Budapest has some universities that offer Master's level Numerical Analysis courses in English (e.g. If there are no other (say, financial) obstacles, you certainly should not forgo the opportunity over silly Numerical Analysis worries.Īnd if you're absolutely hell-bent on taking Numerical Analysis, there's another option. I encourage you to attend BSM if at all possible. In fact, the BSM experience will probably look better on your application than any number of numerical analysis classes taken at your home institution. Egerváry's algorithm (the “Hungarian method”) for the optimum assignment problem.The combinatorics you inevitably pick up during the BSM is looked upon very favorably in some fields of applied mathematics. Applications: the minimum cost integer flow problem, the optimum assignment problem. Integer programming with a totally unimodular coefficient matrix. The branch and bound method for integer programming. Applications: the Ford-Fulkerson theorem for the maximum flow problem the minimum cost flow and the multi-commodity flow problems two-player, zero sum games. Algorithmic complexity of the linear and integer programming problems. The duality theorem of linear programming. The concept of duality in linear programming. Boundedness of the objective function of a linear program.
A necessary and sufficient condition for the solvability of systems of linear inequalities: the Farkas-lemma.
Solving systems of linear inequalities with the Fourier-Motzkin elimination. Linear algebra revision: fundamental operations on matrices, determinants. Solving IP problems with Microsoft Excel. Using decision variables, incorporating logical constraints. Modeling practical problems as IP instances. Solving LP problems with Microsoft Excel. Modeling practical problems as multivariable LP instances. Graphical solution for two-variable problems. The maximum network flow problem, the Ford-Fulkerson algorithm. Matchings in bipartite graphs, the augmenting path algorithm. Related technologies: decision support systems, rule-based languages. Semantic aspects of Enterprise Application Integration. Declarative technologies and parallel/multi-core computing. Application areas of declarative programming. Major implementations of declarative languages. W14: Declarative and Semantic technologies – an outlook. The underlying reasoning algorithms – a brief overview. W13: Building and using ontologies The Protégé ontology editor, its user interface and services. Property axioms: subproperties, equivalent and inverse properties. Class axioms: subclasses, equivalence and disjointness. Constructs for building classes: property restriction, intersection, union, complement. A hierarchy of DL languages: AL, ALC, SHIQ, SROIQ and beyond. The main building stones of DLs: concepts and roles. Terminological and assertional knowledge: the TBox and the ABox. The RDF Schema: classes, properties, hierarchies, restrictions. W10: Advanced RDF constructs: reification, containers, collections. The basics of Resource Description Framework (RDF): Uniform Resource Identifiers (URIs), triples, notational variants. A roadmap from the today's internet to the Semantic Web. Basic technologies of the today's web: HTML, XML. Practical applications of the constraint technology – highlights. W8: Reified constraints, domain- and bound-entailment. Labeling options: variable/value selection, direction, user-defined labeling. W7: The CLP(FD) library: arithmetic and membership constraints. The background of finite domain constraint solving: Constraint Satisfaction Problems. Constraint Logic Programming (CLP) – basic principles. W6: An overview of SICStus Prolog libraries. W5: An overview of built-in predicate groups. Transforming an algorithm with mutable variables to Prolog. W4: Efficient programming in Prolog: the cut predicate. Basic list handling predicates: append, naïve and efficient reverse, member, select. Execution models for Prolog: goal reduction and procedure-box. W2: Advanced Prolog control constructs: disjunction, negation, if-then-else. Simple Prolog programs: declarative reading and procedural execution. Basic constructs of the Prolog language: clauses, variables, constants. Imperative and declarative programming, a comparison.
Semantic and declarative technologies, an overview. W1: Background: propositional and first order logic.
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