Final letter grades have been posted. Good work everyone!
(PS--if you checked before 12:45 pm on Thursday, please check again
now--they have been corrected.)
We went over the old final during the review session--here are the
smartboard notes from the review session:
Grades to date have been posted, and here is a copy of last
semester's final exam, plus solutions. Happy to cover any of
this during the review session.
Your exam will have different
questions of course, with some kinds of questions replaced by other
kinds, but this gives a good idea.
Review session-- Tonight at 6:30 to about 7:30, in JEM
366 (just up the hall from our usual classroom). Will mostly
be covering related rates, optimization, and graphing.
Overheads from Alice Dean's talk:
Extra Credit Talk
Date: Thursday, 05/05/05
Time: 3:30 � 4:30 p.m.
Location: SMC Campus, Jeanmarie 362
Title: Characterizations of Unit-Bar
Dean, Department of Mathematics and Computer Science, Skidmore
Representations of graphs using horizontal bars for vertices and
vertical visibilities for edges have been studied since the mid
1980s, motivated by applications to circuit design and display of
data. Graphs that can be represented in this way have been fully
characterized, but the bar lengths may differ by impractical
amounts. I consider graphs that can be represented using bars all of
equal length. These graphs, called unit-bar visibility graphs
(or UBVGs), have not been fully characterized. I will
discuss results for several classes of graphs, including trees and
outerplanar graphs. The final result is a characterization of the
triangulated polygons (TPs) that are UBVGs. The
characterization uses a character string associated with each TP to
determine if a UBV layout exists and if so, to produce such a
for the final exam. The final exam will emphasize chapter
5. You can find a practice test at:
tests. In fact, this is probably one of the best places
to study for all the chapters, since some multiple choice questions on
the final will be very similar to these. Additional problems may be
taken from (or similar to) these drills:
It is too scary (and probably not even possible) to do every problem
from every drill--just do one from each drill, and note which you are
uncertain about, then go back and do a couple more of that type.
Do this as many times as you have time for.
There will also be a "delta-epsilon" problem, of much the same
flavor as # 15 - 18 in section 2.4, a related rate problem, an
optimization problem, a graphing problem (factored derivatives will be
given), and a proof of the derivative of some like a quotient/product
rule or trig function or its
inverse. These 5 questions will be worth more than the multiple
may have FOUR sheets of notes, front and back, as usual.
However, in addition, you may bring photocopies
of the flyleaves of your text (two pages
from the front of the book, four from the back) to use during the
Math Awareness Month!
Wednesday April 27
2:30 � 4:15
Screening of �The Proof�
Andrew Wiles announced a proof of Fermat�s Last Theorem, a
conjecture that had fascinated mathematicians for more than 300
years. This video tells the story of Andrew Wiles and his proof.
(This video should be of particular interest to those of you
attending the Hudson River Conference on 4/30 since the invited
address will be about this theorem - and the HRUMC speaker, Ken
Ribet, also appears in this video.)
3:40 Screening of �The Right Spin�
Awareness Month 2005 special video:
the story of a dramatic rescue in space and the mathematics
behind it told by Astronaut Michael Foale and narrated by Robert
Osserman. Guaranteed to make you appreciate Calc.III (35 minutes)
If you can�t
come to all of the celebration
you are welcome to �drop in� for part of it!
Sponsored by Math Department and Pi Mu Epsilon.
Reminder on the population lab-- It
says you must research population literature, including IntelPop.
The site for IntelPop is in the references (section 5.2, second
listing), but here is a direct link for your convenience:
The java applet is pretty easy to use.
Due dates have been posted for
Chapter 5 Challenge problems and the last Maple lab. Do the
Maple lab as soon as possible, since it will help with homework as
In order to provide out-of-class time
for the populations project, class will not meet on 4/22, and the
due date for Part III (section 3.3.1) has been moved to 4/25.
Challenge problems for chapter 4 are due Wednesday, 4/20.
Lab 6 is due Friday, April 15. This is a good warm-up for
section 4.6, and will help reinforce important concepts for the test
on the 12th.
4.3 no 47, which is:
limit( sqrt(x^2+1)-x, x = infinity).
figured it out right after class and boy do I feel stupid...
many times have I said that if you see square root-y things, it is
always a good idea to try multiplying by the conjugate? Be good
if I followed my own advice, hmm?
mult top and bottom of this by the conjugate, and then it is easy to
see the limit is 0.
||The third hour
test will be on Tuesday, April 12. The test will cover sections 3.3-3.8, 3.10, 4.1-4.5. You should study from the tutorial
tests. There will be questions (proofs) for the derivatives
of the trig and inverse trig functions.
Also helpful are the
derivatives, differentiation methods, curve analysis, and mean value theorem tutors
under the tools menu in Maple.
Here are a some drills:
Lhopital drill inf limits,
for inc/dec and questions about f' or f'' pos/neg, and global extremes.
Do not include endpoints for local extremes. Also, on #7 there are
asymptotes at C and E so the function and its derivatives do not exists
there, also skip the 9th one since it has a confusing wrong answer given),
1st deriv test drill
Bacteria Project Revisions:
- Include the names of you partners in
- Include a copy of the original data you were
given by your bio partners.
- If you used the Maplets posted on the
website to determine the parameters, include screen captures in
- Organize information so that it will be easy
for your bio partners to understand:
- Label data sets and plots
- Insert comments above Maple code to
explain what you are doing and why.
- Introduce the answers to the questions in
part 3 so the bio partners will know what you are discussing.
- Edit as though this were an English paper
(in some sense it is�the point of your writing classes is to
develop the skills you need to make reports like this meet
professional standards). Use complete sentences, check grammar
and spelling, etc.
- Analyze all four data sets you were given.
They may not all exhibit logistic growth�that is ok, but you need
to explain why you chose whatever other model you did choose. It
may be that no matter how hard you try with various pairs of data
points and (and values of M for the logistic curve) you still
don�t get a great fit�this is ok as long as you give some
explanation of what might be causing the difficulty.
- If the are questionable data points, ask
your bio partners about it and include the explanation in your
Extra Credit Talk--
Time: 3:30 � 4:30 p.m.
Location: SMC Campus, JEM 362
Problem in Extremal Graph Theory
Schmidt, Department of Mathematics, Emory University
have proven to be a very important mathematical model. For example,
computer or telephone networks can be viewed as graphs. Often, one
would like to build a graph that has a certain property. A natural
question then arises:
does one have to spend to build the graph with the desired
discuss such a question as asked by Paul Erdos and its solution.
previous knowledge of graph theory is assumed.
Extra credit opportunities: Extra credit
is available for attending any of the
Senior Seminar talks and
writing up a two or three paragraph synopsis of the talk. You
may attend as many as you would like.
examples on Maple:
sec3-6 no 59.mw,
no 60.mw (not enough detail for the challenge problem, but enough to get
An example using Maple to plot the tangent
line to a function
3.6-3.11 due: 4/1/05, no fooling.
The next hour test will be on Tuesday, March 8, and will cover
sections 2.5 through 3.4.
The second hour
test, on Tuesday, October 19, will cover sections 2.6 through 3.2.
part will be similar, both in content and format, to the first hour
test (multiple choice). You should study from the tutorial
tests. However, there isn't a very large selection there of
problems to practice on (although 3.2 is good)--you should do as many of the
"drill" problems from the inclass demos as possible, since I
am likely to take problems from there for the test as well.
You should be able to compute the slope of the tangent line
(derivative) using the limit definition of the derivative. You
should be able to tell if a function is continuous and if it is
differentiable. You should also be able to sketch a graph of a
function and the tangent line at a point.
There is also an excellent Maple tutor--go to
tools/tutors/calc--single variable/differentiation methods. Do A LOT
of practice with the product and quotient rules!
The second part of the test will ask you to prove at least two of
the differentiation rules--constant multiple, power, sum, product,
quotient, various trig rules.
Here are some good review sources:
Also do the examples in the inclass demos that will generate
different problems for you, for example at the bottom of http://archives.math.utk.edu/visual.calculus/2/definition.8/index.html
, and http://archives.math.utk.edu/visual.calculus/2/formulas.3/8.html
These are good for practicing using the limit definition to find
Here are some good practice finding tangent lines and using the
product and quotient rules with the trig functions.
product rule egs,
quotient rule egs,
Due dates for the next set of challenge problems and lab have been
EXTRA CREDIT TALK--Extra credit is available for attending
this talk. As usual, write up and turn in 2 paragraphs about
the talk (due the Tuesday after break) for credit. This is a
very entertaining and easy to understand speaker.
Rick Cleary Talk
Grades to date have been posted. See me for your code or if
you have any questions.
Here are some Maplets that may be useful for the populations
project. WARNING--do NOT use the Curve Fitting tool inside
Maple--it will fit to lines or polynomials, NOT the
exponential/logistic curves which you need for this project.
Some "sexy" maple:
labs/fancy Maple/torus graph.mws.mw
calc1/maple labs/fancy Maple/surreal shells submit.mws
In order to provide out-of-class time
for the populations project, class will not meet on 2/23.
Populations project due dates:
Part I (section 3.1.2)-due: 3/4. Part II (section 3.2)- due:
4/1. Part III (section 3.3.1) - due: 4/22.
Happy Valentine's Day!
Is there any interest in Tatoos for Pi-Day?
(3/14). We could probably get the department to order us some.
Let me know ASAP.
The date of the extra credit talk has been
changed to next week--2/18/05.
Maple lab 2 is due 2/14/05
Solutions to HT I from last semester:
acdbbcbbadebc. Note that problems 12 and 13 are from 2.5 which
will not be covered on our test.
Credit talk: David Wood will be speaking at the UVM
Math department colloquium this week as well as in the combo
seminar. The colloquium talk is aimed at a general audience and
should be quite accessible.
about a page of notes/observations from the talk for extra credit.
2/11/05 (Changed to 1/18/05 !!!)
4:00 � 5:00 p.m.
Location: 004 Kalkin, UVM Campus
Title: Drawing of Graphs in Two and
The first hour test is scheduled for Tuesday, February 8.
The test will cover sections 1.1 through at least part of 2.4, and assumes you
have a thorough mastery of the appendix reviews.
may use one page of notes, front and back, during the test.
You may also use a calculator on the test--graphing or non-graphing
The first hour test will be very similar, both in content and
format, to the tutorial quizzes at:
tests. You will have to change the chapter in order to get
problems from chapter 2. However, there may also be a
"delta-epsilon" problem, of much the same flavor as # 19 -
32 in section 2.4. Here is an hour test from last
semester: HT1f04.pdf. You should also spend some time with the graphical view at http://math.hws.edu/javamath/config_applets/EpsilonDelta.html
Some other good study problems: http://archives.math.utk.edu/visual.calculus/1/vertical.1/index.html
Maple printouts--the Maple tutors and assistants, as far as I know,
won't print directly from Maple. If you need a print out of
something you have done on one of them, the quickest way I know is
to press alt/PrtScrn (the PrtScrn button is usually on the
upper right of the keyboard) while the window is up. This
copies the window to the clipboard, and then you can paste it into
another application such as Word, and then print from there.
If you right-click on the image, you can crop it if necessary.
This will work with any active window, not just Maple.
New time for trig review: 7:30 to 8:30 (moved from 8 to 9)
TONIGHT, in JEM 364. Trig review notes:
demos S05/calc-trig review.xbk
demos S05/calc trig review.pdf
And a unit circle chart:
You may order a personal copy of Maple 9.5 at a discounted price of
$75 if you wish: Secure ordering address: http://webstore.maplesoft.com
. The NEW Promotion Code is: AD7229 Course Name: Math
seems to work if \\raptor\mapl95
does not work.
Due Wednesday 1/19--
a print out of a Maple worksheet with just your name on it so that
I know that you are able to get on Maple and get started.
There will be a Maple help session in JEM 142 on 1/20 from 6:30 to
7:30 for the first Maple lab and a trig review session on 1/24 in JEM
364 from 8-9 pm.
The 2/6 hour test date on the First Day Handout
was a typo--it should have been 2/8 and has been corrected.
The other two hour test dates, 3/8 and 4/12, are correct.
link for the resources (eg tutorial quizes) that goes with our book
seems to have changed. I think this is the new link: Book
I wish to bring to your attention that once again this year there
will be a conference for undergraduate students interested in
mathematics during the Spring semester. The twelfth annual Hudson
River Undergraduate Mathematics Conference (HRUMC)
will take place on Saturday,
April 30, 2005 at Williams
College in Williamstown, Massachusetts.
The keynote speaker will be Ken Ribet of UC Berkeley. In the past
several years, a contingent of students and faculty from St.
Michael's has gone to the HRUMC, and
several students and faculty members have
given presentations at previous conferences. For more information
about this meeting, you can check out the conference homepage at http://www.skidmore.edu/academics/mcs/hrumc.htm.
At this site, you can find details about last
year's conference which was held at Mount Holyoke College.
At the HRUMC, some talks are given on original research in
mathematics or a related field (done by students, faculty, or
jointly), while others are expositions of interesting work that has
been accomplished and discoveries that have been made in mathematics
(typically not discussed in regular course work). If you think that
you might be interested in giving a talk or attending the conference
to see what it's like, please let me
or anyone else in the mathematics department
know. If you'd like to get more information about this opportunity,
just e-mail me back or stop by my office and I'd be happy to discuss
it more with you. I have copies of recent conference programs if
you'd like to get a feel for what the conference involves and the
type of talks given. I look forward to hearing back from some of you
about this opportunity.
There will be
Help Sessions Mon-Thu 7:30 - 9:00 pm in STE 334, starting date TBA. Note--this
is in St. Eds, and NOT in the hall our class is in.
There will be a trig review--Date TBA
There will be a Maple help session if you would like help with the
first lab. Time/location TBA
Some of the interactive material in
the Visual Calculus modules uses ActiveMath, which does not work
under Internet explorer. There is a way to see/use the
activemath notebooks. To
start with, you need to be running under Netscape, not Internet
Explorer. If you don't have Netscape, you can down load it for
free here: http://www.netscape.com/download/
(choose the full install when prompted)
You also need the LiveMath Plug-in for
netscape. You can download it free here: http://www.livemath.com/download/
(click on the icon for "Windows for Netscape based
browsers", assuming you are running some version of Windows).
You only need the freeware--you don't have to buy anything!
CAVEAT: This worked for me, but comes with no
guarantees--it may or may not work with the way your computer is
configured. The helpdesk does not in general support netscape--if
you have a problem, you can ask, and they may be able to help you, but
DO NOT hassle them if they can't.
PLEASE, PLEASE: If
you happen to be one of the folks that is able to get this to
work, please, please share your resources with classmates you
may not be able to. Thank you!
Some career resources:
of people with exciting real jobs using Math,
More people using
Listing Services, Comprehensive
resources from SIAM, AWM
Career resource site.
The department has (in George's
office) a CD-ROM and videotape entitled Careers in
Mathematics created by three major professional societies of
mathematicians (AMS, MAA, and SIAM). He also has video tapes
of a panel and presentation by recent SMC math alums.
There is also this note from
"This summer I have been in
contact with a number of St. Michael's mathematics alumni in a wide
variety of careers, in such areas as statistical data analysis,
actuarial consulting, software engineering and other
computer-related fields, education (at the secondary and university
levels), and even flying (specifically as a USAF pilot).
These alumni are willing to be resource/contact people
representing a variety of careers. If
you wish to be in contact with an SMC alumnus from a particular
mathematics-related field, then let me know and I will try to
connect you with an appropriate person. I
recently have given a few of my advisees e-mail addresses of
mathematics alumni who are pursuing careers in an area of interest
to them, and could do a similar service for any of you that are
sure to click on "refresh" when you open these pages to be
sure you get the most current postings.
||The postings on
this site have all been tested and all work. If you have any
difficulty getting material off this site, you can try any of the
1. See if someone in your study group was able to print the
file you want and make a photocopy of it.
2. Try using one of the lab computers in case the problem is
with how your own computer is configured.
3. Using Explorer, right click on the link, select "save
target as", then save the file to your home computer. You
should be able to open and print it from there.
4. Contact Cynthia Kelley at 654-2756 or firstname.lastname@example.org. She is the
person for website trouble shooting.
Resource Center runs excellent workshops every semester on study skills, time management,
test-taking techniques, etc. For details: SRC study skills