Regression Models and Knowledge Processing

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

Θεωρία Ομάδων

Δράση ομάδας σε σύνολα και σε ομάδες (μετάθεση αναπαράσταση, Τροχιές, Σταθεροποιητές, Λήμμα Τροχιά-Σταθεροποιητής), Λήμμα του Burmside, Μεταβατική Δράση, Δράση ομάδας με συζυγία (κανονικοποιητής, κεντροποιητής), ημιευθύ γινόμενο ομάδων (Διεδρική ομάδα), Αβελιανές ομάδες (Ελεύθερη αβελιανή ομάδα πεπερασμένης βαθμίδας, Ελεύθερη στρέψης αβελιανή ομάδα, Περιοδική αβελιανή ομάδα), Το Θεώρημα διάσπασης πεπερασμένα παραγόμενων αβελιανών ομάδων (αναλύσιμες και μη αναλύσιμες), Θεωρήματα του Sylow (Η μέθοδος της απαρίθμησης, η κυκλική μέθοδος), Απλές ομάδες, Ομάδες μικρής τάξης, Επιλύσιμες ομάδες (Ομ

Stochastic Processes with complete connections and Learning Theory

Stochastic processes with complete connections - Definition - Basic notions - The homogeneous case - Stochastic properties - Application of stochastic processes with complete connections to Learning Theory - Introduction to Learning theory - some notions of learning theory - The modelling of the learning phenomenon, -The model of the stimulus choice.

Theoretical Mechanics

Kinematics of a mass particle - Forces and laws of motion - Conservation theorems - Systems with one degree of freedom - Oscillations - Stability of equilibrium points - Phase diagrammes - Central forces - Kepler’s problem - Systems of mass particles - Noninertial frames of reference.


Theory of elastic waves - Quantification of earthquakes - Plate tectonics theory - Seismotectonics of the Aegean area - Macroseismic effects of earthquakes.

Stochastic Strategies

Stochastic problems - Stochastic networks - Stochastic problems of tools replacement and repairing - Renewal theory - Inventory.

Probability Theory II

The algebra of events - Probability Space - The axioms of Probability - Random variables - The notion of stochastic distribution - Multidimensional random variables - Multidimensional distribution functions - Marginal distributions - Denumerable multidimensional random variables - Continuous multidimensional distributions - Multidimensional normal distribution - Stochastic independence - Conditional Probability - Conditional density - Conditional distributions - Mean values for multidimensional random variables - Conditional mean values - Regression line - Mean square error - Random variabl

Numerical Analysis

Structure of Computational systems and algorithms, number systems and errors - Interpolation and approximation (interpolation by Lagrange and Newton polynomials) - Numerical integration (midpoint, trapezoid and Simpson’s rules, Romberg integration) - Numerical solution of non-linear equations (bisection method, secant, regula-falsi and modified regula-falsi, Newton’s method) - Introduction to iterative methods for linear systems and ODE.


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