Γενικά Μαθηματιικά Ι - Τμήμα Γεωλογίας

Πίνακες (πράξεις, ιδιότητες), ορίζουσες (ιδιότητες), αντίστροφος πίνακα, βαθμίδα πίνακα (rank), διερεύνηση και επίλυση γραμμικών συστημάτων. Αναλυτική Γεωμετρία (εξίσωση ευθείας και επιπέδου, εξίσωση κύκλου κλπ.) κυλινδρικές και κωνικές επιφάνειες. Συναρτήσεις μίας μεταβλητής. Σειρές Taylor-Maclaurin, γραφική παράσταση. Ολοκληρώματα. Συναρτήσεις πολλών μεταβλητών (όριο, συνέχεια κλπ.), διπλά και τριπλά ολοκληρώματα.

Theoretical Informatics

Sets, relations, algorithms. Analysis of algorithms. Alphabets, languages and regular languages. Finite automata: deterministic, non-deterministic and equivalence. Finite automata and regular expressions. Decidability results.

Introduction to Computer Programming

Computer hardware - Computer software - Programming languages - An introduction to problem solving with Fortran 90/95 - The structure of a program in Fortran 90/95 - Simple input and output - Control structures (if, select case, D0-End do) – Array processing (one dimensional and multidimensional matrices) - Functions - Subroutines - Modules - IMSL libraries - File organization (sequential files, direct access files) - Applications to mathematical problems.

Introduction to Algebra

Elements of set theory (sets - functions - relations - equivalence relations -partial ordering on sets - nets) Natural numbers and Integers (mathematical induction -Zorn’s lemma - natural numbers - cardinality of sets - axiom of choice) - Elements of group theory (groups - subgroups - group generated by set - cossets - normal subgroups -isomorphism theorems - cyclic groups - groups acting on sets - direct product of groups).

Calcuslus I

Basic notions - Sequences and series of real numbers - Power series - Real functions - Limits - Continuity - The Derivative - Applications of the derivative - Taylor series - Study of functions.

Linear Algebra I

Vector spaces - Finite dimensional vector spaces - Matrices - Determinants - Matrices and Linear Transformations.

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