Some reasons to teach lattice theory to undergraduates

First-year students in mathematics and computer science are often troubled with the Schröder-Bernstein theorem, which proves that the natural ordering between cardinal numbers is in fact a partial order, but has a lengthy and convoluted proof. A more accurate study of order structures (often neglected by basic course) would, however, allow to see this fact as an almost immediate consequence of a much simpler, and very powerful, theorem due to Bronislaw Knaster and Alfred Tarski. Continue reading

A stupidly easy way to hack into computers

Do you have a SSH server running somewhere? Have you ever wondered why it gets hammered by brute-force password guess attacks all the time? My server got 4669 login attempts on 2013-01-12. Have you ever wondered what these guys do if they actually manage to get into your server? Have you ever wondered which passwords actually get tried, in order not to use them yourself?

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