I also posted Homework 12 solutions. At this point, I don't know if I'll be posting HW 11 solutions.
And finally: HAPPY HOLIDAYS AND HAVE A WONDERFUL WINTER BREAK!
A few words about the final exam. It will be take-home and there will be six problems on it. I am planning to assign it on the last day of class, December 8 and give you about a week to do it. If this date doesn't work for you, please let me know ASAP.
Contrary to what I may have said, we will have one more furlough day this semester: November 5 (Thursday). There will be no class that day. This is the day I will assign (take-home) Midterm 2, so you will at least get some extra time to do it.
And lastly, I will have extra office hours next Wednesday, October 28, from 12 to 1 PM.
My plan is to summarize and finish the topology part of the course (i.e., the notions of connectedness and compactness of subsets of Euclidean space) this week. I will not talk about general topological and metric spaces, although I encourage you to read about them in Fleming.
In case you thought topology is just an abstract branch of mathematics with no applications, check out this aricle. In fact, topology has many applications to diverse fields as physics, robotics, chemistry, and many others. (Though as it always goes, topology was originally invented/discovered to solve "internal", or "pure", mathematical problems.)
Tomorrow, September 8 (due to a specialist exam I'm giving), my office hours will be from 1:30 to 2:30. Sorry for the inconvenience.
For grading the homework I will use the rewrite system. This means that after I grade your homework, you will be allowed to revise and rewrite it based on my comments and suggestions. The revised homework is always due the first class session after you receive your homework back. The revised assignment will then be regraded and the score you receive will be the score I will use for your final grade. However, there is one basic rule: you have to try to solve every assigned problem the first time around (which means you have to write down your attempt at a solution), otherwise you will not be allowed to do a rewrite of that problem.
And last but not least, Homework 1 has been posted and is due on Tuesday, September 1. In the future, homework will usually be due on Thursdays.
This material is rather challenging. I am happy to report that in spite of the challenging nature of the material many of our undergraduates have been equal to the task of dealing well with it. You should not take this course unless you have had prior experience with proving things and with mathematical abstraction. We don't have higher level honors courses but if we did these courses would be among them. It is also absolutely necessary for more advanced work in mathematics and can come in handy in other branches of science and engineering.
In previous calculus courses you learned to differentiate and integrate functions of one or more real variable and to apply these techniques to solve problems of various sorts. You probably didn't pay may attention to mathematical rigor. In fact, when you studied things like integration formulae in several variables you probably didn't pay much attention to intellectual rigor either. I assume that part of the reason you are taking this course is to get all that stuff straight.