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Just a list of miscellaneous math links that are interesting to me.
Papers by Paul Erdős. In particular, this website has the series of papers which gave rise to the theory of random graphs.
M.E.J. Newman "The structure and function of complex networks" A great review of large complex networks and how random graphs are used to model them.
Some open problems:
Kahn-Kalai conjecture: The threshold of G(n,p) containing some n-vertex graph can occur at most a factor of log n later than the "expectation" threshold. See here for the complete statement of the problem.
Hadwiger-Nelson problem. How many colors do you need to color the plane so that no two points of distance 1 from each other have the same color? The exact number is unknown but it is relatively easy to see that it must be one of 4, 5, 6 or 7.
If R(k,k) is the k'th Ramsey number, then does R(k,k)^(1/k) exist?