Hello, my name is Andrew Oldham and I am a propspective PhD student in Pure Mathematics. I studied in Manchester at Manchester Metropolitan University for my Bachelors degree in Mathematics where I obtained a First Class degree and I have also studied at the University of Nottingham where I studied a Msc in Industrial Mathematics and Scientific Computation where I obtained a Merit. During my undergraduate degree I introduced myself to Pure Mathematics through a Real Analysis textbook, which I read in it's entirety along side studying for my degree. My undergraduate degree did not cover much mathematics via rigorous proof so I am covering the holes in my backrgound in preparation for the PhD (and beyond). I shall record my progress on this website uploading my LaTeX proofs to textbook exercises as I read through books. I will answer or attempt to solve each exercise in the books that I read. Listed below are the books that I have read so far with links to Latex proofs of the exercises.