Freie Universität Berlin, Berlin, Germany | Marwan Benyoussef
- Teaching Assistant, Algebra I
AG Komplexe Analysis, under the direction of Prof. Dr. Alexander Schmitt
- Oct 2023 – Present
- Conducting central exercise class for Algebra I module, including the following concepts: Affine algebraic varieties, rings, ideals and modules, noetherian rings, local rings and localization, primary decomposition, finite and integral extensions, dimension theory, regular rings.
Freie Universität Berlin, Berlin, Germany
- Teaching Assistant, Algebra and number theory
AG Komplexe Analysis, under the direction of Prof. Dr. Alexander Schmitt
- Oct 2023 – Present
- Lecturing the following concepts: Divisibility in rings (especially the ring of integers and polynomial rings); residual classes and congruences; Modules and ideals, Euclidean, principal ideal and factorial rings, the square reciprocity law, prime number testing and cryptography,the structure of abelian groups (or modules over PIDs), theorem on symmetric functions, field extensions, Galois correspondence, Constructions with compass and ruler, non-abelian groups (Lagrange’s theorem, normal subgroup, solvability, Sylow groups).
Freie Universität Berlin, Berlin, Germany
- Teaching Assistant, Cybersecurity
AG Mathematik und Informatik, under the direction of Dr. Aruni Choudhary
- Mar 2023 – Sep 2023
- Conducted exercise class for Cybersecurity module, including the following concepts: authentication mechanisms, security models (Access Control Matrix Model, the Take-Grant Protection Model, the Bell-LaPadula and related models, the Chinese Wall Model, the Lattice Model of Information Flow), capability based systems and hardware protection mechanism concepts (protection rings). The course included also implementation vulnerabilities such as race conditions, stack and heap overflows, integer overflows, and return oriented programming.
- Problems that arise when humans interface with security e.g., password habits and password entry mechanisms, human responses to security prompts, incentives and distractors for better security, or reverse Turing tests.
Freie Universität Berlin, Berlin, Germany
- Teaching Assistant, Algebra and number theory
AG Komplexe Analysis, under the direction of Prof. Dr. Alexander Schmitt
- Oct 2022 – Mar 2023
- Substituted a colleague for one class. The course included the following concepts: Divisibility in rings (especially the ring of integers and polynomial rings); residual classes and congruences; Modules and ideals, Euclidean, principal ideal and factorial rings, the square reciprocity law, prime number testing and cryptography,the structure of abelian groups (or modules over PIDs), theorem on symmetric functions, field extensions, Galois correspondence, Constructions with compass and ruler, non-abelian groups (Lagrange’s theorem, normal subgroup, solvability, Sylow groups).
Freie Universität Berlin, Berlin, Germany
- Teaching Assistant, Proseminar on “Proofs from THE BOOK”
AG Komplexe Analysis, under the direction of Prof. Dr. Alexander Schmitt
- Oct 2022 – Mar 2023
- Conducted a proseminar on “Proofs from THE BOOK”, including the following concepts: basics of linear algebra, analysis, number theory and some elementary but ubiquitous concepts and reasoning from discrete mathematics. The goal for students is to understand some of the proofs that Paul Erdos calls “The Proofs from THE BOOK”. These proofs are intended to be highly efficient, concise and beautiful in terms of technique and scope.
Freie Universität Berlin, Berlin, Germany
- Teaching Assistant, Geometry
AG Komplexe Analysis, under the direction of Prof. Dr. Alexander Schmitt
- Apr 2022 – Sep 2022
- Conducted exercise class for Geometry module, including the following concepts: Conic sections (parabolas, ellipses, hyperbolas: definition and alternative characterization, technical applications; Dandelin spheres), Transformations in Euclidean and affine geometry (congruence of triangles: main theorem of affine geometry; congruence of conics in Euclidean and affine geometry; classification of quadrics in n-dimensional affine space; lines on two-dimensional quadrics).
- Projective Geometry (Perspective Transformations; The Projective Plane: Construction and Models; The Double Ratio: Definition, Properties and Technical Applications; Conics in Projective Geometry)
- Hyperbolic geometry (introduction of the Poincaré model of the hyperbolic plane)
Freie Universität Berlin, Berlin, Germany
- Teaching Assistant, Algebra III
AG Komplexe Analysis, under the direction of Prof. Dr. Alexander Schmitt
- Oct 2021 – Mar 2022
- Conducted exercise class for Algebra III module, including the following concepts: Čech cohomology, schemes, cohomology of affine schemes, projective spaces, line bundles on projective spaces and their cohomology, group schemes, algebraic groups.
- Teaching Assistant, Algebra II
AG Komplexe Analysis, under the direction of Prof. Dr. Alexander Schmitt
- Apr 2021 – Sep 2021
- Conducted exercise class for Algebra II module including the following concepts: categories and functors, additive and abelian categories, cohomology, ringed spaces, sheaf theory.
- Teaching Assistant, Algebra I
AG Komplexe Analysis, under the direction of Prof. Dr. Alexander Schmitt
- Oct 2020 – Mar 2021
- Conducted central exercise class for Algebra I module, including the following concepts: Affine algebraic varieties, rings, ideals and modules, noetherian rings, local rings and localization, primary decomposition, finite and integral extensions, dimension theory, regular rings.
Paris, France
- Math Tutor
Undergraduate Linear Algebra and Calculus tutor
Paris-Sud University, Orsay, France
- Part-time Lecturer
C++ and Object Oriented development and algorithms optimization lecturer