Introduction to basic problems, sums and recurrences, elementary number theory, properties of binomial coefficients, special numbers, discrete probability theory, generating functions.
Riemann integration, fundamental theorem of calculus, techniques and applications of integration, improper integrals, basic transcendental functions, infinite series, convergence tests, Taylor polynomials, power series.
Fundamental properties of real numbers, sequences and subsequences, Bolzano-Weierstrass theorem, limits of functions, continuity, intermediate and extreme value theorems, differentiation and its applications, mean value theorems.
Propositional logic, quantification, methods of proof, sets, relations, functions and operations, equivalence relations, cardinality, introduction to algebraic structures.
Systems of linear equations and inequalities, matrices, determinants, inverses, Gaussian elimination, geometric approach to linear programming, basic combinatorics, binomial theorem, finite probability theory, conditional probability, Bayes' theorem, random variables, expected value, variance, decision theory.
Vector calculus, functions of several variables, directional derivatives, gradient, Lagrange multipliers, multiple integrals and applications, change of variables, coordinate systems, line integrals, Green's theorem and its applications.
Functions, limits, continuity, differentiation and applications, integration, fundamental theorem of calculus, techniques and applications of integration, improper integrals and series, Taylor polynomials, power series, basic transcendental functions.
*Private Law Legal Entities: Associations, foundations and a brief explanation on partnerships and stock companies.
*Public Law Legal Entities: State-concept of the rule of law and dignity of man; sovereignty of the state, legislative power and duties, executive power and duties, judicial power, equality before law, fundamental rights and liberties, social-economic rights and duties; liability of the state, jurisdiction of the state, treaties, disputes between states. State economic enterprises.
Social relations and law; different legal systems (common law-equity and European Law); branches of law (public law-private law); source of law; application of law and interpretation; rights (acquisition of right and bona fides; exercise of rights and good faith); capacity; mentally disordered persons and minors. Personal status; domicile.
Aims to acquaint students with computers as tools of information processing. General headings include: concepts of information processing; components of computers: hardware and software; overview of software types: spreadsheets, word processors, databases; exercises with application programs.