Reddit mentions of An Invitation to Modern Number Theory

I like An Invitation to Modern Number Theory. A little less readable (imo) but Diaconus had a pretty good article that he published a while ago.

I'm no expert, but from what I understand, Random Matrix Theory is primarily concerned with the eigenvalues matrices whose entries are drawn from some distribution. For many 'natural' distributions, you find that the eigenvalues follow a sem-circlular-law. The five-second explanation of this is that, since eigenvalues are the roots of the characteristic polynomial of your random matrix, and you're in some sense drawing random characteristic polynomials, roots of said polynomial tend to 'repel'. How they repel, what that looks like, etc. etc. is the basic gist of a lot of this work.