Ramanujan Graphs: Generating Functions and Expander Graphs

Related lectures (28)

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Covers the analysis of functions, composition, and mathematical induction.

Focuses on open problems and the importance of reformulating problems with better tools and intuition.

Covers the Poisson Paradigm, including the First/Second Moment Method and Martingales, discussing dependency graphs and Chernoff bounds.

Covers Dijkstra's algorithm and its application to the all-pairs shortest path problem.

Explores the Ford Fulkerson algorithm, Max-Flow Min-Cut theorem, Incidence matrix, and network optimization complexity.

Explores Markov's theorem, Chernoff bound, and probability theory fundamentals, including good coloring, 2-colorable graphs, and rare events.

Covers the basics of computational complexity, including big O notation and complexity classes.

Covers thermodynamic concepts and exam questions from 2012, 2013, and 2015.

Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

Explores the FKG inequality in percolation theory and the reverse FKG theorem.