Βιβλίο θεωρίας γραφημάτων και μαθηματικής λογικής από το ανοικτό πανεπιστήμιο,

This a very brief introduction to Graph Theory in 29 slides.

This is the home page for a series of short interactive tutorials introducing the basic concepts of graph theory. There is not a great deal of theory here, we will just teach you enough to wet your appetite for more!

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

Τα πολύ βασικά μέρη της θεωρίας Γραφημάτων χώρις σε πρόχειρες σημειώσεις.

Contents: Introduction; General Markov Chains; Reversible Markov Chains; Hitting and Convergence Time, and Flow Rate, Parameters for Reversible Markov Chains; coupling theory and examples; Special Graphs and Trees; Cover Times; Symmetric Graphs and Chains; Advanced L^2 Techniques for Bounding Mixing Times; A Second Look at General Markov Chains; Some Graph Theory and Randomized Algorithms; Continuous State, Infinite State and Random Environment; Interacting Particles on Finite Graphs; Markov Chain Monte Carlo.