Dr. J. E. Lin, Ph. D., Brown University
Coordinator, Mathematics Enrichment Program
Summer Enrichment Program in Mathematics and Technology for Talented Youth,
George Mason University, Fairfax campus. 1994 - Present.
Recognized in the Mason Spirit 2001 Winter Issue http://spirit.gmu.edu/archives/01winter/mathoutreach.html
Associate Professor Emeritus
Department of Mathematical Sciences
George Mason University
4400 University Drive
Fairfax, Virginia 22030
U. S. A.
Ph.D. in Mathematics, 1976 Brown University
. Providence, Rhode Island. U. S. A.
Ph.D. Dissertation Advisor: Walter A. Strauss
Dissertation title: Time Decay of Two Conservative Equations
B.S. in Mathematics, 1969
National Tsinghua University
. Hsinchu, Taiwan
Field of interest
: Partial differential equations with emphasis on the stability and complete integrability for nonlinear evolution equations.
Manuscripts accepted for publication
Nonexistence of nontrivial solutions with decay order for some nonlinear elliptic equations. To appear in Journal of Nonlinear and Convex Analysis.
Research conference organized
NSF-CBMS Conference on Nonlinear Wave Equations.
Principal Speaker: Professor Walter A. Strauss (Brown University),
George Mason University, January 16 – 20, 1989.
Nonlinear Wave Equations
by Walter A. Strauss. CBMS Regional Conference Series in Mathematics (Number 73).
American Mathematical Society 1990.
Institute of Mathematics, Academia Sinica, Taipei, Taiwan. October 6-12, 2016; May 19-June 14, 2016; June 9-30, 2015; January 4-16, 2013; January 11-20, 2012; January 3-12, 2011; January 5-12, 2010; March 21-April 18, 2008.
Nonexistence of nontrivial solutions for some nonlinear elliptic equations in Rn. NCTS International Workshop on Geometric Analysis & Subelliptic PDEs, National Taiwan University, Taipei, Taiwan. May 24-26, 2016.
On the Integrability of Nonlinear Evolution Equations: one-spatial dimension and two-spatial dimensions. Mini-Workshop on Analysis and Differential Equations, Academia Sinica, Taipei, Taiwan, January 12-14, 2013.
Current Ph. D. student
(Co-advising with Padmanabhan Seshaiyer) Manal Badgaish
Advisor to graduated Ph. D. students
1. Edward Bosch (CSI/SCS 2005 Ph. D.). Title of the thesis “Perturbed neural network backpropagation learning and adaptive wavelets for dimension reduction for improved classification of high-dimensional datasets”
2. Blane Laubis (CDS/COS 2009 Ph. D.). Title of the thesis “Optimal Investment Allocation in a Jump Diffusion Risk Model with Bond and Stock Investments: An Analysis of Several Examples”
Advisor to graduated Master degree students
1. Yukiko Yarnall (March 2016): Paper presentation 'Newton's Method under Weak Kantorovich Conditions'
2. Mahyar Alizadeh (December 2015): Paper presentation 'Kantorovich's Theorem on Newton's Method'
3. Sakti Anupindi (August 2014): Paper presentation 'Applications of Ekeland Variational Principle'
Ph.D. dissertation committee member
CSI/CDS/SPACS: David Baughman, Gautami Erukulla, Rommel Epinosa, Xianjun Hao, Mohammed Kamal, Hyunyal Kim, Truong Le, Haidong Lu, Juan Luna, Andrey Makeev, Lijue Wang, and Kenneth Wolfram, Keun-Hang Yang, and Le-Yi Yang.
Economics: Edward Hirshman.
Mathematics: Paul Salamonowicz and Andrew Samuelson.
Physics and Astronomy: John Kroon and Jason Lee.
Systems Engineering and Operation Research: Yi-Chuan Lu.
1. (with Isah Bala Yabo and Basant Kumar Jha) Combined Effects of Thermal Diffusion and Diffusion-thermo Effects on Mass Transfer Flow in a Vertical Channel with Thermal Radiation. Applied Mathematics 7 (2016) 2354-2373.
2. (with Chun-Te Lee, Chun-Che Lee, and Mei-Li Liu) On the numerical modeling of capillary flow dynamics in a microchannel model using finite element method.
Journal of Applied Mechanics and Technical Physics, Volume 57, Issue 5, (2016) pp. 937-948..
3. (with Manal Badgaish and Padmanabhan Seshaiyer) Nonlinear Dynamics and Analysis of Intracranial Saccular Aneurysms with Growth and Remodeling
. Journal of Nonlinear Dynamics, Volume 2016 (2016), Article ID 2869083. http://www.hindawi.com/journals/jndy/2016/2869083/
4. Time Decay for the Solutions of a Fourth-Order Nonlinear Schrodinger Equation.
Contemporary Mathematics, Volume 581 (2012), pp. 169-174.
5. Local Time Decay for a Quasilinear Schrödinger Equation.
Methods and Applications of Analysis, 16, (2009), 313 – 320.
6. (with Blane Laubis) Optimal Investment Allocation in a Jump Diffusion Risk Model with Investment: A Numerical Analysis of Several Examples
. 2008 Actuarial Research Conference Proceedings, appeared on ARCH 2009 (Electronic).
7. Local time decay for a nonlinear beam equation.
Methods and Applications of Analysis, Volume 11, No. 1 (2004) pp. 65 – 68.
8. (with H. H. Chen) On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension
. International Journal of Mathematics and Mathematical Sciences, Volume 2004, No. 58 (2004) pp. 3117-3128.
9. (with H. H. Chen) On the integrability of nonlinear evolution equations in two-spatial dimensions
. Proceedings of ICCM2001, New Studies in Advanced Mathematics. Vol.4 (International Press, Somerville, MA) (2004) pp. 659-664
10. (with E. Bosch) Wavelet-based dimension reduction for hyperspectral image classification
. Algorithms and Technologies for Multispectral Hyperspectral, and Ultraspectral Imagery, Proceedings of SPIE Vol. 5093 (2003) pp. 57-69.
11. On the Symmetries, Constants of Motion, and the Hamiltonian Structure of the
Modified Kadomtsev -Petviashvili Equation
. Bulletin of the Institute of Mathematics, Academia Sinica 19 (1991) pp. 11-19.
12. (with H. H. Chen) On the Integrability of Nonlinear Evolution Equations
Nonlinaer Semigroups, Partial Differential Equations, and Attractors, edited by T. L. Gill and W. W. Zachary, Lecture Notes in Mathematics, Vol. 1394 (1989) pp. 30-43.
13. (with H. H. Chen) Integrability of Nonlinear Wave Equations
. Integrability in Dynamical Systems, edited by J. Buchler, J. Ipser, and C. Williams, Annals of the
New York Academy of Sciences, 536 (1988) pp. 91-99.
14. (with H. H. Chen) Factorization of the Recursion Operators and the Integrability of Nonlinear Evolution Equations
. Topics in Soliton Theory and Exactly
Solvable Nonlinear Equations, edited by M. Ablowitz, B. Fuchssteiner, and M. Kruskal (World Scientific Publishing Co., 1987) pp. 97-107.
15. (with H. H. Chen) On the Infinite Hierarchies of Symmetries of Symmetries and Constants of Motion for the Kadomtsev-Petviashvili Equation
. Physica D, 26 (1987) 171-180.
16. (with H. H. Chen) On the Integrability of Multidimensional Nonlinear Evolution Equations
. Journal of Mathematical Physics, 28 (1987) 347-350.
17. (with H. H. Chen and Y. C. Lee) On the Direct Construction of the Inverse Scattering Operators of Integrable Nonlinear Hamiltonian Systems
. Physica D, 26(1987) 165-170.
18. Asymptotic Behavior in Time of the Solutions of a System of Multidimensional Coupled Nonlinear Schrödinger Equations
. Tamkang Journal of Mathematics, 17 (1986) 27-30.
19. Local Energy Decay for waves Governed by a System of Nonlinear Schrödinger Equations in a Nonuniform Medium
. International Journal of Mathematics and Mathematical Sciences, 8 (1985) 621-623.
20. (with H. H. Chen and Y. C. Lee) A New Hierachy of Symmetries for the Integrable Nonlinear Evolution Equations
. Advances in Nonlinear Waves, Volume II, edited
by L Debnath (Pitman, New York, 1985) pp. 233-239.
21. On a Nonlinear Modulated Dispersive Wave
. Proceedings of the National Science Council of the Republic of China, 8 (1984) 129-131.
22. (with H. H. Chen and Y. C. Lee) On a New Hierarchy of Symmetries for the Kadomtsev-Petviashvili Equation
. Physica D, 9 (1983) 439-445.
23. (with H. H. Chen and Y. C. Lee) On a New Hierarchy of Symmetries for the Benjamin-Ono Equation
. Physics Letters A, 91 (1982) 381-383.
24. Decay of the Local Energy of a Two-dimensional Wave in a Nonlinear Weakly Negative Dispersive Medium
. Physics Letters A, 91 (1982) 278-279.
25. (with H. H. Chen) Constraints and Conserved Quantities of the Kadomtsev-Petviashvili Equations
. Physics Letters A, 89 (1982) 163-167.
26. (with H. L. Hwang, D. C. Liu, and J. J. Loferski) Numerical Analkysis of Junction-depth Effect in the Grating-type Si Solar Cell.
Journal of Applied Physics, 52 (1981) 1548-1551.
27. On the Generalized Korteweg-de Vries Equation
. Manuscripta Mathematica, 30 (1980) 417-423.
28. Superexponential Decay of Solutions of a Semilinear Wave Equation
. Journal of Functional Analysis, 31 (1979) 321-332.
29. (with Walter A. Strauss) Decay and Scattering of Solutions of a Nonlinear Schrödinger Equation
. Journal of Functional Analysis, 30 (1978) 245-263.
30. Asymptotic Behavior in Time of the Solutions of Three Nonlinear Partial Differential Equations
. Journal of Differential Equations, 29 (1978) 467-473.
31. (with Elfriede Wenzelburger) Reduction of all three-term syzygies
. Publicationes Mathematicae Debrecen, 21 (1974) 57-59
Research Experience for Undergraduates : Summer 2012 (George Lytle) and Summer 2013 (Peter Morfe).
Contracted by ICF Consulting Services for the National Geospatial-Intelligence Agency for evaluating the use of the geometric partial differential equations in the image analysis (April 5, 2004 – May 12, 2004).
1. George Mason University Faculty Study Leave (Spring 2008)
2. George Mason University Faculty Study Leave (Fall 1997)
3. George Mason University International Incentives Grant (1997)
4. George Mason University Research Grant (1990-91)
5. George Mason University Graduate School Visiting Fellow Program (1989)
6. NSF-CBMS Conference on Nonlinear Wave Equations (National Science Foundation) at George Mason University, January 16-20, 1989.
7. George Mason University Summer Stipend Grant (1986).
8. George Mason University Research Grant (1984-85)
9. National Science Council of Republic of China (Taiwan) Research Grant (1977-81)
1. George Mason University Graduate Research Assistantship (1990)
2. George Mason University Graduate Research Assistantship (1988)
3. George Mason University Graduate Research Assistantship (1987)
Professional Development (faculty seminars)
1. Heat Equation, Co-organizer and speaker, Spring 2016
2. Partial Differential Equations, Co-organizer and speaker, 2002-2003.
3. Large-scale structure of space-time, Co-organizer, 2000-2003.
4. Financial Engineering, Co-organizer and speaker. 1999-2000.
5. Nonlinear Optics, Co-organizer and speaker, 1997-98.
6. Signal Processing, Co-organizer and speaker, 1995.
7. Kalman Filtering, Co-organizer and speaker, 1991-92.
8. Image Analysis, Co-organizer and speaker, 1990 – 91.
9. Inverse Scattering Theory, Co-organizer and speaker, 1987-90.
10. Optimization Theory, Co-organizer and speaker, 1987-89.
11. Topics in Fourier Analysis with Applications, Co-organizer and speaker, 1986-89.
12. Applied Mathematics, Co-organizer and speaker, Spring 1985.
13. Nonlinear Analysis/Partial Differential Equations, Co-organizer and speaker, Fall 1983.
14. Inverse Problems in Geophysics, University of Wyoming, Co-organizer and speaker, Spring 1983
1. On the Stability of the Solitary Waves, Academia Sinica, Taipei, Taiwan. October 11, 2016.
2. On the Shallow Water Wave Equations, SIAM Research Symposium, Department of Mathematical Sciences, George Mason University, October 4, 2013
3. On the Integrability of Nonlinear Evolution Equations: one-spatial dimension and two-spatial dimension, Mini-Workshop on Analysis and Differential Equations, Academia Sinica, Taipei, Taiwan, January 12 – 14, 2013.
4. Time Decay for the Solutions of a Fourth-order Nonlinear Schr?dinger Equation, Academia Sinica, Taipei, Taiwan, January 11, 2013.
5. Time Decay for the Solutions of a Fourth-order Nonlinear Schr?dinger Equation, National Cheng Kung University, Tainan, Taiwan, January 10, 2013.
6. On Mathematics and Methodology, School of Journalism and Communication, Xiamen University, China, May 31, 2012.
7. Time Decay for the Solutions of a Fourth-order Nonlinear Schr?dinger Equation, Xiamen University, China. May 30, 2012.
8. Introduction of Semigroup Theory to the Nonlinear Partial Differential Equations, Academia Sinica, Taipei, Taiwan. January 16, 2012.
9. Time Decay for a Coupled Nonlinear Schr?dinger Equations. SIAM Conference on Analysis of Partial Differential Equations, San Diego, CA November 14 – 17, 2011.
10. Local Time Decay for a Quasilinear Schrodinger Equation, Georgia Southern University, Statesboro, GA, March 13, 2011,
11. On a higher-order wave equation. Institute of Mathematics, Academia Sinica, Taiwan, January 5, 2011.
12. Local time decay for a quasilinear Schrödinger equation, Academia Sinica,Taiwan, January 12, 2010.
13. Nonlinear Evolution Equations, SIAM Club Symposium, George Mason University, November 6, 2009.
14. On the local time decay of the solutions of some nonlinear evolution equations, Academia Sinica, Taiwan, January 7, 2009.
15. On a fully nonlinear Schrödinger equation, George Mason University, November 21, 2008.
16. On the integrability of nonlinear evolution equations, Academia Sinica, Taiwan, August 8, 2008.
17. On the integrabilty of nonlinear evolution equations, Fu Jen University, Taiwan, August 7, 2008.
18. Time stability analysis for dispersion model, Academia Sinica, Taiwan, April 14, 2008.
19. On some nonlinear Schrödinger equations, National Chiao Tung University, Taiwan, April 11, 2008.
20. On some nonlinear Schrödinger equations, National Central University, Taiwan, April 10, 2008.
21. On some nonlinear Schrödinger equations, Academia Sinica, Taiwan, April 3, 2008.
22. On a nonlinear beam equation. George Mason University, December 3, 2004.
23. Local time decay for a nonlinear beam equation. Georgetown University, November 15, 2004.
24. On the integrability of nonlinear evolution equations. Academia Sinica, Taiwan, January 2, 2003.
25. On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimensions. Georgetown University, September 6, 2002.
26. On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimensions. 2001 International Congress of Chinese Mathematicians, Taiwan, December 20, 2001.
27. Time decay of the local energy for a two-dimensional dispersive wave. 73rd Annual Meeting of the Virginia Academy of Sciences, May 23-26, 1995, Virginia Military Institute, Lexington, Virginia.
28. Neural Networks: an introduction and some applications, Math Club, George Mason University, March 27, 1993.
29. On the new invariants and the Lax-pair operators for the Korteweg-de Vries equation and other similar equations, George Mason University, March 22, 1985.
30. New invariants and Lax pairs for KdV and other integrable equations, Brown University, March 15, 1985.
31. On the Kadomtsev-Petviashvili equation – a nonlinear dispersive wave equation with two spatial dimensions, University of Wyoming, October 27, 1982
32. On the symmetries and the nonlinear integrable evolution equations, NSF-CBMS Research Conference on Nonlinear Waves and Integrable Systems, East
Carolina University, June 24, 1982.
33. On a two-dimensional nonlinear dispersive wave, Aldridge Laboratory of Applied Geophysics, Columbia University, May 6, 1982.
34. On the conserved quantities of the Kadomtsev-Petviashvili equation, University of Maryland, April 7, 1982.
Research lecture organized
Lectures on Neural Networks by Professor Su-Shing Chen, Graduate School Visiting Fellow Program, April 10 – 14, 1989.
Research conferences attended
1. Nonlinear Phenomena: A View from Mathematics And Physics National Taiwan University, Taipei, Taiwan, January 10 - 14, 2011
2 2010 Conference in Differential Equations, National Taiwan University, Taiwan, January 8 – 9, 2010.
3. Mini-Workshop on Strongly Nonlinear Wave Equations. National Taiwan University, Taiwan, August 6, 2008.
4. NSF-CBMS Regional Conference on Water Waves: Theory and Experiment. Howard University, May 13 – 18, 2008.
5. Nonlinear Waves Conference in honor of Professor Walter Strauss on the occasion of his 70th birthday, Brown University, May 8 – 11, 2008.
6. International Congress of Chinese Mathematicians, Taiwan, December 17 - 22, 2001.
7. Nonlinear Wave Equations Conference in honor of Professor Walter Strauss on the occasion of his 60th birthday, Brown University, May 2 – 3, 1998.
8. Exploring the World of Computer Networks, Teleconference, George Mason University, September 30, 1993.
9. Problems in Collective Computation, Washington, D.C., June 23, 1989.
10. International Joint Conference of Neural Networks 1989, Washington, D.C., June 18 – 22, 1989.
11. Frontiers of Massively Parallel Computation, George Mason University, October 10 – 12, 1988.
12. Workshop on Connectionist Models in Computational and Cognitive Science, May 3 – 5, 1987.
13. Pattern Recognition in Natural and Artificial Neural Systems, Boston, MA, June 6, 1986.
14. Research and Development Opportunities in Dynamic Character Recognition, George Mason University, March 26, 1986.
15. Applications of Artificial Intelligence, George Mason University, March 4, 1986.
16. Winning Grants, Office of Research, George Mason Univesrity, February 5 – April 17, 1986.
17. Minimax Methods in Critical Point Theory and Applications to Differential Equations, NSF-CBMS Regional Conference, University of Miami, Coral Gables, Florida, January 8 – 12, 1984.
18. Mathematical Methods in Hydrodynamics and Integrability in Related Dynamical Systems, La Jolla Institute, La Jolla, California, December 7 – 9, 1981
All courses taught:
Undergraduate level: PAGE 125 and 225 (1989-1992), Pre-calculus Mathematics, Quantitative Reasoning, Introductory Calculus with Business Applications, Introductory Probability and Statistics, Linear Mathematical Modeling, Analytic Geometry and Calculus I, II, and III, Matrix Algebra, Elementary Differential Equations, Theory of Differential Equations, Introduction to Advanced Mathematics, Mathematics for Elementary School I and II, Number Theory, Geometry, Introduction to Applied Mathematics I and II, Advanced Calculus I and II, Linear Algebra, Probability, Functions of a Complex Variable, Modern Applied Mathematics II, Math Numerical Analysis I, Reading and Problems, and Topics in Applicable Mathematics (Neural Networks).
Graduate level: Principles of Analysis I, Linear Analysis I and II, Complex Analysis, Ordinary Differential Equations, Partial Differential Equations, Probability, Neural Networks, Shape Optimization, Navier-Stokes Equations, Navier-Stokes Approximations, Nonlinear Functional Analysis, Nonlinear Partial Differential Equations, Graduate Seminar, and Independent Reading and Research.
Special summer courses taught
1. The Applications of Graph Theory in the Network Analysis, School of Journalism and Communication Xiamen University, Xiamen, China. June 30, 2014 – July 4, 2014.
2. Nonlinear Dynamics, Tsinghua University, Beijing, China. August 15 – August 26, 1999.
Teaching workshops attended
1. Math Convocation for Honors Summer Math Camp, Southwest Texas State University, San Marcos, Texas, February 8, 1997.
2. Cultural Diversity Workshop, George Mason University, May 22 – 29, 1989.
3. Workshop on Legal Issues in Higher Education, George Mason University, October 8, 1986.
4. Workshop on Effective Teaching, George Mason University, March 4, 1986.
Outreach (non-GMU) courses taught
Multivariable Calculus and Elementary Differential Equations, Fairfax County Public Schools, 1993 – 2002.
1. Coordinated and taught the Community Math Help program, Tysons-Pimmit Regional Public Library, Falls Church, Virginia, January 1999 - June 2001. recognized in the Mason Spirit 2001 Winter Issue http://spirit.gmu.edu/archives/01winter/mathoutreach.html
2. Coordinated and taught the Mathematics for Underrepresented Students, George Mason University, summer 1997 and summer 1998.
1. Promotion and Tenure Committee, 1987- 2016.
2. Co-organized the Mathematics and Biology activity for the Mathematics Awareness Month, April 24, 1999.
3. Co-organized the Mathematics and Internet activity for the Mathematics Awareness Month, April 26, 1997.
4. Grievance Committee, 1995-1996.
5. Participating in the Outreach program with local companies, Fall 1995.
6. Faculty Advisor, Mathematics Club, 1992-1999.
7. Putnam Mathematics Competition (Supervisor), 1992, 1993, 1994, and 1996.
8. Colloquium Chair, Center for the Applications of Mathematics, 1989-1991.
9. Appeals Committee, 1989-90.
10. CIT Research Internship Faculty Advisor, 1989-90.
11. Search Committee, Spring 1987.
12. Undergraduate Committee, 1985-1995.
13. Committee on the Revision of the Undergraduate Programs, 1985-1987.
14. Policy and Hiring Committee, 1985-1987.
7/10/1989, Fall 1989, 8/22/1990, 6/28/1993, Spring 1993, 12/2/1996, and 8/22/1997 (University Welcome Week)
1. COS Executive Council, 2015 - 2016
2. COS Nominating Committee, 2010-2011.
3. Chair, CAS Graduation Appeals Committee, 1998-2000.
4. CAS Bylaws Committee, 1993-1995.
5. CAS Graduation Appeals Committee, 1991-93, Chair (1991-92).
6. CAS Compensation and Benefits Committee, 1988-90, Chair (1988-89).
7. CAS Academic Policy and Planning Committee, 1984-87
1. Adult Learning and Executive Education Committee, Chair, September 2014 – August 2015
2. Non-traditional, Interdisciplinary, and Adult Learning Committee, September 2013 – August 2014
3. Admissions Committee, September 2011 – August 2013 (Chair, September 2012 – August 2013)
4. Minority and Diversity Issues Committee, September 2009 – August 2011
5. Minority and Diversity Issues Committee, 2009 – 2011.
6. Reviewed two faculty study leave proposals for the Office of the Provost, 2008.
7. Nontraditional, Interdisciplinary and Adult Learning Committee, 2006 - 2007
8. Committee for the Virginia State Science and Engineering Fair, 2006
9. Admissions Committee, 2004 – 2006
10. Minority and Diversity Issues Committee, 2002 - 2006
11. Teaching Effectiveness Committee, 2002-2004.
12. Project Advisory Group for the grant Building Bridges for Asia-Pacific Studies: Language, Culture, and Connectedness, 2002-2004.
13. Academic Appeals Committee, 2002 – 2003.
14. Chair, Minority and Diversity Issues Committee, 1998 - 2000.
15. Chair, Minority Affairs Committee, 1997 - 98.
16. Advisory Board Member, Center for Asia-Pacific Economic Cooperation, 1996 - present.
17. Future Unlimited – Exploring Careers in Mathematics and Sciences, George Mason University, March 16, 1996.
18. Non-traditional, Interdisciplinary, and Adult Learning Committee, 1994 - 96.
19. Mentor for the Minority Student Service, 1993 - 96, 1997 - 99.
20. Cultural Diversity Committee, 1989 - 94.
21. Minority Affairs Committee, 1987 - 90.
22. International Programs Grants and Contracts Subcommittee, 1984 - 1986.
Student organizations service
1. Faculty advisor to Chinese Students and Scholars Association, 2008 – 2016.
2. Faculty advisor to ROC Students Association, 2008 - 2016.
3. Faculty mentor to Sino-American 1+2+1 Dual Degree Program, 2007 - 2010.
Fairfax County Elementary and Middle School Science and Engineering Fair Judge. May 7, 2016.
2. Siemens Competition Stage 1 Judge. October 5-9, 2014.
Thomas Jefferson High School for Science and Technology Science Fair, 1999.
1. Trustee Assembly, Fairfax-Falls Church United Way, 1997-2000.
2. Regional Council, Fairfax-Falls Church United Way, 1996-2000.
3. High school talks at Thomas Jefferson High School for Science and Technology in 1989 (Neural Networks), 1990 (Topics in Neural Networks), 1993 (Mathematics of Neural Networks), and 1997 (Career as a Mathematician).