I am glad that I decided to do M381 this year. ( Plans are M381 / M373 this year and MST209 / M336 next year. ) I am looking forward to Book 2 of M373: Linear Programming using the Simplex Method. And about the Logic part of M381 I can only say that it would be nice to finally understand Godel, Escher and Bach ( re-read perhaps ) as it leads up to understanding Godel's incompleteness theorems.
Number Theory is what truly fascinates me about maths. Because it is deep, I suppose. Numbers are everywhere. Numbers are universal. As in universe-al perhaps ( ... ). Imagine an intelligent civilization on a distant planet in the universe. If they are intelligent than they must have numbers and thus prime numbers. The movie 'Contact' based on the book of Carl Sagan was about how we would establish contact with extra-terrestrial life. Almost inevitably prime numbers are involved. There is a short paper written by a number theorist that explains how this communication might work, 'Prime numbers and the search for E.T.' ( pdf )
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