# Syllabus for Math 491 - Real Analysis II

Professor: Mark McClure

## Course purpose

• To finish up a few things from Real I
• To have fun!

• Paper
• Pencil
• Brain
• Text

## Evaluation

• Presentation: You will earn up to 100 points for teaching one class this semester. We have a handout with detailed information.
• Exams: There will be two exams during the semester worth about 100 points apiece. Likely dates for the exams are:
• Wednesday, February 24
• Wednesday, April 20
• Quizzes: There will be two quizzes each two weeks ahead of an exam:
• Wednesday, February 10
• Wednesday, April 6
• Final exam: There is a final exam scheduled for 8:00 AM on Friday, April 29.
• Discourse: You can earn up to 20 points by participating in our online discussion forum.
• Homework: I will collect and grade some homework.
• Late work: In general, I don't accept late work.
• Cheating: I don't deal with cheating. If I suspect cheating strongly enough, I simply refer you to the provost and fail you for the class.

## A bit more on grades

The standard 90-80-70-60 scale will guarantee you an A, B, C, or D. However, it is quite likely that the final scale will be shifted down from this. I cannot give you an exact scale now, since your score will be somewhat influenced by your relative standing in the class; i.e. if Bob has fewer points than Alice, then his grade will certainly not exceed Alice's. I can, however, let you know what skills I believe will merit certain grades.

• To pass this class you must (at a minimum) know the basic definitions and theorems (e.g. continuity, differentiability, IVT, MVT), be able to apply those definitions and theorems to solve some simple problems (e.g. use IVT to approximate polynomial roots), and be able to prove some of the basic results (e.g. that differentiability implies continuity).
• The conditions to earn a C are somewhat similar. However, I would expect you to know {\em most} of the theorems and definitions we encounter and be able to apply them to problem solving and in well written proofs. Some examples of topics I would want the C student to be comfortable with, but not necessarily the D student, include suprema and infima, subsequences, topology, continuity of derivatives, and rearrangements of series. (Note: I don't mean to imply that you don't need to know about these topics to pass. I'm simply saying that I expect the C student to be comfortable with the intricacies of these topics, whereas the D student might not be.)
• To earn a B in this class you must be able to state, apply, and possibly prove virtually all of the basic definitions and theorems, be creative enough to solve new and interesting problems, and consistently write mathematics well.
• In addition to the requirements for a B student, the A student will successfully struggle with some very challenging problems. By "successfully struggle with", I mean that the student will spend some (probably significant) time with the problem, find the crux of the solution, and write a beautifully well written solution or proof to the problem.