Source: Brandon Haun website, Jul 2015
1) I’ll start with a basic discussion of symmetry. To ground ourselves, we’ll study wallpapers and arrive at the notion of a ‘group’ in trying to capture our analysis mathematically.
2) We’ll leap over to the more technical, but (with a little bit of perspiration) just as pretty world of number theory and modular forms. I’m of the opinion that most mathematicians that work with these objects probably couldn’t explain to you in any intuitive sense why we should care about them or why they show up in math and physics. Because I am no better, I’ll perhaps only spend enough time here to convince you that modular forms are special, which will make their reappearance later all the more shocking.
3) We’ll finally be ready for our first glimpse at a bit of mathematical moonshine, but we’ll postpone the full discussion, which includes ideas from physics, until the next blog post.