Στατιστική Ανάλυση του Χάους

Δυναμικά συστήματα – Ολοκληρωσιμότης – Ευστάθεια – Χάος – Στατιστικές ιδιότητες – Εργοδικότης – Μίξη – Συστήματα Kolmogorov – Φασματική Θεωρία – Φασματική Ανάλυση Δυναμικών Συστημάτων – Χάος και Στοχαστικές Διαδικασίες – Προβλεψιμότης – Ο Τελεστής του Χρόνου.


Βασικές έννοιες - Ιστορικά Παραδείγματα Κρυπτοσυστημάτων - Το Κρυπτοσύστημα RC4 - Το Κρυπτοσύστημα DES - Βασική Υπολογιστική Θεωριά Αριθμών - Τα Κρυπτοσυστήματα RSA και Rabin - Πρωτόκολλο Ανταλλαγής Κλειδιού Diffie-Hellman - Κρυπτοσυστήματα ElGamal και Massey-Omura - Συναρτήσεις Συμπύκνωσης - Ψηφιακές Υπογραφές RSA, ElGamal και DSA.

Observatory Astronomy and Astrophysics

Sun as a typical star. Stars: Characteristics, classification, distances, photometry, H-R diagram - Stellar evolution: Equations of state, gravitational collapse, nucleosynthesis, neutron stars, black holes - Interstellar medium: Transfer equation, dispersion phenomena - Galaxies. Experimental astronomy: The celestial sphere. Telescopes - Classification of galaxies using the Palomar Sky Survey plates.

Mathematical Statistics

Distributions of functions of random variables - Normal distribution and the derived distributions from the normal - The exponential family - Sufficiency of a statistic for a parameter or for functions of parameters. The Rao-Blackwel theorem - Completeness and uniqueness - Unbiased estimators with minimum variance - The Cramer-Rao inequality - Efficient statistics - Consistent statistics - Maximum likelihood and moment estimators and their properties - Prior and posterior distributions and Bayes estimators - The minimax principle - Interval estimation.

Classical Control Theory

Introduction to the concepts of systems signals and Automatic Control, (brief historical review, basic structure of feedback control, examples) - Mathematical concepts and tools for the study of continuous and discrete time signals and systems. (Laplace transform, z-transform, applications, block diagrams and signal flow graphs) - Classification of signals and systems.

Differential Manifolds I

Tensor Algebra - Differentiable manifolds - Differentials of mapping - Tangent space - Tensor fields - Examples of manifolds - Distributions - Connections.

Partial Differential Equations

First order Partial Differential Equations - Classification of Equations and Characteristic - Initial Value problems - Systems of PDEs - Classification and Initial Value Problems.

Galois Theory

Construction of fields. Algebraic extensions - Classical Greek problems: constructions with ruler and compass. Galois extensions - Applications: solvability of algebraic equations - The fundamental theorem of Algebra - Roots of unity - Finite fields.

Mathematical Logic I

Propositional and predicate calculus - Soundness and Completeness theorems.


Subscribe to RSS - 7th