This is an archived website for MA74 from Fall 2006. Below are some links to class handouts, exams, etc.
I plan to run the course a bit differently during Spring 2007, so do not mistake this as a reference for current announcements. The assignments and exams varied considerably in difficulty, so keep in mind that the numeric scoring varied appropriately. For general reference, an overall raw score of 75% was enough to earn an 'A.'

A Practice Exam

Second Exam

Third Exam

Final Exam Questions

Long rambling notes from mid semester, mostly about functions, these are really bad and will be edited

Notes on products and relations, not quite as bad, and last HW assignment

Quiz 1

Quiz 2

Quiz 3

Quiz 4

Quiz 5

Long Quiz

Long Quiz, the legend continues

Last Quiz

MA74 Syllabus, Fall 2006, section 2, UC Berkeley

Where and When: T-Th, 3:30-5:00, 70 Evans

Textbook: The Nuts and Bolts of Proofs, by Antonella Cupillari. Other assorted readings will be assigned periodically, via handouts or weblinks.

Grading: We will have three midterms, on 9/19, 10/24, and 11/21 (all Tuesdays). They are worth 10%, 15%, and 20% of your final raw score, respectively. Rather than plan ahead as if I know for certain exactly what topics will be covered on each test, I will just promise you a review guide (usually in the form of 'bullet points') at least one week prior to each test, which will outline exactly what you will be responsible for.

On Tuesdays when we don't have a midterm, we will have a quiz. Your cumulative quiz and homework score will be worth 20% of your final raw score. The specifics of how these will be graded will vary from quiz to quiz and assignment to assignment. I reserve the right to spontaneously assign (or not assign) homework (including reading). However, everything will be posted online as the semester moves along. Consider the announcements on my website to be 'official,' if they differ from what you recall from lecture.

The final exam is Tuesday 12/19, from 12:30-3:30, and it is worth 35%. In summary, we have:

10%-15%-20% for M1-M2-M3
20% for HW and quizzes
35% final exam

In the end I expect there will be a curve, meaning that I will decide the grade cutoffs based on how the semester goes. However, I minimally guarantee a '10-point curve.' This means I will only possibly revise the 90-80-70-60 letter grade cutoffs downward. My prediction is that the final cutoffs will be closer to a 15 point curve, but the whole reason for having a curve is because I honestly don't know yet.

Policies: Somewhere out there is an official University policy for everything, such as DSP, athletic competitions, legitimate absence due to illness, etc. It is your responsibility to be aware of such policies and plan accordingly. In general, if you come to me before an assignment is due, then I will be happy to make any reasonable accomodations, even last minute if necessary. However, absolutely no late anything is accepted, ever, no make up exams, etc., without prior notice. Do not even request it. You are enrolled in this class and are fully aware of requirements and dates; part of the reason for putting things online is to make this easier on you. If you come to me with a lame request after you have missed something, I will most likely make you feel stupid and then turn you away. (Consider this further preparation for your transition to upper division math.)

Comments: Roughly, we will cover basic material essential to understanding mathematical rigor, followed by more of the same, and ending with still more of the same.

What I am really getting at is this: It is pointless to try to list a schedule of topics ahead of time, since their choice will depend almost entirely on the pace and understanding of the class as a whole. I am predetermining that the specific mathematical content will be flexible, and in fact I invite comments and suggestions along these lines. The goal is, at the end of the semester, for you to be able to read and communicate mathematics at the level demanded of upper division classes here at UCB. I do not pretend as if I have some surefire outline for accomplishing this goal, but I sincerely guarantee my energy and assistance in helping you achieve it.

Some things are certain however. One is that, for the most part, your written work will be the basis of how you are evaluated as a mathematician. Of course, this means that it must be logical, clear, concise, etc. but most importantly it must communicate an autonomous and logically sound statement. In other words, what you write, in response to a question, must be readable and understandable by someone external to the situation, who is familiar with basic definitions and notation. Further, it must rest on proper mathematical reasoning, in the appropriate context. In the event of a gap or flaw in a solution, it is also your responsibility to acknowledge the full extent of the missing content. Any efforts to the contrary are intellectually dishonest.

In other words, mathematics is no longer a game between teacher and student, where you try to solve as many problems as fast as you can without sincere regard for accuracy. In proof based mathematics, it is a serious mistake to communicate a solution that you erroneously believe to be correct. This is much worse than communicating the far more intelligent and accurate 'I don't know.' A mathematician would never guess and try to pass his guess along as if it were a verified mathematical fact. (That is why we qualify our statements with a variety of words, e.g. 'conjecture' vs. 'theorem' vs. 'definition.')

Rather, it is important to scrutinize your work in search of mistakes that you missed, and to be the foremost skeptic with regard to your own arguments. Anything less is irresponsible. Honest mistakes are inevitable anyway, so do not complicate things by presenting arguments that you knowingly suspect are mistaken. If you are guessing, acknowledge that you are guessing, and if you know that you are wrong, say so. If there is one thing you can truly learn and benefit from in this course, it is how to go about the aforementioned scrutiny, not only in your mathematical thinking and writing, but in every aspect of your academics.