Instructor
John E.
McCarthy
Class
TuTh 1.00-2.30 in 218 Cupples I
Office
105 Cupples I
Office Hours M
2:00-3:00, Th 3:00-4:00, F: 4:00-4:45.
Phone
935-6753
Text Structure and Proof: 4/09/04
Exams There will be two exams in the course:
1) Exam 1 In class, Thursday,
March
4
2) Exam 2 Final exam, on
Tuesday, May
11, 1-3 pm
Homework
There will be weekly homework sets during the semester, handed out on Tuesday in class and due the following Tuesday. Homework Problems
Prerequisites
Calculus III, 233.
Content
The purpose of this course is to teach you how to prove theorems.
Basis for Grading
The midterm will be 20% of your grade, the final and the
homework 40% each.
Homework
Homework is the most important part of the course. Whilst talking
to other people about it is not dis-allowed, too often this
degenerates
into one person solving the problem, and other people copying them
(often justified to themselves by saying "I provide the ideas, X
does
the details" - but the details are the key. If you can't translate
the idea into a real proof, you don't understand the material well
enough).
So I shall introduce the following rules:
(a) You can only talk to some-one else about a problem if you
have made a genuine effort to solve it yourself.
(b) You must write up the solutions on your own. Suspiciously
similar write-ups
will receive 0 points.
Note, too, that a significant part of this course
is learning how to write mathematics. Thus serious attention
will be paid to how the solutions are written up. They should
be written in full English sentences, and it should be clear
what is going on (so, for example, if the argument is lengthy,
dividing the proof into well-marked stages is a good idea).
Faulty logic will be penalised with negative points.
So, if you cannot prove something is true in general, but can do
so if you assume an extra hypothesis, you should say so,
and state the extra hypothesis you need. This will earn partial
credit. But if you claim to prove the result in general, whilst
implicitly assuming this hypothesis, you will lose many points,
and may end up getting less than zero on a problem.
If you really have no idea how to prove something, don't waffle.
If you have an idea that you cannot make into a rigourous proof,
say
"This is an idea, but I cannot make it into a rigourous proof".
I do expect you to come to class every day, and to participate in class discussions. I also expect you to stay abreast of the material we are covering, and may call on you at any time to answer a question.
Web Pages
The following web page may give some interesting sidelights on the material.
The MacTutor History of Mathematics Archive
Bibliography
The following is a brief bibliography you may find useful.
S.G. Krantz The elements of Advanced Mathematics
J.P. D'Angelo and D.B. West Mathematical thinking
I. Lakatos Proofs and Refutations
M. Aigner and G.M. Ziegler Proofs from the Book