This will be my final post associated with the Analysis I course, for which the last lecture was yesterday. It’s possible that I’ll write further relevant posts in the nearish future, but it’s also possible that I won’t. This one is a short one to draw attention to other material that can be found on the web that may help you to learn the course material. It will be an incomplete list: further suggestions would be welcome in the comments below.
A good way to test your basic knowledge of (some of) the course would be to do a short multiple-choice quiz devised by Vicky Neale. If you don’t get the right answer first time for every question, then it will give you an idea of the areas of the course that need attention.
Terence Tao has also created a number of multiple-choice quizzes, some of which are relevant to the course. They can be found on this page. The quiz on continuity expects you to know the definitions of adherent points and limit points, which I did not discuss in lectures.
The first five posts on this blog in the IA Analysis category are devoted to the questions on this course in the 2003 Tripos. The course has not changed much since then, so these questions are similar to the kind of thing that could be set now. I try to say not just what the answers are but how I thought of them, how I decided what to write out in detail and what just to assume, and so on. They may be of some use when you prepare for the exams.
A long time ago I wrote a number of informal discussions of undergraduate mathematical topics. My ideas about some of these are not always identical to what they were then, but again you may find some of them helpful, particularly the ones on analysis.
If I think of further resources, I’ll add them to the post.
Finally, I’ve very much enjoyed giving this course — thanks for being a great audience (if that’s the right word).