Section 1, 18.100B, Analysis I, Fall 2010.
Lecturer: Richard Melrose.
Lectures: 9:30-11:00, Tuesdays and Thursdays in 4-237

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Analysis 1, 18.100*

RBM Office hour:W 9:30AM-11AM in Room 2-174

You can ask me about the lectures (you can do that during lectures too of course) or about the homework or we can talk about something even more interesting. You are welcome to email me questions -- to rbm at math dot mit dot edu -- and you will likely get an answer!

Grader

Weixuan Lu who also will hold an Office Hour: W 4-5 in Room 2-085

Classes: T/R 9:30-11 in Room 4-237

Text and aim of the course

Walter Rudin: Principles of Analysis. Due to the idiotic copyright laws a new version costs a bundle. You should be able to pick up a second-hand copy for much less -- or there are `international editions' of unknown (to me) legality for even less. You can also probably find scanned copies, but I would guess that these are simply illegal.
The book itself you might find hard reading since it is very much the opposite of a bloated calculus textbook. Don't worry if you need to spend several hours on a page! Apart from going through most of one-variable calculus rigorously, a primary aim of the course is to ensure that students can write clearly and concisely. In particular it is not enough to blunder across `the correct answer', it is just as important to understand why things are true. See the comments on final grades below.
Beyond calculus of one variable -- functions, differentiability and (Riemann) integrability -- we will talk about metric spaces. These are a very important class of topological spaces -- so the notion of continuity is defined for maps between metric spaces -- which are important in many areas of mathematics. The course is intended as a gateway to other undergraduate and hence to graduate courses. After taking this course you can take for instance 101, 102, 103, 112, 701, 901.

Homework and Tests

Homework will be due on Thursdays. Paper homework must be put in the tray in 2-108, marked 18.100B Melrose, by 11AM on Thursdays -- or given to me in lecture -- since I will pick it up after the lecture. No late paper homework will be accepted. Either TeX output or scanned-to-pdf files can be emailed to me (and only me, not the grader) at rbm at math dot mit dot edu any time up to 5PM on the Thursday on which it is due. Late homework will be accepted in electronic form only -- so it is late if it arrives after 5PM -- it will be graded but marks will be deducted according to a scheme that will remain private.
Solutions will be posted on Thursday evenings.
About collaboration etc. I don't much mind how you go about learning and doing the homework is supposed to be part of that, but I draw the line somewhere short of copying from someone, or somewhere, else. It is fine if someone explains it to you, or if you read someone else's solutions, but you should produce your own version.

Lecture contents (last modified 3 November)

Final Grades

Final grades for 18.100B, for people in Section 1, will be computed in two distinct ways and the actual grade will be the better of the two. I do not suggest relying on the second method! Final grades for 18.100C are computed based on required attendence at the weekly `recitation' and given that, the 18.100B component forms 80% of the total. Meaning of grades: I have found the only really hard separating lines to draw are usually A+/A and A-/B+. I don't mind if every one gets an A+ since they will have earned it.