Instructor: Jessica Sidman
Office: 402a Clapp Lab
Phone: 538-3251
Email: jsidman
Office hours: M 1-2 (special real analysis hour), T 3-4, Th 3-4
Text: Elementary Analysis: The Theory of Calculus, Kenneth A. Ross, 1980, ISBN 0-387-90459-X.
New and used textbooks will be on sale at the Odyssey Bookstore. If you choose to purchase the text from another source it is your responsibility to make sure that you have the correct edition ready for use when classes begin. I think this is the 14th printing of the book. Please try to get a copy that is from the 12th printing or later. (There is a note from the author stating that page numbers changed starting with the 12th printing.)
Why should you care about real analysis?
- Real analysis provides the theoretical underpinnings of calculus and differential equations. To truly understand how these subjects work, you need to understand some real analysis.
- In applications of mathematics, functions are often approximated by series, and a deep understanding of convergence from analysis is important.
- Real analysis is a good subject for building careful, rigorous thinking. Applying these ways of thinking to situations that you are already familiar with from calculus will help you to understand what it means to really understand and know a subject.
What are we going to do in this class?
- The key concept that makes calculus possible is the idea of a limit. We're going to spend a lot of time talking about limits in the context of sequences, series, and functions.
- The functions that we can apply calculus to need to be continuous. We'll discuss continuity from a rigorous point of view to supplement your intuitive graphical understanding.
- We'll discuss differentiation and integration, covering important theorems.
Homework:
- Why do we do it? The point of doing homework should be to aid your understanding of the subject. With that in mind, I would rather having you getting help, from me or a friend, than being frustrated and stuck. Getting help is a valid step in attaining your goal of understanding the material.
- The cover sheet and acknowledgements: Please staple a cover sheet to each homework assignment that you turn
in. You can find links to cover sheets from the daily schedule. Although I
encourage you to receive help, it is important to me that you acknowledge it. You can do this by writing in the names of any sources that you may have turned to for help in the space provided on the cover sheet next to the problem number.
- The rules for what you write: It is very important that you keep your understanding firmly in mind when you write up the homework to turn in. I want you to try as hard as you can to work with the following rules in mind.
- You should carry enough away from your discussion of a problem that you could reconstruct the solution on your own.
- You should truly believe that you understand everything that you write down. Sometimes you will have some ideas in mind, but they may be hazy or some steps will be a little unclear to you. In that case, write up as much as you can, but try to indicate clearly where you are not sure of yourself. This will help me give you feedback that really gets at the places where you need it the most.
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Re-writes: Sometimes, re-writing the solution to a problem can be a real learning experience. However, depending on re-writes too much can lead to disorganization and homework pile-ups. I will allow re-writes on a case-by-case basis, generally only if your original work indicates hard work but is C-grade or lower. I will average the original score with the score from the re-write.
I know that this kind of reflective homework write up is a difficult thing, but developing an accurate sense of when you really do know something is a true sign of intellectual maturity.
Exams: There will be two exams and a final. New exam information: Each of the two exams will have a portion
given in class as well as a take-home portion. The in-class exams are tentatively scheduled for
March 2nd and April 13th.
Grading: Your grade for the course will be determined as follows:
- Classwork (including written homework, short presentations of problems, and possibly quizzes): 30 %
- Exam I: 22%
- Exam II: 23%
- Final: 25%
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