Mathematics: Best Sets of Lecture Notes and Articles by Alex Youcis.
From the post:
Let me start by apologizing if there is another thread on math.se that subsumes this.
I was updating my answer to the question here during which I made the claim that “I spend a lot of time sifting through books to find [the best source]”. It strikes me now that while I love books (I really do) I often find that I learn best from sets of lecture notes and short articles. There are three particular reasons that make me feel this way.
1.Lecture notes and articles often times take on a very delightful informal approach. They generally take time to bring to the reader’s attention some interesting side fact that would normally be left out of a standard textbook (lest it be too big). Lecture notes and articles are where one generally picks up on historical context, overarching themes (the “birds eye view”), and neat interrelations between subjects.
2.It is the informality that often allows writers of lecture notes or expository articles to mention some “trivial fact” that every textbook leaves out. Whenever I have one of those moments where a definition just doesn’t make sense, or a theorem just doesn’t seem right it’s invariably a set of lecture notes that sets everything straight for me. People tend to be more honest in lecture notes, to admit that a certain definition or idea confused them when they first learned it, and to take the time to help you understand what finally enabled them to make the jump.
3.Often times books are very outdated. It takes a long time to write a book, to polish it to the point where it is ready for publication. Notes often times are closer to the heart of research, closer to how things are learned in the modern sense.
It is because of reasons like this that I find myself more and more carrying around a big thick manila folder full of stapled together articles and why I keep making trips to Staples to get the latest set of notes bound.
So, if anyone knows of any set of lecture notes, or any expository articles that fit the above criteria, please do share!
I’ll start:
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Fascinating collections of lecture notes and articles, in no particular order with duplication virtually guaranteed. Still, as a browsing resource or if you want to clean it up for others, it is a great resource.
Enjoy!