1

Dr. Erwin A. MacN. George
Dept. of Applied Mathematics & Statistics
602 Route 25A, Stony Brook University
Saint James, NY11780-1403 Stony Brook, NY11794-3600
USA USA
Telephone: (631) 584-3274 Telephone: (631) 632-8370
E-mail :
URL :

PROFILE

Skilled research and teaching academic with a master’s in pure mathematics and a doctorate in applied mathematics. Ten years experience teaching a wide variety of undergraduate and graduate university mathematics/applied mathematics/statistics courses. Research Interests: computational fluid mechanics, numerical analysis, parallel computing, partial differential equations, ordinary differential equations, biological and medical mathematics, atmospheric science, earth science, oceanography, mathematics education.

Education

Ph.D. in Computational Applied Mathematics
Stony Brook University, Stony Brook, NY, USA / 1998-2003
Dissertation topic: A Numerical Study of Rayleigh-Taylor Instability
Advisor: Dr. James Glimm
M.A. in Mathematics
PennsylvaniaStateUniversity, University Park, PA, USA / 1994-1996
B.A. with Honours in Mathematics; minor in French
University of Guelph, Guelph, Ontario, Canada / 1989-1993

RECENT Experience

Postdoctoral Research and Teaching Fellow
Postdoctoral Research Associate
Research Assistant
Teaching Assistant
Instructor / Aug. 2004 –present
Jan. 2004 – Aug. 2004
1999 – Dec. 2003
1998 – 2000
spring 2000 and summers 2002-2004
Stony Brook University, Stony Brook, NY, USA
Teach linear algebra, advanced calculus, differential equations, and statistics.
Teaching assistant for numerical analysis and differential equations courses.
Write and grade portions of the Applied Mathematics and Statistics doctoral qualifying exam.
Research assistant/associate on topics such as astrophysical jets, fluid mixing, front tracking, the level set method, parallel programming, image processing.
Develop front tracking and total variation diminishing computational codes for use on the parallel computers at Oak Ridge National Laboratoryand the National Energy Research Scientific Computing Centre (NERSC).
Major writer of NERSC computer time request proposal for the Applied Mathematics and Statistics department.
Affiliate at Brookhaven National Laboratory.
Instructor
Teaching Assistant / 1996-1998
1994-1996
PennsylvaniaStateUniversity, University Park, PA, USA
Taught algebra, trigonometry, pre-calculus, ordinary and partial differential equations, and linear algebra. Was teaching assistant for calculus courses.
Wrote, proofread, and graded examinations for multi-section courses. Proofread workbook and solutions manual being written by a faculty memberfor a business calculus course.

PROFESSIONAL ORGANIZATION MEMBERSHIPS

Society for Industrial and Applied Mathematics; American Mathematical Society; American Physical Society; Mathematical Association of America; National Geographic Society.

Publications

  1. The influence of scale breaking phenomena on turbulent mixing rates (E. George, J. Glimm, X. Li, Y. Li, X. Liu. SUBMITTED to Physical Review Letters).
  2. Self similarity of Rayleigh-Taylor mixing rates (E. George and J. Glimm, Physics of Fluids , vol. 17, issue 5, article 054101, May2005).
  3. Shock wave interactions in spherical and perturbed spherical geometries (S. Dutta, E. George, J. Glimm, J. Grove, H. Jin, T. Lee, X. Li, D. H. Sharp, K. Ye, Y. Yu, Y. Zhang, and M. Zhao, Nonlinear Analysis, IN PRESS, Elsevier, 2005).
  4. A Numerical study of Rayleigh-Taylor instability (E. George, Doctoral Dissertation, December 2003).
  5. Simulation of fluid mixing in acceleration driven instabilities (E. George, J. Glimm, X. L. Li, Z. L. Xu, Computational Fluid and Solid Mechanics 2003 [Proceedings of the 2nd MIT Conference on Computational Fluid and Solid Mechanics, Edited by K.J. Bathe],pp. 908-911, Elsevier, 2003).
  6. Simplification, conservation and adaptivity in the front tracking method (E. George, J. Glimm, J. W. Grove, X. L. Li, Y. J. Liu, Z. L. Xu, N. Zhao, Hyperbolic Problems: Theory, Numerics, Applications [Proceedings of the 9th International Conference on Hyperbolic Problems, Edited by T. Hou and E. Tadmor], pp. 175-184, Springer-Verlag, 2003).
  7. Numerical methods for the determination of mixing (E. George, J. Glimm, X. L. Li, A. Marchese, Z. L. Xu, J. W. Grove, D. H. Sharp, Laser and Particle Beams, vol. 21, pp. 437-442, 2003. Los Alamos National Laboratory report No. LA-UR-02-1996).
  8. A comparison of experimental, theoretical, and numerical simulation Rayleigh-Taylor mixing rates (E. George, J. Glimm, X.-L. Li, A. Marchese, Z.-L. Xu, Proceedings of the National Academy of Sciences [USA], vol. 99, no. 5, pp. 2587-2592, March 2002).

SELECTED PRESENTATIONS

  • Self similarity of Rayleigh-Taylor mixing rates: Applied Mathematics Seminar, StonyBrookUniversity, October 2004.
  • A comparison of experimental, theoretical, and numerical simulation Rayleigh-Taylor mixing rates: American Physical Society, Division of Fluid Dynamics Meeting, Dallas, TX, November 2002.
  • A comparison of experimental, theoretical, andnumerical simulation Rayleigh-Taylor mixing rates : Society for Industrial and Applied Mathematics 50th Anniversary and Annual Meeting, Philadelphia, PA, July 2002.
  • Front tracking in two space dimensions : Applied Mathematics Seminar, StonyBrookUniversity, June 2000.

HONOURS

  • Department of Energy sponsorship to attend the ACTS (Advanced Computational Testing and Simulation) Toolkit workshop, October 2001, Lawrence Berkeley National Laboratory.
  • National Science Foundation VIGRE (Vertically Integrated Grants in Research and Education) Doctoral Fellowship (2002 - 2003), Department of Applied Mathematics and Statistics, Stony Brook University.
  • Research Assistantship (1999 - 2002, 2003),Department of Applied Mathematics and Statistics, Stony Brook University.
  • Teaching Assistantship (1998 - 2000), Department of Applied Mathematics and Statistics, Stony Brook University.
  • Turner Fellowship (1998 - 2002), Department of Applied Mathematics and Statistics, Stony Brook University.
  • Teaching Assistantship, Department of Mathematics, PennsylvaniaStateUniversity (1994 - 1996).
  • Dean's List, University of Guelph, (spring 1990, spring 1991).

SKILLS

  • C, MPI, C++, Fortran77, Fortran90, Unix shell programming, Awk, Perl, HTML.
  • MATLAB, Maple, Graphics calculators, Lotus 123, Excel.
  • LaTex, AMS-Tex, emacs, vi, Wordperfect, Word.
  • French (read/write/speak).

references

1)Dr. James Glimm (Ph.D. dissertation advisor) - Distinguished Professor and Chair of the Department of
Applied Mathematics and Statistics.
P-138A MathematicsTower
Department of Applied Mathematics and Statistics
StateUniversity of New York at Stony Brook
Stony Brook, NY11794-3600, USA
Telephone: (631) 632-8355; FAX: (631) 632-8490
E-mail: Home page:
2)Dr. Xiaolin Li (Ph.D. dissertation committee chair) - Professor and Graduate Programme Director, Department of Applied Mathematics and Statistics.
1-121 MathematicsTower
Department of Applied Mathematics and Statistics
StateUniversity of New York at Stony Brook
Stony Brook, NY11794-3600, USA
Telephone: (631) 632-8354; FAX: (631) 632-8490
E-mail: Home page:
3)Dr. Alan Tucker(Primary teaching referee) - Distinguished Teaching Professor and Director of Undergraduate Studies, Department of Applied Mathematics and Statistics.
P-138 MathematicsTower
Department of Applied Mathematics and Statistics
StateUniversity of New York at Stony Brook
Stony Brook, NY11794-3600, USA
Telephone: (631) 632-8365; FAX: (631) 632-8490
E-mail: Home page:

TEACHING STATEMENT FOR ERWIN A. MACN. GEORGE

A revolution in my ideas about how mathematics should be taught occurred during my second semester of calculus as an undergraduate at theUniversity of Guelph. The instructor, Professor Jack Weiner, despite a large class size, was able to accomplish what I had seen other instructors attempt with only limited success: he engaged every student in the class by making sure we actively participated in discussions, did and presented examples in class, and provided continuous feedback on whatever we did not understand, all with a goal of ensuring that we left the classroom with a clear understanding of the topic that was taught. Needless to say, I have attempted to incorporate Professor Weiner's approach as an integral part of my classroom teaching style.

My initial experiences with university level teaching, beginning in 1994, involved conducting recitations. It was easy in that context to thoroughly engage students in a class and get the feedback necessary to ensure that a given topic was clearly understood by all. During the summer of 1995, my role shifted to that of course instructor, and with this expanded

responsibility, I reflected more carefully on the core reasons for Professor Weiner's success. I had also in the precedingyear taken a course on teaching university level mathematics, using the book How to Teach Mathematics by Steven G. Krantz. In preparing to teach my first full course, I turned to the ideas expressed in that book and my observations of the habits of my past good teachers, like Professor Weiner, in determining how to become an effective teacher. Over the years, those ideas have been refined, and they will continue to be refined since I believe that one of the key attributes of a successful teacher is the desire to continue to learn new ways of improving one's teaching skills.

I have found the following to be the key principles behind obtaining and maintaining a “Weinerian'' classroom, in which each student is actively trying to learn and is willing to ask the necessary questions to do so and, furthermore, is leaving the classroom with not only a clearer idea of the topic taught but also of how to learn. First, one must establish mutual trust and respect with students. Second, one must be very accessible both in and out of the classroom. Third, one must have a continuous manner of assessing the level of understanding by students of the course material. Fourth, one must be extremely knowledgeable and enthusiastic about mathematics, science, and other fields impacted by mathematics.

And finally, on a related note one must be supremely well prepared for each lecture.

The establishment of mutual trust and respect with students comes with being unambiguously clear at the start of a course about the academic and behavioural expectations, particularly regarding how grades will be assigned. It also comes with encouraging student questions in and out of class and always answering those questions thoughtfully. Additionally, it comes with addressing any student concerns immediately, leading naturally to the second key principle of accessibility.

I find that students react more positively in class when they are sure that any questions will be answered either there or out of class. I typically have significantly more than the suggested number of office hours, and also have an open door policy. On a few occasions, I have even taken a class on a “field trip'' to my office at the end of the first lecture just to emphasize my desire to have them use my office hours. I encourage the use of e-mail for questions and always respond promptly. I have found this level of attention encourages students to ask more questions than they otherwise would have done, which in turn allows me to better tailor my course presentation to their benefit.

I believe in the continuous, fair evaluation of student performance. My courses are liberally sprinkled with quizzes and homework sets due for grading, so that students are required to work continuously and thus keep up with the course material. This frequent evaluation of studentsmakes midterms and finals seem less daunting to them. It has the added benefit of keeping me abreast of which topics may need additional attention. A fixed number of the lowest scores of each student from these copious quizzes and homework sets are discarded, so that he/she is allowed time to adjust to the rigours of my classroom without penalty. Solutions to quiz, homework, and examination problems are made available to students in a timely manner. I have found this continuous work policy very helpful in ensuring that students keep up with the course work and hence know what is going on in class and are willing to participate more.

Being extremely knowledgeable about mathematics, science, and other fields impacted by mathematics ensures that one has the ability to put what the students are learning into a larger context; something which many students desire as a motivation for studying some of the abstract ideas in mathematics. I often discuss how the topic being taught impacts

my research or that of my colleagues. And I continually strive to expand my knowledge of all things mathematical so that I may better situate the topics being taught in a larger context.Related to this principle is my belief that a student should not only be taught about the subject matter at hand but should also be taught study skills which work best in learning mathematics. I discuss frequently in class some of the study techniques which work, such as continually doing work and never falling behind. Also, I have found that my enthusiasm for mathematics and, more generally, learning is contagious in the classroom.

Being well prepared, for me, means having a variety of ways of presenting material, with a view to gauging via student feedback which approach is best. One should have thought deeply about the subject one is about to teach as well as how best to teach it. For example, I think carefully about the balance between presenting finished material versus leading students to discovery when preparing for a specific class or an entire course. Whenever time and the material permit, I employ the discovery approach since it engages students more during class and appears to help in their retention of the results of that discovery. One should be careful not to follow too inflexible an approach in teaching; adjustments should be made to incorporate the feedback given by students. And the key way to develop this flexible classroom style is extensive preparation.

I have taught a wide variety of courses, ranging from pre-calculus tograduate level. Many have involved the use of technological tools such as programmable graphing calculators and maple, and I am therefore very comfortable with using technology to enhance my presentation of topics.I am willing to teach a very wide variety of courses, including those not in my area of expertise. I welcome the challenge of teaching outside my area of expertise as a learning opportunity. My preference for teaching includes courses on calculus, advanced calculus, linear algebra and applications,

ordinary differential equations, partial differential equation, numerical analysis, abstract algebra, real analysis, complex analysis and applications, fluid dynamics, and high performance computing. I am also interested in conducting and/or participating in teaching workshops for graduate students in your department who will be or are teaching. I have a passion for teaching which I wish to spread to the new generation of graduate students in the mathematical sciences.

TEACHING EXPERIENCE (up to the spring2005 semester)

StonyBrookUniversity, Stony Brook, NY (1998 – present)

POSITION / COURSE / COURSE DESCRIPTION
Instructor / Elements of Statistics (Applied Math. 102) / Use/misuse of statistics in real life; basic measures of central tendency & dispersion, frequency distributions, probability, binomial & normal distributions, confidence intervals, hypothesis testing, chi-square test,regression.
Instructor / Matrix Methods and Models (Applied Math. 201) / Basic properties of matrix algebra, matrix norms, eigenvalues, solving systems of equations; applications to economics, growth models, Markov chains, regression, linear programming.
Computer software packages used.
Teaching Assistant / Numerical Analysis (Applied Math. 326) / Direct and indirect methods for the solution of linear & nonlinear equations. Computation of eigenvalues and eigenvectors of matrices. Quadrature,differentiation, and curve fitting. Numerical solution of ordinary and partialdifferential equations.
Teaching Assistant / Applied Calculus IV: Differential Equations (Applied Math. 361) / Homogeneous & inhomogeneous linear differential equations; systems of lineardifferential equations; power series & Laplace transform solutions; partial differential equations, Fourier series.
Instructor / Alliance for Graduate Education and the Professoriate Intensive Mathematics Seminar / Review of differential equations, advanced calculus, and linear algebra for undergraduate science students planning to apply to graduate schools.
Instructor / Analytical Methods for Applied Mathematics & Statistics (Applied Math. 501) / (GRADUATE COURSE) Review of techniques of multivariate calculus, convergence and limits, matrix analysis, vector space basics, and Lagrange Multipliers.

PennsylvaniaStateUniversity, University Park, PA (1994 – 1998)

POSITION / COURSE / COURSE DESCRIPTION
Instructor / College Algebra I (Math. 21) / Quadratic equations; equations in quadratic form; word problems; graphing; algebraic fractions; negative and rational exponents; radicals.
Instructor / College Algebra II and Analytic Geometry (Math. 22) / Relations, functions, graphs; polynomial, rational functions, graphs; word problems; nonlinear inequalities; inversefunctions; exponential, logarithmic functions; conic sections; simultaneous equations.
Instructor / Plane Trigonometry (Math. 26) / Trigonometric functions; solutions of triangles; trigonometric equations; identities.
Teaching Assistant / Techniques of Calculus (Math. 110) / Functions, graphs, techniques of differentiation &integration, exponentials, improper integrals, applications.
Teaching Assistant / Calculus with Analytic Geometry (Math. 140) / Functions; limits; analytic geometry; derivatives, differentials, applications; integrals, applications.
Instructor / Matrices (Math. 220) / Systems of linear equations; matrix algebra; eigenvalues and eigenvectors; linear systems of differential equations.
Instructor / Ordinary and Partial Differential Equations (Math. 251) / First- and second-order equations; special functions; Laplace transform solutions; higher order equations; Fourierseries; partial differential equations.

RESEARCH STATEMENT FOR ERWIN A. MACN. GEORGE

My research primarily examines various aspects of the fluid mixing problem Rayleigh-Taylor instability. This classic fluid instability occurs when a perturbed interface between two fluids of differing densities is subjected to a steady gravitational acceleration directed from the heavy to the light fluid, resulting in bubbles of light fluid and spikes of heavy fluid each penetrating into the opposite phase. It arises in a wide variety of important scenarios, such as supernova explosions, the geological evolution of underground salt domes and volcanic islands, and inertial confinement fusion

(where it can degrade the energy yield of the fusion target). Rayleigh-Taylor instability has been widely studied experimentally, theoretically, and numerically at universities and laboratories around the world. However it remains a difficult phenomenon to correctly model via theoretical or numerical simulation techniques, and good experiments are difficult to conduct. Part of my research involves working on a non-diffusive front tracking code and a diffusive total variation diminishing (TVD)level-set code for use in studying three-dimensional Rayleigh-Taylor instability numerically. I will discuss the two main results (so far) from my dissertation and subsequent research.

Most numerical simulations of incompressible flow Rayleigh-Taylor instability greatly under-predict the experimentally-determined value of the acceleration rate of the bubble envelope, one of the most important macroscopic properties of the flow.Theory and experiment agree in their determination of this mixing rate, but most numerical simulations under-determine the rate by a factor of two. We examined reasons for this discrepancy.For weakly compressible flow, thefront tracking simulations have mixing rates in or near the experimental range. In contrast, the untracked TVD simulations have mixing rates far below the experimental range. Front tracking simulations have no interfacial mass diffusion; TVD simulations and other simulations which under-determine the mixing rate do. We demonstrate that the lower mixing rate found in weakly compressible untracked simulations is caused primarily by a reduced buoyancy force due to numerical interfacial mass diffusion. Quantitative evidence includes results from a time dependent Atwood number analysis of aTVD diffusive simulation, which yields a diffusively-renormalized mixing rate coefficient for the diffusive simulation in agreement with experiment.Moreover, we achieve approximate agreement of mixing rates among experiments, theory, and allproperly reinterpreted weakly compressible simulations.