3rd

Name: 
3rd

Introduction to Meteorology and Climatology

Functions of several variables - Limits and continuity - Partial derivatives - Differentiation of scalar and vector functions - The chain rule - Higher order partial derivatives - Directional derivatives - Taylor’s formula - Extremes of real valued functions - Lagrange multipliers - The implicit function theorem and the inverse function theorem.

Probability Theory I

The sample distribution space - events - classical definition of mathematical probability - statistical regularity - axiomatic foundation of probability - Finite sample distribution spaces - combinatorics - geometric probabilities - Conditional probability - independence - Univariate random variables - distribution functions - function of a random variable - moments, moment-generating function - probability generating function - Useful univariate distributions: Discrete (Bernoulli, Binomial, Hypergeometric, Geometric, Negative Binomial, Poisson), Continuous (Uniform, Normal, Exponential, Ga

Αναλυτική Γεωμετρία ΙΙ

Ευκλείδεια Γεωμετρία: Ταξινόμηση ισομετριών στο ευκλείδειο επίπεδο και στον τρισδιάστατο ευκλείδειο χώρο. Εφαρμογές (Κοινή κάθετος ασυμβάτων ευθειών, απόσταση σημείου από ευθεία και επίπεδο, δέσμες ευθειών και επιπέδων). Καμπύλες δεύτερης τάξης στο ευκλείδειο επίπεδο (Έλλειψη, υπερβολή, παραβολή, αναγνώριση καμπύλης). Επιφάνειες δεύτερης τάξης στον τρισδιάστατο ευκλείδειο χώρο (Ελλειψοειδές, μονόχωνο και δίχωνο υπερβολοειδές, παραβολοειδή, κύλινδροι, κώνοι, αναγνώριση επιφάνειας, εφαπτόμενο επίπεδο).

Topology of Metric Spaces

Basic notions of the Set Theory - Metric spaces - Topology of metric spaces - Convergence of sequences - Continuous functions - Compactness and Connectedness of metric spaces.

Calculus III

Functions of several variables - Limits and continuity - Partial derivatives - Differentiation of scalar and vector functions - The chain rule - Higher order partial derivatives - Directional derivatives - Taylor’s formula - Extremes of real valued functions - Lagrange multipliers - The implicit function theorem and the inverse function theorem.

Algebraic Structures I

Groups, subgroups, group generated by set- Homeomorphisms of groups- Lagrange’s theorem- Order of a group element- Euler’s theorem, Fermat’s theorem- Normal subgroups- Isomorphism theorems- Cyclic groups and their classification – Action of a group on a set- Permutation groups- Dihedral groups- Direct sums of groups.

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