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Random Matrix Theory (RMT) is a vibrant area of research in mathematical physics at the intersection of analysis/probability, operator theory, statistics, combinatorics, number theory, quantum chaos to name only a few of a growing list of related areas.

In this talk I will try give a "graduate student introduction" to RMT by deriving the limiting probability distribution of the largest eigenvalue in the the Gaussian Unitary Ensemble (GUE) in so-called edge-scaling limit (this one of the Tracy-Widom distributions, named after our own Craig Tracy and his collaborator Harold Widom). All the terms used above will be explained. If time permits I will introduce some related results that Prof. Tracy and I proved recently.