The course deals with systems of linear differential equations, stability theory, basic control theory, some selected aspects of dynamic programming, optimal linear quadratic control or Kalman filter. The theory of the course is useful in applications in various areas such as physics, biology and econonomy, in addition to engineering applications.
Textbook and other material
E. Sontag, Mathematical Control Theory, Deterministic finite dimensional systems, 2nd edition, Springer. (S)
- Teacher: Yishao Zhou
The course covers:
* TeX and LaTeX. Presentations in Beamer and PowerPoint.
* Orientation and published in mathematical journals. Writing scientific papers in mathematics.
* Mathematical popular science. Writing a popular science article in mathematics.
* To hold lectures and presentations in mathematics.
- Teacher: Torbjörn Tambour
Logic II is a second tier logic course, on the advanced level, which gives an introduction to modern mathematical logic. It includes Gödel incompleteness theorems, computability theory, model theory, nonstandard analysis, axiomatic set theory, ordinal and cardinal numbers, equivalents of the axiom of choice.
The course covers rings, ideals, prime ideals, nilpotents, zero-divisors, modules, Noetherian rings, Hilbert's basis theorem, finite extensions and Noetherian normalization, varieties, Nullstellensatz, prime ideal spectra, localization, primary decomposition. Algebraic geometry is the study of solutions to systems of polynomial equations. Commutative algebra is the underlying machinery. The course will give an introduction to these areas.
The course covers integration and measure theory and functional analysis, integration of measurable functions (Lebesgueintegraler), convergence theorems, product measure, Fubini's theorem, Banach spaces including LP-room and fundamental theorems on linear operators and functionals. Areas of application are in Fourier analysis, ergodic theory, probability theory, Sobolev spaces and partial differential equations.