TEACHING MERITS
Alik Ismail-Zadeh
TEACHING
EXPERIENCE
2024-2026, lecture course "Introduction to Computational Geodynamics" (WSs), Karlsruhe Institute of Technology, Karlsruhe, Germany
2024-2026, lecture course "Introduction to Geohazards and Disaster Risk Analysis" (SSs), Karlsruhe Institute of Technology, 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, Computer Science, and AI
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 the Earth, as well as in experimental techniques enabling high-precision laboratory analysis, and in computational and AI tools permitting faster and more accurate quantitative modeling, are transforming the geosciences. Characteristic of this new intellectual landscape is the need for strong interaction across traditional disciplinary boundaries, particularly among mathematics, computer science, and the Earth sciences. However, Earth science curricula at many universities have not kept pace with these developments. Although most geoscience students complete several semesters of prerequisite courses in mathematics and the physical and/or computer sciences, they typically gain too little education and experience in quantitative thinking and computation to prepare them for participation in the emerging world of quantitative geosciences.
During the twentieth century, the educational path leading to professional degrees in the geosciences in developed countries became largely standardized. Undergraduates (Bachelor students) interested in geosciences usually begin their studies with prerequisite courses, typically one or two semesters of mathematics and several semesters of physics. For most geologists and geophysicists, this early university experience - much of it preceding serious engagement with geology itself - marks the end of their formal education in mathematics. In some universities, this prerequisite mathematical education is delivered by mathematics departments as a service to students who take these courses only because they are required for a degree in gosciences or for admission to Earth science programs. Many of these students lack genuine enthusiasm for mathematics and perceive such courses merely as obstacles on the path to a career in the geosciences. Not surprisingly, faculty teaching these service courses are often ill-prepared to draw meaningful connections between the prerequisite material and exciting developments in the geosciences. The disparity in both sophistication and difficulty between these educational tracks can be striking.
These traditions have led to a deep bifurcation in both culture and quantitative competence across scientific disciplines. On one branch lie mathematics, the physical sciences, and computer science. Scientists trained along this path achieve a high level of quantitative expertise. They typically develop mastery of multivariable calculus, differential equations, linear algebra, tensor analysis, probability, and statistics. Programming and computational proficiency are also expected. Beyond textbook knowledge, quantitative reasoning constitutes the core of daily scientific practice in these fields, expressed through a rich interplay of theory, experiment, and computation [1].
On the other branch lie the geosciences. With few exceptions, Earth scientists rarely attain mathematical competence beyond elementary calculus and basic statistics. Although computers are ubiquitous, many geologists rely primarily on standard commercial software and nowadays on AI tools. While sophisticated tools are widely used, relatively few academic geologists feel comfortable teaching the underlying principles, and even fewer can implement basic algorithms themselves. Many require consultation with mathematical geoscientists or geostatisticians for anything beyond elementary statistical analysis, and mathematical rigor in published geological research is too often insufficient or absent.
Moreover, the increasing speed and accessibility of computing enable a growing number of geoscientists without substantial mathematical training to explore complex models and draw conclusions from them. In some cases, numerical modeling has become a dominant research approach. Such work often involves formulating reasonable, evidence-based assumptions for complex Earth systems, assigning parameter values, sometimes arbitrarily, and running simulations. This raises a critical question: how much confidence can we place in results when the underlying mathematical understanding is limited? For instance, models of lithospheric dynamics may involve dozens of adjustable parameters, yet their influence on results is not always adequately analyzed or explained. This situation recalls the well-known dictum, "with four parameters I can fit an elephant". As Robert May observed [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 ... Removing this link means that we are seeing ... 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, hundreds of research proposals and articles in quantitative geosciences continue to emerge each year, often authored by individuals with limited expertise in applied mathematics and numerical modeling.
The cultures of students following these two paths of quantitative development differ accordingly. Students (and their instructors) in mathematics and the physical sciences tend to emphasize principles, abstraction, and reasoning, whereas those in geosciences often focus on mastering extensive bodies of factual knowledge. While this distinction is somewhat stereotypical and can be mitigated by effective teaching, it nonetheless exerts a strong influence on undergraduate education.
To participate fully in future research, scientists must be fluent not only in the language of geoscience but also in those of mathematics and computation. This challenge cannot be addressed simply by specifying minimal mathematical requirements and delegating their instruction to mathematics departments. The issue is deeper: science itself is divided into two cultures - one quantitative and one not. If the geosciences are to integrate fully into the broader landscape of quantitative science, both geologists and non-geologists will require a fundamentally different kind of education.
What can be done? For several years, I have been developing an integrated curriculum in which mathematics, computer science, and geosciences are taught in a coordinated manner. Students intending to pursue research careers in quantitative Earth sciences - whether in academia or industry - should engage in such integrated study immediately after completing prerequisite coursework. At the undergraduate (Batchelor) level, students first acquire foundational knowledge in each discipline, after which they enter the domain of quantitative geoscience. The core concepts of these fields should be introduced at a high level of sophistication and explicitly connected to relevant geoscientific problems.
A central goal of this curriculum is to demonstrate how each discipline contributes to understanding Earth's phenomena, how these phenomena reinforce quantitative reasoning, and how traditional disciplinary boundaries are becoming increasingly artificial. Integration enables students to learn the languages of different disciplines in context. Scientists educated in this way, regardless of their eventual specialization, would share a common scientific language, facilitating cross-disciplinary communication and collaboration.
To conclude, I echo the words of Richard Feynman, who noted that two cultures divide those who have experienced the power of mathematics in understanding nature from those who have not. Mathematics provides one of the most effective frameworks for understanding complex natural systems, and strong mathematical training for geoscientists is essential if we are to enable talented individuals to tackle the most important problems in the 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 the following PhD students
-
Elena Bushueva (2001-2003)
-
Dmitry Krupsky (2004-2006)
-
Ilya Turov (2015-2017)
-
Natalya Zeinalova
(2021-2025)
-
Youtian Yang
(2025-2026)
-
Stephan Vygovskiy
(2026-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, USA
The authors are distinguished geodynamicists with decades of experience in numerical modeling. They are at the forefront of geodynamical modeling and are responsible for the initial development and continued improvement of state-of-the-art codes. They have written a clear and comprehensive book that everyone working in the field of geodynamics would be well advised to read and keep handy for future reference. - Professor Gerald Schubert, University of California, Los Angeles, USA
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, USA
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.