Colorado School of Mines.

Program: Curriculum Reform Committee \& NSF Programs, Pedagogy and Process.
Title: Differential Equations: Creating an Applications Driven Course.
Co-PI: B. Bath.
Amount: $4,995.87.
Period: Summer \& Fall 1997.
Students involved: Nadine Filosi, graduate student.
• Source: Colorado Advanced Software Institute (CASI).

Program: CASI Undergraduate Research Grant Program.
Title: Computational Analysis of Electromagnetic Scattering.
Co-PIs: J. DeSanto \& M. Misra.
Amount: $3,000.
Period: AY 1997-1998.
Student involved: Grant Erdmann, undergraduate student.
• Source: Colorado School of Mines.

Program: Technology Fee Committee.
Title: A Student Computing Laboratory in Mathematical and Computer Sciences.
Co-PI: B. Bath.
Amount: $57,500 (excluding cost sharing of $15,000 by MCS Department).
Period: Fall 1996.
Students involved: undergraduate and graduate students in MCS courses, all MCS majors.
• Source: National Science Foundation.

Program: Numeric, Symbolic and Geometric Computation Program.
Division of Computer-Communications Research.
Title: Symbolic Software for the Investigation of Nonlinear Partial Differential Equations.
Award Number: 9625421.
Amount: $87,000 (excluding cost sharing $14,908 from CSM).
Period: 09/15/1996-08/31/1999.
Student involved: Unal Goktas, Ph.D.\ student.
• Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Development of a Mathematica Program for the Painlevé Integrability Test of Nonlinear Differential Equations.
Award Number: 9300978.
Amount: $5,000.
Period: 05/01/1996-08/31/1996.
Student involved: Antonio Miller, undergraduate student.
• Source: Department of Defense.

Program: Multi-disciplinary University Research Initiative (MURI).
Air Force Office of Scientific Research (AFOSR) Computational Electromagnetics Initiative.
Title: Electromagnetic Scattering from Rough Surfaces.
Co-PIs: J. DeSanto \& M. Misra.
Amount: $290,000.
Period: 01/01/1995-12/31/2000.
Students Involved: Grant Erdmann, undergraduate student, Jeff Boleng, graduate student.
• Source: National Science Foundation.

Program: Scientific Computing Research Environments for the Mathematical Sciences (SCREMS).
Title: Mathematical Sciences Computing Research Environment.
Co-PIs: E. Van Vleck, M. Misra, G. Fairweather \& J. Scales.
Amount: $50,000, matched by CSM with $80,655.
Period: AY 1994-1995.
Students involved: Chris Elmer and Unal Goktas, master students.
• Source: National Science Foundation.

Program: Numeric, Symbolic and Geometric Computation Program.
Division of Computer-Communications Research.
Title: Development of Symbolic Software for Nonlinear Partial Differential Equations.
Award Number: 9300978.
Amount: $69,923 (excluding cost sharing $4,000 from CSM).
Period: 09/01/1993-08/31/1996.
Students involved: Chris Elmer and Unal Goktas, master students.
• Source: National Science Foundation.

Program: Instrumentation and Laboratory Improvement (ILI).
Title: Toward making Mathematics a Laboratory Science.
Co-PIs: F. Hagin, B. Bath, R. Underwood \& J. Cohen.
Amount: $43,000 (excluding cosh sharing by CSM with $43,000).
Period: AY 1990-1992.
• Source: Thunder Basin Coal Company, Wright WY.

Program: Advanced Computing.
Title: The Bulldozer Project.
Amount: $12,000 (of which $5,000 was student support).
Period: December 1990-July 1991.
Student involved: William Murphy, master student.

At Other Institutions

• Source: NATO.

Title: Research Fellowship.
Amount: $7000 + salary for 10 months.
Period: 1985-1986, Iowa City, Iowa.
• Source: NATO.

Title: Research Fellowship.
Amount: $6000 + salary for 10 months.
Period: 1983-1984, Iowa City, Iowa.

2  Undergraduate Research and Unfunded Research

• Field Sessions & REU Projects
1. Development of Algorithms and Mathematica Software for the Symbolic Computation of Conservation Laws of System of PDEs in Multi-dimensions,
   Location & Date: MCS, Colorado School of Mines, Summer 2004.
   Sponsor: Supplemental Award, Research Experiences for Undergraduates (REU) Program, National Science Foundation.
   Clients: W. Hereman and M. Colagrosso
   Students involved: Lindsay Auble, Robert `Scott' Danford, Forrest Lundstrom, Maxine von Eye.
2. Development of Algorithms and Mathematica Software for Higher Euler and Homotopy Operators of Nonlinear Partial Differential Equations and Differential-Difference Equations.
   Location & Date: MCS, Colorado School of Mines, Summer 2003.
   Sponsor: Field Session 2003 \& Supplemental Award, Research Experiences for Undergraduates (REU) Program, National Science Foundation.
   Clients: W. Hereman and M. Colagrosso
   Students involved: Ingo Kabirschke, Frances Martin, Kara Namanny, Adam Ringler, and Ryan Sayers.
3. Design and Implementation of Symbolic Algorithms for Recursion Operators of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
   Location & Date: MCS, Colorado School of Mines, Summer 2002.
   Sponsor: Supplemental Award, Research Experiences for Undergraduates (REU) Program, National Science Foundation.
   Students involved: Douglas Baldwin and Jack Sayers.
4. Design and Implementation of Symbolic Algorithms for Testing Exact Solutions of Nonlinear Partial Differential Equations.
   Location & Date: MCS, Colorado School of Mines, Summer 2002.
   Sponsor: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines, Research Experiences for Undergraduates (REU-site) Program, National Science Foundation.
   Students involved: Jason Blevins and Jeff Heath.
5. Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations.
   Location \& Date: MACS, Colorado School of Mines, Summer 2002.
   Sponsor: Supplemental Award, Research Experiences for Undergraduates (REU) Program, National Science Foundation.
   Students involved: Paul Blanchard, John Milwid, and Matthew Porter-Peden.
6. Design and Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.

MCS, Colorado School of Mines, Summer 2001.
Sponsor: Research Experiences for Undergraduates (REU) Program, National Science Foundation.
Students involved: Douglas Baldwin and Benjamin Kowalski.
7. Symbolic computation of tanh solutions of nonlinear partial differential equations.

MCS, Colorado School of Mines, Summer 2000.
Sponsor: {\em Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines}, Research Experiences for Undergraduates (REU) Program, National Science Foundation.
Client: Willy Hereman.
Students involved: Steve Formenac, Andy Menz, and Douglas Baldwin.
8. Symbolic computation of tanh and sech solutions of nonlinear partial differential and differential-difference equations.

MCS, Colorado School of Mines, Summer 1999.
Sponsor: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines, Research Experiences for Undergraduates (REU) Program, National Science Foundation.
Client: Willy Hereman.
Students involved: Linda Hong, Ryan Martino and Joel Miller.
9. Development of a Mathematica Program for the Painlevé Integrability Test for Systems of Nonlinear Differential Equations.

Field Session MCS, Colorado School of Mines, Summer 1997.
Client: Willy Hereman.
Student involved: Michael Colagrosso.
10. Computational Modeling of Rough Surface Scattering.

Field Session MCS, Colorado School of Mines, Summer 1996.
Clients: John DeSanto, Willy Hereman & Manavendra Misra.
Students involved: Grant Erdmann, Amy Sinex & Colleen Craig, undergraduate students.
Others team members: Jeff Boleng & Morrakot Khebchareon, graduate students.
11. Development of a Mathematica Program for the Painlevé Integrability Test for Nonlinear Differential Equations.

Field Session MCS, Colorado School of Mines, Summer 1995.
Client: Willy Hereman.
Students involved: Tracy Otto & Antonio Miller, undergraduate students.
 
• Collaborative Research Projects on Wavelets (Software Design)
1. Michel Grundland, Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada.
2. Barend Herbst and Karin Goosen, Department of Applied Mathematics, University of Stellenbosch, Matieland, South Africa.
3. Lucas Monzon and Gregory Beylkin, Department of Applied Mathematics, University of Colorado, Boulder, Colorado.

 
• Collaborative Research Projects on Integrability of PDEs and DDEs, Symmetries, Conservation Laws, Special Solutions (including Software Design)
1. Michel Grundland, Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada.
2. Bernard Deconinck, Department of Applied Mathematics, University of Washington, Seattle.
3. Ünal Göktas, Wolfram Research, Inc., Champaign, Illinois.
4. Mark Hickman (sabbatical visitor, February 4-June 10, 2002), Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.
5. Jan Sanders & Jing Ping Wang, Department of Mathematics and Computer Science, Free University, Amsterdam, The Netherlands.
6. Willy Malfliet, Department of Physics, University of Antwerp, Antwerp, Belgium.
7. Thomas Wolf, Brock University, St. Catharines, Ontario, Canada.
8. Frank Verheest, Institute for Theoretical Mechanics and Astronomical Observatory, University of Ghent, Ghent, Belgium.