CAM oral exam

Informations about the oral CAM exam

  • The CAM admission commission schedules an oral exam, if it is unclear if the knowledge of some candidate is sufficient. For candidates with non-mathematical degrees an oral exam is prescribed without exception.
  • The oral exam has to check that the knowledge of a candidate is sufficient for a successful CAM study.
  • Basic knowledge (absolutely necessary) [see Footnote *]:
    • Good knowledge in Analysis: norms, sequences, series, differentiation and integration, both also in a multi-dimensional setting, ordinary differential equations. We want to see especially also a good understanding of theoretical results like the Picard-Lindelöf theorem of existence and uniqueness of ordinary differential equations (ODEs).
    • Good knowledge of linear algebra: vector spaces, linear mappings, determinants, eigenvalue theory.
  • Additional knowledge [see Footnote *]:
    1. Basic knowledge of functional analysis: Banach spaces, Hilbert spaces, examples like Lp- or Sobolev spaces
    2. Basic knowledge of partial differential equations: examples of PDEs, classification (elliptic, parabolic, hyperbolic), existence and uniqueness of solutions.
    3. Basic knowledge of numerical analysis: Solution of linear and nonlinear systems, interpolation, quadrature, numerical solution of ODEs.
    4. Basic knowledge in optimization: optimization problems, solution methods
  • The CAM oral exam should cover topics in one of the additional knowledge domains 1 and 2 and one in the domains 3 and 4. It can also extend to other subjects like the candidate’s Bachelor thesis.

Footnotes:

  • [*] Note that this is a purely personal list of topics which is not complete as well. It is intended to give you an impression what I (Nicolas Neuss) personally consider relevant. Other examiners may vary.