Dror Bar-Natan: Classes: 2002-03: Math 157 - Analysis I: (134) Next: Term Exam 2 Previous: Class Notes for the Week of November 25 (8 of 8)

# About the Second Term Exam

Our second term exam will look a lot like the first, but notice the following:
• The material for the second exam is all of chapters 7 through 12 of Spivak's book ("Three Hard Theorems" through "Inverse Functions"). Unlike what I said before to some students, the material in chapters 1-6 is not officially included, though, of course, what chance have you got answering questions about the continuity of inverse functions (say), if you aren't yet absolutely fluent with the notion of continuity?
• Some of the questions may have a part in which you will be required to reproduce an example or a definition or a proof given in full in the class or in the text. The class material is important; I put proofs on the blackboard because I really want you to understand them. Doing lots of exercises is great, but the most important exercises are the ones that are called "theorems" and are shown in class; that's precisely why they are shown in class. You may want to prepare a list of all topics touched in class (you may reach 50 or even 100), and you may want to go over this list several times until you are sure you understand everything in full.
• Remember, you really understand a mathematical definition / theorem / claim / lemma / anything only when you have fully internalized it and made it your own. Check if you can say to yourself one of the following:
1. "Gosh this is so right. I would have done it in just the same way" (sometimes add: "if I was a little smarter when the issue first came up").
2. "Hey, I can do it better! Here's how...".
It's worthwhile! Your grades will be higher, you will have gained more from this (and other) classes, and there is a lot of satisfaction and joy when you succeed. I internalized this sometime in my second year as an undergrad and it was the most important thing I learned that year.

self-portrait by ZS

• I will not distribute a "Sample Exam" this time, but for what it's worth, here's last year's second term exam(s): LastYear.pdf, LastYearMakeup.pdf.
• I'd be very happy to post the solutions of homework assignments 5 through 11 on this web site, provided people who got good grades will allow me to scan their solutions!