What to do? Write a short summary in your own words of the principal ideas and concepts discussed in the course during the quarter. For each concept, you should include, if appropriate, (a) an intuitive discussion of what the concept "means", (b) a formal definition if it is different, and (c) important rules or theorems we developed to deal with the concept. You may want to illustrate some of the concepts with examples. Don't include proofs.
Format. The summary should be written in complete sentences and paragraphs, with formulas to make ideas clearer---just like the textbook in style, but in your own words. But it should be no longer than five pages (a good job can be even be done in three or four). Please handwrite legibly or type. Use mathematical notation as approproate, and invent notation that you can easily use on your wordprocessor, like LIM f(x) = 0, or df/dx=327 x^15, etc.
Deadline. The final version is due by 5pm on Fri Dec 11 in my mailbox (or earlier, in class). If you wish, you can hand in a full or partial rough draft by Thurs Dec 3. I will comment on it and return it by Tues Dec 8. In fact I strongly encourage you to write a one-page summary of *part* (eg. Chapter 2) of the quarter, and hand that in earlier to get feedback about the style and level of detail.
How to go about it: The tricky part to an assignment like this is choosing what to omit and what to write about in what level of detail. I suggest the following approach: imagine you are talking with a mathematically-minded relative who asks you, "so, what did you do in in calculus this quarter?" How you would answer him/her in just a few sentences? Focus particularly on bringing out linkages behind the various topics we discussed, and don't worry about leaving out details. You don'thave to discuss things in the same order as the book or the class notes---I'm very open as to the structure you want to use for your thoughts, as long as it isn't just a "shopping list" of concepts, without a sense of what leads to what else.
How not to go about it: Don't sit at your desk with the textbook, flipping from section to section and extracting all the important looking formulas and definitions. We'll cover about 3 chapters of the textbook, which is impossible to distill into 5 pages using this technique since everything looks important. Instead write yourself an outline and expand on it iteratively. I AM NOT CONCERNED IF YOU LEAVE OUT SOME MINOR IDEA OR OTHER, just as I am not concerned that you will not remember all of the course next year. Of course, if you leave out 3 weeks worth of material, I will want to know why, and the reason had better be something else than that you didn't understand it too well.
Why am I giving you a paper to write in a math class? First, to help you study for the final. Second, to give you even more practice writing about technical subjects, and in distilling the crucial ideas from a large amount of material. Finally, to try to help you fix important concepts from the course in your mind so that they stick with you longer. This is a core course sequence, and it would be a shame if all that stuck in your mind was a morass of formulas.
What to do if you are really pressed for time. Write a shorter summary. Start with an outline and just expand on it less. Don't save time by starting writing "cold". It will take you longer. I guarantee it. A well thought out and balanced 2 page paper can get a 20/20 grade. A paper that leisurely explores functions in 3 pages and then scrunches everything else into one more page because it's 3am and you still have a Hum paper to finish will get a much worse grade.
The use of formulas in mathematics dates back to the 16th to 18th centuries. Here's a medieval statement about area and circumference of a circle:
Latin: Multiplicatio medietatis diametri in se ejus quod proveniet in quantitatem in quam cum multiplicatus diameter provenit circumferentia aequalis superficies circuli.
Translation: Multiplication of half of the diameter in itself, and of that which results with the quantity, with which if one multiplies the diameter then one obtains the circumference, equals the area of the circle.
Formula: Let pi=C/d. Then A=(d/2)^2*pi. [Here C,d, and A are the circumference, diameter, and area respectively]
Which is clearer?