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Graph Theory and Applications

The graph theory was born with the intelligent observation of the mathematician Euler about the impossibility of all the bridges of the city of Königsberg only once. In this course we propose the study of complicated problems in industry and network theory using the techniques of graph theory.


Part 1

  1. Sparse and nowhere dense graphs.

  2. Examples, Duality with dense graphs, algorithms, logical characterization. Introduction to network theory.


Part 2

  1. Linear systems

  2. Matrix algebra, convex optimization, linear regression, linear dynamic systems.

Part 3

  1. Dynamic systems and probability

  2. Basic probability theory, dynamic systems and probability, discrete stochastic processes.

  3. Entropy

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