Some of you may have noticed that the PMATH 365 notes for this week (the week of 2013-03-11) mostly have not been posted. I am currently in the process of transcribing these notes from photos of the blackboards I took in class (since my laptop’s battery died numerous times). With the recent introduction of tensor fields and the accompanying wonderful notation, I am sure everyone can appreciate how disgusting this task is, so please be patient.
I highly suggest reading John Lee’s book Introduction to Smooth Manifolds (the 2012 edition, which for UW students is legally available for free online through Springer). It seems the course is being taught almost verbatim from this book despite the official textbook being the first volume of Spivak’s A Comprehensive Introduction to Differential Geometry. Although I make sure to keep my notes complete, the sheer volume of formulas in this course is making it difficult to keep them clean and legible, so reading Lee will probably leave you much less confused.