TEACHING MERITS
Alik Ismail-Zadeh
TEACHING
EXPERIENCE
·
2024-2025, lecture course
“Introduction to Computational Geodynamics”, Karlsruhe Institute of Technology,
AGW, Karlsruhe, Germany
·
2022-2023, online lecture
course "Advancing Frontiers of Disaster Science" at universities in
Azerbaijan, India, Mexico, and USA
·
2021 (workshop), block
lecture course on inverse problems and data assimilation, Abdus Salam
International Center for Theoretical Physics (ICTP), Trieste, Italy
·
2015 (workshop), block
lecture course on natural hazards and disasters, Abdus Salam International
Center for Theoretical Physics (ICTP), Trieste, Italy
·
2014 (summer school),
block-lecture course on Computational Geodynamics, University of the Chinese
Academy of Sciences, Beijing, China
·
2012 (winter semester),
lecture course “Modeling of Geodynamic Processes”, Karlsruhe Institute of
Technology, Germany.
·
2007-2012, block lecture
course “Data Assimilation and Inverse Problems in Geodynamics”, Abdus Salam
International Center for Theoretical Physics (ICTP), Trieste, Italy.
·
2005-2007 (winter
semesters), lecture course “Introduction to Tectonic Stress Analysis and
Modeling”, Karlsruhe University, Germany.
·
2004-2005 (winter semester),
curriculum “Physics of the Earth” and lecture course “Computational Fluid
Dynamics of the Earth”, Karlsruhe University, Germany.
·
2001-2005, block lecture
course “Numerical Modeling of Nonlinear Dynamics of the Lithosphere”, Abdus
Salam International Center for Theoretical Physics (ICTP), Trieste, Italy.
·
1998-2000 (summer
semesters), lecture courses “Foundations of Geophysics and Geodynamics” and
“Computational Geodynamics”, M. Gubkin Russian State
University of Oil and Gas in Moscow, Russia.
TEACHING
PHILOSOPHY
My
teaching philosophy is as follows. A professor should
(i) be a
qualified expert in a main topic of lecture courses;
(ii) have broad and deep knowledge of
the subject of the courses as well as a basic knowledge in wider scientific
areas;
(iii) employ both approaches from
reductionism to holism and vice versa in an educational process;
(iv) link theoretical and experimental
approaches, lectures and practical courses;
(v) look for solutions of scientific
puzzles together with students;
(vi) bring a humor in a teaching
process and a freedom of expressions; and
(vii) teach students to think, but not
just to collect new knowledge without a subsequent analysis.
TEACHING
APPROACH
Integrated
GeoScience, Mathematics, and Computer Science
Education
“It is
impossible to explain honestly the beauties of the laws of nature in a way that
people can feel,
without their having some deep understanding of mathematics” – R.
Feynman.
Great advances in understanding of the Earth as well
as in experimental techniques, allowing for high-precision laboratory analysis,
and in computational tools, permitting accurate numerical modeling, are
transforming the geoscience. Characteristic of this new intellectual landscape
is the need for strong interaction across traditional disciplinary boundaries:
mathematics, computer science and Earth sciences. Earth science curricula at
many universities have not kept pace with these developments. Even though most
geoscience students take several semesters of prerequisite courses in
mathematics, the physical and/or computer sciences, these students have too
little education and experience in quantitative thinking and computation to
prepare them to participate in the new world of quantitative geosciences.
During the XXth century, the educational path leading
to professional degrees in Earth sciences in developed countries became rather
standard. Undergraduates interested in geosciences begin their studies with a
set of “prerequisite” courses, typically one or two semesters of mathematics
and a few semesters of physics. For most geologists and geophysicists, this
early university experience, most of it preceding serious engagement with
geology itself, is the end of their education in mathematics. For reasons of
history, this prerequisite mathematical education is delivered by departments
as a service to students who take them because it is required for a degree in
geosciences or for entry into Earth science school. Many of the students taking
these courses have no real enthusiasm for mathematics and perceive these
courses simply as obstacles to be overcome on the way to a career in Earth
sciences. Not surprisingly, the faculty who teach these service courses are
ill-prepared to make connections between what is presented in the prerequisites
and what is exciting in the geosciences. The difference in sophistication (and
difficulty) of the quantitative content of these separate tracks can be
startling.
These traditions have resulted in a deep bifurcation in culture and
quantitative competence among the scientific disciplines. On one branch are
mathematics, the physical and computer sciences. “Scientists educated along
this branch achieve a high level of quantitative expertise. They generally have
some mastery over and comfort with not only multivariate calculus and
differential equations, but also linear algebra, Fourier analysis, probability,
and statistics. All scientists in these areas are expected to be able to
program as well as to use computers themselves. Beyond textbook knowledge of
mathematical and computational methods, quantitative thinking is the daily
essence of the science to which this educational path leads, and this is
expressed in a rich interplay of theory, experiment, and computation” [1].
On the other branch are geosciences. With insignificant exceptions, Earth
scientists today rarely achieve mathematical competence beyond elementary
calculus and maybe a few statistical formulae. Although everybody uses a
computer, geologists rarely use anything but standard commercial software.
Virtually all geologists today must use some sophisticated programs (e.g.,
ABAQUS, CONMAN, FLAC, MARC, PDE2D for modeling, AVS, AMIRA, IDL for
visualization), yet distressingly few academic geologists feel comfortable
teaching the underlying principles to their students, and fewer are able to
program even a rudimentary software implementation of such an algorithm
themselves. Most geologists require consultations with mathematical
geoscientists and geostatisticians in
order to do anything but the simplest statistics, and all too often
mathematical analysis in published geological papers is inadequate or omitted
entirely.
Moreover, the increasing speed and ease of use of computer enables an
increasingly large number of Earth scientists who have no substantial
background in mathematics to explore mathematical models and draw conclusions
about them. In some sense it becomes a fashion today when geologists make
numerical modeling as their primary research method. Such activity usually
consists of representing sensible and evidence-based assumptions as the
starting point for a complicated Earth system, assigning particular
parameters (often in an arbitrary way), and then letting this
complicated system run. How we can trust geoscientists whose knowledge in
applied mathematics leaves hope for improvement, when they present, let say,
numerical results of a model of dynamics of the Earth lithosphere and try to
explain some natural observations by their model which employs a few dozen (!)
of turning parameters? Sometimes they do not even clarify an influence of these
parameters on the model results. Perhaps such geoscientists did not hear a
dictum by famous physicist E. Fermi: “With four exponents I can fit an
elephant”. Lord Robert May of Oxford writes [2]: “This represents a
revolutionary change in such theoretical studies. Until only a decade or two ago,
anyone pursuing this kind of activity had to have a solid grounding in
mathematics. And that meant that such studies were done by people who had some
idea of how the original assumptions related to the emerging graphical display
or other conclusions on their computer. Removing this link means that we are
seeing arguably an increasingly large body of work in which sweeping
conclusions are drawn from the alleged working of a mathematical model, without
clear understanding of what is actually going on”. Nevertheless,
a hundred of research proposals and articles on quantitative geosciences are
emerging every year where authors are not competent in applied mathematics and
numerical modeling.
The cultures of students following the two paths of quantitative competence,
not surprisingly, are also different. Whereas the students (and their teachers)
on the mathematical and physical science branch are focused on principles and
reasoning as the goal of their education, students (and teachers) on the
geology branch find themselves focused more on mastering huge arrays of facts.
Although this characterization is partly a stereotype and good teaching can
help bridge these cultures, undergraduates are strongly influenced by these
ideas.
In order to participate fully in the research of the future, it will be
essential for scientists to be conversant not only with the language of
geosciences but also with the languages of mathematics and computers. It is
important to recognize that the problem cannot be solved by specifying minimal
mathematical expertise for future geologists and geophysicists and assigning
our colleagues in the mathematics department the task of inculcating this
expertise in our students. Today we have two cultures within science itself,
one mathematical and the other not. If Earth Science is to assimilate into the
world of quantitative science, geologists and non-geologists alike will need a
different kind of education than we provide today.
What can be done? I suggest to develop an integrated
curriculum in which mathematics, computer science, and geosciences are
introduced together. Students interested in a research career in the
quantitative Earth sciences (whether in academia or in industry) should get the
integrated study course immediately after the prerequisite courses in
mathematics, physics, computation, and geosciences. Initially (during the first
two-three semesters of their university’s study) the students receive
background knowledge in each scientific discipline, and then they enter into the world of quantitative geosciences. The basic
ideas of each of these disciplines should be introduced during this integrated
course at a high level of sophistication in context with relevant geological
problems.
A major goal of the course is to show the students how each discipline
contributes to understanding the Earth’s phenomena, how these phenomena
illustrate and reinforce our quantitative understanding of phenomena in the
world, and how the boundaries between disciplines are becoming arbitrary and
irrelevant. Integration will allow students to learn the languages of the
different disciplines in context. Scientists educated in this way, regardless
of their ultimate professional speciality, would
share a common scientific language, facilitating both cross-disciplinary
understanding and collaboration.
To summarize, I would use the words of R. Feynman, who said that “two cultures
separate people who have and people who have not had this experience of
understanding mathematics well enough to appreciate nature once”. Mathematics
provides the best way of understanding complex natural systems, and a good
mathematical education for geoscientists is the best route for enabling the
most able people to address really important problems
in Earth sciences.
1. Bialek, W.,
and Botstein, D., 2004. Introductory science and mathematics education for
21st-century biologists. Science, 303: 788-790.
2. May, R., 2004. Uses and abuses of
mathematics in biology. Science, 303: 790-793.
POPULAR SCIENCE
I have been popularizing a
scientific knowledge on geosciences as well as on disaster science. Since 1998
I am chairing discussions in EuroScience working
group on problems of science and urgent problems of society. I have been an
organizer of the two workshops on topic of science, risk
and sustainability during European Science Open Forums (in Budapest 2002,
Stockholm 2004, Munich 2006, Barcelona, 2008, Turin 2010, Dublin 2012, Trieste
2020).
SUPERVISION
I have supervised four PhD students
-
Elena Bushueva (2001-2003)
-
Dmitry Krupsky (2004-2006)
-
Ilya Turov (2015-2017)
-
Natalya Zeinalova
(2021-present)
TEXTBOOKS
Computational
Methods for Geodynamics (2010) describes all the numerical
methods typically used to solve problems related to the dynamics of the Earth
and other terrestrial planets – including lithospheric deformation, mantle
convection and the geodynamo. It starts with a
discussion of the fundamental principles of mathematical and numerical
modeling, which is then followed by chapters on finite difference, finite
volume, finite element, and spectral methods; methods for solving large systems
of linear algebraic equations and ordinary differential equations; data assimilation
methods in geodynamics; and the basic concepts of parallel computing. The final
chapter presents a detailed discussion of specific geodynamic applications in order to highlight key differences between methods and
demonstrate their respective limitations. Readers learn when and how to use a
particular method in order to produce the most
accurate results. This combination of textbook and reference handbook brings
together material previously only available in specialist journals and
mathematical reference volumes, and presents it in an
accessible manner assuming only a basic familiarity with geodynamic theory and
calculus. It is an essential text for advanced courses on numerical and
computational modeling in geodynamics and geophysics, and an invaluable
resource for researchers looking to master cutting-edge techniques.
“An
outstanding synthesis of contemporary issues in geodynamics with a rigorous but
highly accessible treatment of modern methods in numerical modeling. I have no
doubt that this book will be an invaluable resource for students and
researchers entering the field of computational geophysics for years to come.”-
Professor David Bercovici, Yale University
“This
is the most current and complete book on computational geodynamics. I would recommend
this book to every aspiring student or researcher interested in computations.”
- Professor David Yuen, University of Minnesota
Data-Driven
Numerical Modelling in Geodynamics: Methods and Applications (2016) describes the methods and numerical approaches for data
assimilation in geodynamical models and presents several applications of the
described methodology in relevant case studies. The book starts with a brief
overview of the basic principles in data-driven geodynamic modelling, inverse
problems, and data assimilation methods, which is then followed by
methodological chapters on backward advection, variational (or adjoint), and
quasi-reversibility methods. The chapters are accompanied by case studies
presenting the applicability of the methods for solving geodynamic problems;
namely, mantle plume evolution; lithosphere dynamics in and beneath two
distinct geological domains – the south-eastern Carpathian Mountains and the
Japanese Islands; salt diapirism in sedimentary
basins; and volcanic lava flow.
Applications
of data-driven modelling are of interest to the industry and to experts dealing
with geohazards and risk mitigation. Explanation of the sedimentary basin
evolution complicated by deformations due to salt tectonics can help in oil and
gas exploration; better understanding of the stress-strain evolution in the
past and stress localization in the present can provide an insight into large
earthquake preparation processes; volcanic lava flow assessments can advise on
risk mitigation in the populated areas. The book is an essential tool for
advanced courses on data assimilation and numerical modelling in geodynamics.