Teaching

Duke Kunshan University

At Duke Kunshan University I have taught several undergraduate mathematics courses, listed below in increasing code order.

  • MATH 201 Multivariable Calculus: This is a required course for students in several majors in the Division of Natural and Applied Sciences, and an elective for students in other majors. I taught this course in Fall 2019 to a class of 70 students. The course covers functions depending on several variables, differentiation (partial derivatives, directional derivatives, gradient), optimization, integration over surfaces and volumes, and the fundamental integration theorems (Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem) that generalize to more than one dimensions the Fundamental Theorem of Calculus. Further details, including the syllabus, are available on the course page.

  • MATH 302 Numerical Analysis: This is a required course for students in the Mathematics and Computer Science tracks of the Applied Mathematics and Computational Sciences major, and an elective for other majors. I taught this course six times from 2020 to 2024 to classes averaging around twenty students. The course focuses on the theoretical foundations and practical implementation of numerical algorithms and it uses the Julia programming language, chosen for its speed and suitability for scientific computing. Topics include root-finding methods, interpolation, numerical differentiation and integration, initial and boundary value problems, and direct and iterative methods for linear systems. Further details, including the syllabus, are available on the course page.

  • MATH 303 ODE and Dynamical Systems: This is a required course for students in the Applied Mathematics and Computational Science major, and an elective for other majors. I taught this course eight times from 2020 to 2025 to classes averaging around twelve students. The course focuses on the qualitative analysis of solutions of differential equations and dynamical systems. Topics include solving first-order and linear differential equations, analyzing nonlinear systems via qualitative methods (stability, phase plane analysis, Lyapunov’s method), and exploring bifurcations, limit cycles, and Poincaré maps. The syllabus and lecture slides are available on the course page.

  • MATH 308 Real Analysis: This is a required course for students in the Mathematics track of the Applied Mathematics and Computational Science major, and an elective for other majors. I taught this course four times from 2020 to 2024 to averaging around ten students. Topics include the properties of real numbers and functions, limits, continuity, completeness, compactness, uniform convergence, and Riemann integration. The course emphasizes developing proof-writing skills and logical rigor. Further details, including the syllabus, are available on the course page.

  • MATH 409 Topology: This is a disciplinary course for students in the Mathematics track of the Applied Mathematics and Computational Science major, and an elective for other majors. I taught this course in Spring 2025 to a class of four students. The course discusses both point-set topology and algebraic topology and topics include topology of metric spaces, abstract topological spaces, connectedness, compactness, continuity, completeness, subspaces, product and quotient spaces, separation axioms, homotopies of paths, the fundamental group, covering spaces, and index theory. Further details, including the syllabus, are available on the course page.

  • Independent Study: Independent study offers students the opportunity to explore academic topics beyond the scope of existing DKU courses. For more information, please visit the linked page, and feel free to reach out if you are interested in pursuing an independent study under my supervision.

University of Groningen

At the University of Groningen, I taught several undergraduate and graduate-level (Master’s) courses, listed below in roughly chronological order. In 2015, I also obtained the Undergraduate Teaching Qualification, a proof of pedagogic competence for teachers in academic education.

  • Geometry and Physics: This elective course was offered to students in BSc Mathematics, BSc Applied Mathematics, BSc Astronomy, BSc Physics and Mathematics, MSc Physics, and MSc Applied Physics. I taught it from 2005 to 2007 in small classes, using Henk Broer’s “Meetkunde en fysica, met differentiaalvormen en integraalstellingen” (Epsilon Uitgaven, 1999). The course covered vector fields, differential forms, and Stokes’ theorem in Euclidean space and on manifolds.

  • Metric Spaces: This was a required coursed for students in the programs BSc Mathematics, BSc Applied Mathematics, and BSc Physics and Mathematics, and an elective course in the programs MSc Physics, and and Applied Physics. I taught this course from 2008 to 2012, using W. A. Sutherland’s “Introduction to metric and topological spaces” (Oxford University Press). The course covered basic concepts in metric and topological spaces, such as continuity, compactness, connectedness, and completeness.

  • Conservative Dynamical Systems: This elective Master’s course was co-taught with Heinz Hanßmann in 2009.

  • Advanced Hamiltonian Dynamics: I taught this course in the National Dutch MasterMath program in 2017. The course covered fundamental topics in Hamiltonian dynamics and symplectic geometry. The textbook used was Cannas da Silva’s “Lectures on Symplectic Geometry” (Springer, 2001).

  • Complexity and Networks: This required course for 1st-year MSc students in Mathematics and Applied Mathematics was co-taught from 2017 to 2019. I was responsible for the “Dynamics on Networks” section, which covered synchronization, stability in networked systems, the Kuramoto model, graph Laplacian, and applications to circadian rhythms.

  • Calculus for Chemistry: This required course for 1st-year students in Chemistry and Chemical Engineering was taught from 2014 to 2019 to classes of 250–300 students. The course refreshed basic mathematical skills and covered real functions, limits, derivatives, integration, complex numbers, and differential equations, with applications in physics, economics, and medical sciences. I was elected Teacher of the Year 2016–2017 for this course by BSc Chemical Engineering students. The textbook used was “Calculus: Early Transcendentals” by James Stewart (Cengage Learning, 7th edition, 2012).

  • Complex Analysis: This required course for 2nd-year students in Mathematics, Applied Mathematics, Physics, and Astronomy was taught from 2014 to 2018 to classes of 90–120 students. The course focused on analytic functions, Cauchy-Riemann equations, harmonic functions, complex integrals, Taylor and Laurent series, singularities, and the calculus of residues. The textbook used was “Fundamentals of Complex Analysis” by E. B. Saff and A. D. Snider (Pearson, 3rd edition, 2003).

  • Partial Differential Equations: This required course for 2nd-year BSc Mathematics and BSc Applied Mathematics students was taught from 2015 to 2017 to classes of approximately 60 students. The course covered the classification of PDEs, uniqueness of solutions, and analytical methods such as the method of characteristics, separation of variables, Green’s functions, and Fourier series. The textbook used was “Partial Differential Equations: An Introduction” by W. A. Strauss (Wiley, 2nd edition, 2008).

  • Learning Communities: I co-coordinated Learning Communities, a collaborative setting where Mathematics students learned to read, write, and construct proofs through peer discussions on assigned material.

Xi’an Jiaotong-Liverpool University

At Xi’an Jiaotong-Liverpool University I taught two physics-related courses for students in the BSc program in Applied Mathematics.

  • Classical Mechanics: This required course for third year BSc Applied Mathematics students was taught twice, with significant changes in content and delivery between the two years. In 2013, the course covered Newton’s laws of motion, energy principles, the two-body problem, and rigid body dynamics. In 2014, the course shifted focus and covered similar topics from the Lagrangian and Hamiltonian points of view. The textbooks used were “An Introduction to Mechanics” by D. Kleppner and R. J. Kolenkow (Cambridge University Press, 2010) and “Classical Mechanics” by H. Goldstein, C. Poole, and J. Safko (Addison-Wesley, 3rd edition, 2002).

  • Quantum Mechanics: This elective course for BSc Applied Mathematics students covered wave-particle duality, Schrödinger’s equation, finite-dimensional Hilbert spaces, angular momentum, and perturbation theory. The textbook used was “Introduction to Quantum Mechanics” by D. J. Griffiths (Addison-Wesley, 2nd edition, 2005).