| Course page: |
ON CAMPUS: http://www.math.fsu.edu/~mesterto/Analysis.html (this
page)
OFF CAMPUS:
http://www.math.fsu.edu.proxy.lib.fsu.edu/~mesterto/Analysis.html
(with your FSUID username and password) |
| Professor: | Dr M-G
|
| Office: | 202B Love
|
| Office hours: |
Please check here, where
current times are always posted. Although office hours
are subject to change—due to unforeseeable
circumstances—up to midnight of the previous day
(so it is wise to check here
first), like hurricanes in Hertford, Hereford and
Hampshire, it hardly ever happens. Note that office
hours are primarily for personal matters that cannot be
addressed in class (as opposed to tutorial help, for
which see under Course format and
How to study below) |
| Phone: | (850 64) 42580
|
| Main website: |
Professor M-G's
Home Page Email: |
| Goal (long version): |
To guide you through some of the rigorous
underpinnings of calculus and analysis. Topics include
the real line; sequences and series; compact and
connected sets; limits and continuity; and derivatives
|
| Goal (short version): |
To cause you to understand the text
|
| Class meets: |
In 201 LOV on Tuesdays and Thursdays at 09:15—10:45
|
| Text: |
Abbott, Understanding Analysis (Springer, 2001, ISBN
0-387-95060-5), mainly Chapters 1-5 (but not necessarily in that
order—for example, we may jump from the end of §1.4 to the
beginning of §2.1 and return to §§1.5-1.6 later). Note
that you are expected to bring the text to class each day (unlike,
e.g., a calculus text, it does not weigh a ton) |
| Credit: | 3 semester hours |
| Eligibility: |
You must have the prerequisites listed below, and you must
not have credit for MAA 4226 Advanced Calculus I |
| Prerequisites: |
| (i) |
MAC 2313, MAS 3105 and prior experience with mathematical
proofs from MGF 3301 or MAD 2104; or Professor M-G's
consent and |
| (ii) |
self-motivation and industriousness. Dr M-G's philosophy of
learning is perhaps best expressed by the following
diagram: |
|
| |
ALTERNATIVE THEORIES OF LEARNING VERSUS
PAIN
 |
For further details, please click here.
|
| Communication: |
I will send email to your FSU email account on a regular
basis. It is your responsibility to check it regularly (or arrange to
have my messages forwarded, if you prefer to read your email
elsewhere) |
| Your name: |
 |
|
I don't know who you are, but because
everything works so much better when I do, I would like to
learn your name as soon as possible. So, please take a sheet of
card stock (or even paper), fold it in half, write your name in large letters on
one side and stand it up on your desk so that I can see it.
(Write what you want me to call you: if you're a William who
likes to be called Dubya or a Margaret Jane who likes to be
called Dee Dee, write Dubya or Dee Dee, not William or Margaret
Jane.) Please bring your nameplate to every class
until I have finally learnt your name (which will take
significantly longer than it used to take when I started
out) |
|
| Course format: |
The course will be based on your reading
of the text together with much interactive problem solving, on which
we'll spend most of our time in class. (The book is stuffed with
exercises, as you can easily check for yourself.) After each period I
will set homework for the following period (either at the end of class
or soon afterwards by email). This homework will consist of three
items:
- An exercise or exercises on the current topic or topics
- An assigned reading on the next topic or topics (not uncommonly
the next section or two of the text)
- A problem associated with the topic or topics of the assigned
reading, a good-faith effort at which must be turned in at the
start of the next period (even though it will not be formally
graded)
At the start of each class, I will always assume that you have both
read (not necessarily understood) the assigned reading and at least
seriously attempted (not necessarily completed) the associated problem,
that is, you have completed Items 2 and 3. (I will also assume that you
are going to complete Item 1, but not necessarily in full by the
following period, especially if the homework was set on a Tuesday.) I
will begin the class by highlighting the key points of Item 2, mainly
to jog your memory. I will work from notes that ultimately get posted
here. (These notes are primarily to help me
remember what I decided to cover; however, to the extent that they are
also useful to you, you are welcome to avail yourselves of them.)
We will then proceed to work on problems,
beginning with Item 3, and referring to the text as necessary or as
convenient (e.g., when the goal of the exercise is to complete a proof
that the text leaves unfinished, as on p. 22). Questions may be asked
at any time—and should be, if there's anything you don't
understand. (Perhaps you have a question about the assigned reading
that you anticipate being answered by one or more of the problems we
work together; in which case, it may well be socially minded not to ask
your question at the outset. However, if it turns out that you
anticipated incorrectly, then be sure to ask your question before the
class is over!)
Eighteen-minute quizzes will be given at the
beginning of class on all Tuesdays except May 10, June 28 and August 2.
These 10 quizzes will count for 5% of your grade apiece. On every
Thursday except August 4, we may attempt to end the formal class period
after 60-70 minutes, so that the last 20-30 minutes can be devoted to
individual tutorial help. |
| First homework: |
Before our first meeting at 09:15 on Tuesday, May 10: please read
Sections 1.1 and 1.2 (pp. 1-11) and at least seriously attempt
Exercise 1.2.1 on p. 11. On that day I will assume that you have
completed both of these tasks and are prepared to ask about
anything you didn't understand, because in class our custom will
always be to start working on the exercises after only the briefest of
lectures (whose purpose is to highlight key points of the assigned
reading, based on the assumption that you have actually read
it). |
| Test format: |
Begin each question (but not subsequent parts of the same question)
on a fresh sheet of paper, use one side of the paper only, and have
your solutions stapled together in order at the end of the examination.
Do not use dog ears. (Not owning a stapler is no excuse: I will bring
one to the classroom.) Needless to say, your
name must appear on Page 1 |
| Grades: |
Will be based on 10 quizzes (50% collectively) and two tests (25%
apiece), for which you must use either a pen or a dark pencil.
Note that it is not enough merely to produce an answer. The method by
which you obtain it must be sound and clearly demonstrated: Show all
necessary steps in your method, with enough comments or diagrams to
convince that you thoroughly understand.
Precise cut-off points for A, B and C will be
determined by the distribution of grades at the end of the semester,
but are likely be in the vicinity of 90%, 80% and 70%, respectively. In
borderline cases, a smaller number of completely correct solutions will
carry more weight than a proportionate number of fragmentary answers;
later scores will carry more weight than earlier scores; and a record
of active participation in class will carry more weight than a record
of passive attendance.
Plus or minus grades may be assigned in a manner consistent with
standard University practice.
Please note that partial credit will be awarded
only when part of a solution is completely correct—not when all of
a solution is partially correct, whatever that means, if anything. A
score for a question worth 10 points should be interpreted as follows:
| 10 |
Practically perfect |
9 |
Still very good, but
lacking—or wrong about—a significant detail |
| 8 |
Still good, but lacking—or
wrong about—significant details |
| 7 |
Minimally satisfactory. You
have—just—managed to demonstrate that you basically
understand and are at least capable of getting all details correct
(although it clearly did not happen this time) |
| 6 |
A grade that will not be given |
| 5 |
Half right in some appropriate sense
(e.g., there were two parts, each worth 5 points, and your first part
was practically perfect) |
| 1-4 |
Not even half right and showing
little understanding, but some degree of positive effort |
Also note that a grade of I will not be given to avoid a grade of F or to
give additional study time. Failure to process a course drop will result in
a course grade of F |
Solutions to
homework exercises: |
Will be posted here, but only after being at
least seriously attempted by the class as a whole, and only if
specifically requested (if you ask in class, be advised to back up
your request with an email, otherwise I am likely to forget). I caution
you, however: never read the posted solution to a problem until
first of all you have seriously attempted the problem yourself.
If you have at least made a serious (and I do mean serious)
attempt, then—even if you were unable to complete the problem
yourself—you will benefit from reading the posted solution; if
not, then not (rather, you will merely form a false impression of how
well you understand ... as indicated by the green curve in the above learning-versus-pain diagram) |
| Quiz solutions: |
Will be posted here |
| Test solutions: |
Will be posted here |
| Attendance policy: |
You are expected to attend class regularly, and bear the full
responsibility for learning anything covered during any class that you
miss. |
| Exam policy: |
No makeup exams. An absence may be excused given sufficient
evidence of extenuating circumstances (in which case, extra weight will
be attached to the other exams). But you must either have discussed
the matter with me (well) in advance; or, in the case of illness, have
brought me a note from a physician explicitly stating that you were too
ill to attend class on the day in question. An unexcused absence will
result in a grade of zero |
| Etiquette: |
You are firmly bound by Florida State University's Academic Honor Code. Briefly, you have the
responsibility to uphold the highest standards of academic integrity in
your own work, to refuse to tolerate violations of academic integrity
in the University community, and to foster a high sense of integrity
and social responsibility on the part of the University community. Even
more briefly, you must neither cheat nor enable others to cheat. The
penalties for violations can be severe. Please carefully read the
section in the FSU Student Handbook on the Honor Code and official
procedures for dealing with students who violate it. If you are in any
doubt at all as to what constitutes acceptable behavior in this regard,
you should ask me for clarification.
You are also bound by the ordinary rules and
customs of polite behavior that prevail in a civilized society. I
assume that you know these rules and customs, and I expect you to
comply with them. (In particular, you are not allowed to use a cell
phone or otherwise have private conversations with others during class;
and you are not allowed to create disturbances through arriving late or
leaving early.) |
| Test dates: |
Tuesday, June 28
Tuesday, August 2 |
| How to study: |
It is important that you keep up with the course from the very
beginning, always attempting as many as possible (preferably all) of
the homework exercises. If you get stuck, then send me a question by
email. As soon as I possibly can, which might be as soon as within half
an hour, but might also be a day or two later (I have a life, too, you
know), I will reply—not to you, but rather to the class alias
(after carefully concealing your identity, just in case you are
inexplicably bashful about being perceived as smart enough to ask a
question).
Note, however, the following. First, you must
identify yourself (i.e., you remain anonymous to the other students in
the class, but not to me) in the body of your message (because
your username does not identify you to me): I don't reply to anonymous
email. Second, you should be as specific as possible in describing your
difficulty: the more precisely you identify how you got stuck, the more
helpful my reply is likely to be. |
| Disabilities: | If you have a disability requiring
academic accommodations, then not only should you register with the Student
Disability Resource Center (SDRC),
but also you should bring me written confirmation from SDRC during the
first week of class. This and other class materials are available in
alternative format upon request. |
This syllabus and other class materials are available in alternative format
upon request.
For more information about services available to FSU students with
disabilities, contact the:
"Except for changes that substantially affect implementation of the
evaluation (grading) statement, this syllabus is a guide for the course and
is subject to change with advance notice.''