MASTER OF SCIENCE Computational Mathematics and Modern Information Technologies

Entity-Relationship Data Model: Data structuring, Entity-Relationship Diagrams, Equivalence of EntityRelationship and the Functional Modeling, Algorithms for translating Entity-Relationship Diagrams into Relational and Elementary Mathematical Data Models. Relational Data Model: The structure of the Relational Data Model, Relational Algebra, Relational Calculus, Relational Query Languages, Static Analysis and Optimization, The Theory of Elementary Dependencies, Algorithms for translating Relational schemes into the Elementary Mathematical Data Model. Logic Data Models: Databases and Knowledge Bases, Mathematical Logic, Deductive Databases, Nonrecursive Datalog with Negation, Datalog Model-Theoretic and Fixpoint Semantics. Elementary Mathematical Data Model (EMDM): EMDM Schemes, Constraints, Algorithms for translating EMDM schemes into Entity-Relationship Diagrams and Relational schemes, Modeling Closed Entity-Relationship Diagrams, Equivalence Theorems. Complexity: Complexity of queries, Languages and Complexity, The Complexity of Nulls. Applications: Conceptual design of any Database Management System. Bibliography [1] Abiteboul S., Hull R., Vianu V.: Foundations of Databases: The logical level, Addison Wesley (1994) [2] Thalheim,B.: Entity-Relationship Modeling. Foundations of Database Technology. Springer-Verlag (2000) [3] Mancas C.: Databases and Data Structures: Volume I: Conceptual Data Modeling And Querying. Ovidius University Press (2005, in press) [4] Mancas C.: Databases and Data Structures: Volume II: The Relational Data Model. Ovidius University Press (2005, in press)