Compulsory Elective

Name:
Compulsory Elective

Regression Models and Knowledge Processing

Knowledge Data Processing with statistical methods combined with learning processes, involves:

Κρυπτογραφία

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.

Error Correcting Codes

Hamming Distance - Perfect Codes - Equivalent Codes - Linear Codes - Generator Matrices - Encoding - Parity Check Matrices - Decoding a Linear Code - Majority Logic Decoding - MDS Codes - Hamming Codes - Golay Codes - Reed-Muller Codes

Διαφορίσιμες Πολλαπλότητες ΙΙ

Χώροι (πολλαπλότητες) Riemann. Αφινική σύνδεση ενός χώρου Riemann. Γεωδαι-σιακές γραμμές. Τανυστής καμπυλότητας. Καμπυλότητα τομής. Το θεώρημα F. Schur. Καμπύλες ενός χώρου Riemann. Πεδία Jacobi.

Fourier Analysis

Trigonometric series - Fourier coefficients - Fourier series - Convergence of Fourier series - Theorems of Dini and Dirichlet - Summability of Fourier Series - The space of square integrable functions and Fourier series- Parseval identity - Applications

Stochastic Operational Research

Renewal theory - Semi-Markov processes

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.

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