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Hello! My name is Muireann, pronounced like Marin County with a soft ending, I'm an exchange student from Ireland! I grew up and live in Cork and study in the University there (UCC). I'm a double major in Mathematical Sciences and Physics.
I began university thinking I'd only like Algebra and Applied Maths but have found interest in subjects like analysis. I took Complex Analysis M185 last semester. I'm really liking the approach to this class so far it is very different to anything I've taken before, so I am really looking forward to it.
My other interests are music and sport. I play piano and saxophone, I teach piano at home and currently trying to teach myself the trumpet. I also ran the half marathon across the golden gate last November!
Class Notes Class Notes will be uploaded in a pdf format
Homework Problems Homework will be uploaded here in a pdf format
Interesting Links / Problems
Here I will post any useful links or resources I find myself using. As well as any interesting problems I have that a class mate could shed some light on.
HW4 Lebesgue Integral summary Up until now we had only been solving Reimann Integral. The Lebesgue integral is in some sense a generalization of the Riemann integral. This was only possible with 'Reimann Integrable' functions, i.e not all functions could be integrated. A classic example is f(x) = 1, x is a rational number and zero otherwise on the interval [0,1].
Definition: (Tao) The Lebesgue Integral of simple functions Let
