| Lecture | Tutorial |
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| Weekly hours | 2 | 0 | 0 | 0 |
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Problems from analysis (real analysis, complex functions,
ordinary and partial differential equations),
where computer aided solutions can be obtained, will be presented. The
theoretical background of the problems will be discussed and computers
will be used to solve them.
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 3 | 2 | 0 | 0 |
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Generalized Fourier series and the Sturm-Liouville problem, the
equations of Bessel and Legendre, applications to P.D.E. selfadjoint
and non-selfadjoint problems, solutions of P.D.E. by transform
methods (Fourier and Laplace), Green's functions and applications.
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 3 | 0 | 0 | 0 |
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Introduction: solution of equations of third and fourth degrees by
radicals. Composite extensions, algebraic extensions, algebraically
closed fields, splitting field of a polynomial. Extensions of
embeddings, uniqueness of the root field and of the splitting
field of a polynomial. Uniqueness of finite field. Normal
extensions, Separable extensions, counting embeddings. Galois
extensions and Galois groups. The theorem of the primitive
element. The funfamenral theorem of Galois theory. Solvable
groups and solvability by radicals. Cyclotomic extensions,
realization of abelian groups as Galois groups over the rational
number field. Existence of the algebraic closure of a field,
and additional topics: "constructions with straightedge and
compass", the Fundamental Theorem on symmetric polynomials, norm,
and trace in finite extensions, separability and trace form
Kummer theory.
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 2 | 1 | 0 | 0 |
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The course deals with basic notions of topology (setpoint and
algebraic) which are relevant to high school mathematics:
metric spaces, continuity, compactness and local connectedness,
product topology, Tichonoff theorem, two-dimensional surfaces,
models, Euler characteristic, topological invariants.
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 3 | 1 | 0 | 0 |
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Hilbert spaces, convex sets and projections, orthonormal
systems, examples, normal spaces. Bounded operators, adjoint
space, Hahn-Banach theorem in Hilbert space, Riesz theorem.
Fourier series, Fourier and Laplace transforms, integral
operators, min-max, Hilbert-Schmidt-Mercer theorems.
Functions of compact operators, Dirichlet problems. Applications.
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 2 | 2 | 0 | 0 |
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Selected topics for the following fields: graph theory (planar
graphs, Euler formula, connectivity), topology of surfaces
(triangulation, genus), geometry of surfaces (geodesics,
minimal surfaces, spherical triangles), group theory (abstract
groups, Lagrange theorem, generators).
Return to the faculty subjects list
| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 2 | 1 | 0 | 0 |
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"Construction with straightedge and compasses" is moved to
"Field Theory" (104278). Additional topics: Division rings and
quateruious.
Return to the faculty subjects list
| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 3 | 0 | 0 | 0 |
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 4 | 2 | 0 | 0 |
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| Lecture | Tutorial |
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| Weekly hours | 3 | 2 | 0 | 0 |
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| Lecture | Tutorial |
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| Weekly hours | 3 | 1 | 0 | 0 |
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 3 | 0 | 0 | 0 |
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 3 | 1 | 0 | 0 |
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 2 | 1 | 0 | 0 |
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 3 | 1 | 0 | 0 |
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| Lecture | Tutorial |
Laboratory | Project/Seminar |
| Weekly hours | 3 | 1 | 0 | 0 |
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