The primary goal of this Program is the
promotion of scientific research in the domain of Applied Mathematics. The
Program consists of 4 semesters (starting on October
1, 2008).
The interested students should have a
Bachelor in Mathematics (or a Bachelor in Science). At this Program can enroll up to 30 students.
The admission of Romanian students to this
program is by a written examination aimed to show their general knowledge on
several aspects of Analysis:
1.
Differentiable
functions of several variables. The Mean Value Theorem. The Principle of
Contraction. The Implicit Function Theorem. Convex functions of several
variables.
2.
Banach Spaces. Basic Examples: R^{n}, C([a,b]), spaces of integrable
functions. The topology associated with a norm. Equivalence of norms in R^{n}. The ArzelaAscoli
criterion of compactness in C([a,b]).
3. The norm of a
continuous linear operator acting on a pair of Banach
spaces. The linear operators on finite dimensional Banach
spaces as matrices and their continuity. The inversion of a continuous linear
operator. The Neumann Lemma. The Open Mapping Theorem. The Closed Graph
Theorem. Pointwise convergence and the Principle of Uniform Boundedness.
4.
Spaces with a hermitian product. Orthogonal sequences. Developments in
Fourier series.
The minimal score for admission is 6/10. The
tax of scholarship will be waived for the first ten Romanian students (listed
downward, according to their score).
Foreign students should contact the
Department for International Relations of the University of Craiova (contact person Valentin Oprea, vallyoprea@central.ucv.ro)
