Analysis 1 - Fall 2016 - Bachelor
Keywords: Series of numbers, real analysis, limits, continuity, power series, topology, Riemann integral, series of functions.
Advanced analysis 2 - Spring 2017 - Bachelor
Keywords: Functions of several variables, differentiability, gradient, Hessian, integrals, ordinary differential equations, Banach and metric spaces, Lagrange multipliers.
Analysis 1 - Fall 2017 - Bachelor
Keywords: Series of numbers, real analysis, limits, continuity, power series, topology, Riemann integral, series of functions.
Advanced analysis 2 - Spring 2018 - Bachelor
Keywords: Functions of several variables, differentiability, gradient, Hessian, integrals, ordinary differential equations, Banach and metric spaces, Lagrange multipliers.
Sobolev spaces and elliptic PDEs - Fall 2018 - Master
Keywords: Partial differential equations, Heat equation, wave equation, Duhamel’s principle, heat kernel, Sobolev spaces, weak solutions.
Functional Analysis 2 - Spring 2019 - Master
Keywords: Locally convex spaces, topological dual, inductive limits, continuity, spectral family, Stieltjes integrals.
Evolutional partial differential equations - Fall 2019 - Master
Keywords: Non-linear and quasi-linear PDEs, envelopes, Cauchy-Kowalevski, characteristic varieties, hyperbolic PDEs, parabolic PDEs, kernel, contraction semigroups, Hille-Yosida.
Dynamics and bifurcation - Spring 2020 - Bachelor
Keywords: Local and global behavior of nonlinear dynamical systems arising from maps and ODEs. Theoretical and computational aspects studied. Lyapunov stability.
Algebraic Structures - Fall 2020 - Bachelor
Keywords: Fermat theorem (RSA), Euclide algorithm, groups and morphisms, Lagrange, quotient group, semi-direct product, usual groups (dihedral, quaternions …)
Selected topics from analysis - Spring 2021 - Bachelor
Keywords: Student seminar, each student prepares a specific subject and is evaluated. Focuses and advanced analysis and mathematical physics.
Analysis and PDEs - Fall 2021 - Master
Keywords: Sobolev spaces, weak solutions, heat propagator, convolutions, energy methods, wave equation, harmonic functions, Green’s functions.
Proof from the book - Spring 2022 - Bachelor
Keywords: Student seminar, each student prepares a specific subject and is evaluated.
Measure and integration theory - Fall 2022 - Bachelor
Keywords: Sigma algebras, measures, Borelians, Lebesgue measure and integration, theorems on limits of integrals, density.
Fourier analysis - Spring 2023 - Master
Keywords: Lorentz spaces, Fourier Series, Fourier transform on L1 and L2, convolutions, inversion, Plancherel and Parseval theorems.
Mathematics and computers - Fall 2023 - Bachelor
Keywords: Matlab, Maple, introduction to programming and algorithmics, RSA, linear algebra.
Numerics - Spring 2024 - Bachelor
Keywords: Matlab, algorithmics for mathematics, error propagation, linear algebra, complexity analysis.
Numerics for Differential Equation- Fall 2024 - Bachelor
Keywords: Matlab, error propagation, stability, convergence, Runge-Kutta, Adams-Bashforth, BDF-k.