Conference turris::womannotes-v3

SC,

For most of my life, anything beyond + - / and X made me
feel lost in the universe.  Browsing my husband's book
shelf I found <mumble .. History of Mathematics? mumble>
by Edna Kramer. 

She certainly covers the history ... starts off with sticks
for counting cattle and, 800 pages later, closes with
the 20th century.  Very interesting ... and
reading it made me understand why math left me feeling 
lost.

Until reading Kramer's book, my "mathematical" feet had
no ground under them.  Everything mathematical seemed 
to have sprung full grown from the brow of a text book 
writer.  I felt quite cheered to discover that zero became 
a "legal" number around about the lst millenium; but the
math folks argued about it for a few centuries before
it was finally accepted.  (I guess it was accepted
after all the zero-haters died off.) 

Seeing mathematics "grow" made it far more interesting
to me. 

>    	If you could do it over again, especially, how would you handle
>    	it?

I'd read more of the literature of math. Text books are Cliff Notes; 
they omit the joy.

ps. I remember you posting a note in V1 about your son's dreams when
    he was 3 and the interesting images that came to him. If your
    interested in mathematical imagery ... 
    _The Psychology Of Invention in The Mathematical Field_ 
    Jacques Hadamard, Princeton U Press. 1945 (also in reprint
    by Dover).

    Also,_Autobiography of a Mathematician_ ... a native Hungarian
    who worked on the Manhattan project. He has much to say about
    thinking mathematically.

Excuse verbosity ... an interesting topic. Good luck getting
your degree. Come East for the anniversary event and tell us more.

Meigs

    Last spring, I began taking undergraduate math courses. It was a
    struggle for me to throw out the urge to plug numbers into an equation
    -- just get the answer -- as opposed to solving the problem in a
    general sense.  The course was a good experience, because it provided a
    refresher and a chance to learn problem solving, not just math.  
    
    Good luck in your courses.
    
    CMN

    I *loved* advanced calculus courses in college.  Of course, it helped
    that I had a part-time job programming for the cosmic ray research
    group in the physics department, so I actually got to see people need
    to USE all those fun things like line integrals, Green's Theorem, etc.
    I also had a real good instructor for most of those courses, who
    happened also to be my adviser since in those days computer science was
    not yet a separate department and was under the math department.
    
    Closed-form solutions to complicated problems have a nice esthetic
    appeal!  Especially compared to some of the real-world problems you
    typically run into.  One of the programs I worked on for the physics
    folks was a hairy Fortran program which computed non-closed-form
    solutions to a bunch of ugly partial differential equations that
    described the density of different sorts of cosmic ray particles
    as you integrated the equations from the orbit of Venus to the orbit of
    Mars.  When there was LOTS of grant money, they sent up satellites to
    measure the particles in earth orbit (above the Van Allen belts), and
    when there wasn't much money, which was most of the time, they sent
    the experiment up under a helium balloon which was flown from
    Churchill, of polar bear fame, in northern Canada.  Some of the people
    who worked for the lab got to go to Churchill to fly the balloons, but
    I never managed to swing that.  I did get to help fix the detectors and
    things when they came home, and paint reflective paint on the back of
    the special glass lens on the bottom (anyone who wandered into the lab
    when the thing was there was likely to be handed a paintbrush...). 
    This Rube-Goldberg device recorded its data as one enormous block on
    2400 feet of 7-track tape with a special indestructible tape drive
    which was mounted on the bottom, and we had to boot a special operating
    system in order to read it (since there were no inter-record gaps: one
    BIG record).  We used this data to check the data from the big-grinder
    integral program.  It was a fun place to work, even though it paid the
    same as slinging oatmeal in the cafeteria - all on-campus jobs paid the
    same.  (It was a big deal to me when IO got a raise to MORE than minimum
    wage!)
    
    On the other hand, I haven't used most of that kind of math since!
    
    Have fun learning!
    
    /Charlotte

    A few years ago I was working on my BS EE (my third degree, I already
    had a BS in Accounting and an MBA).  DEC was sending me to school full
    time to Worcester Polytechnic Institute with the stipulation that I
    finish the program in two and a half years.  While other people could
    mix and match courses so they had liberal arts type courses thrown in,
    I had to cram each semester (actually at WPI it was quarters...) with
    all math, science and engineering courses.  I thought Physics and
    engineering were alot of fun but when I got to Calculus 3, I would
    have gotten more pleasure banging my head against a brick wall.  :^)
    I was very fortunate to have had a professor that took the time to
    tutor me (three times a week for one - two hours).  He gave me a
    tremendous amount of energy and the motivation to really want to 
    succeed in the course.
    It probably helped me more in terms of perseverence than in math.
    As with anything else in life - if you need help, don't be 
    hesitant to ask.

    A lot of what you get out of math comes from the type of professor you
    have.  See if you can "feel out" what the professors are like, and
    choose a semester for that course when your preferred prof. is
    teaching.  Or find a mentoring-type professor or a study group you can
    work with when you're doing those problem sessions in areas that are
    most difficult for you.
    
    There are probably also Usenet Newsgroups that might be a help or might
    introduce you to new methods or new people to act as resources, and
    there's also 2B::MATH - the mathematics notesfile....
    
    -Jody
    

    
    I have a BS in CS with a Math minor, and as I graduated almost 3 years
    ago, I remember it all well.  A few tips :
    	1.  Sit in the front row.  The prof is more likely to take the time
    to help a familiar face.  Also, it's less intimidating to ask questions
    if you can't see the rest of the class.  (I went to Pitt with 30,000
    other students, so our classes were LARGE)
    	2.  When you go to take a test :
    	- get minimum sleep the night before
    	- when you first get up re-read over your list of pertinent
    formulas.
    	- when you first get your test, whiz throught it writting down the
    applicable formulas next to each question.  Then go back and take the
    test.  (If you don't remember some, don't worry.  Your brain puts it in
    the background and still thinks about it.)
    	- when you're done, re-do the test.  First just go over every
    single line of every solution.  Then, time permitting, start from
    scratch on junk paper, and re-do every solution.  It's really easy in
    math to do dumb things like add 1+2 and get 2.  (see a *)
    	3.  Try to understand why a formula is the way it is.  Without that
    understanding, it's easy to forget.
    	4.  Try to like it.  
    
    Good luck!
    
    Rachael
    

       I agree with all of Racheal's suggestions except 'get a minimum of
    sleep'.  The one thing I try to do before any test is get a good
    night's sleep, because I can't think when I'm tired.  And I find
    that when I'm alert (well-rested) I can remember things and make
    things up :-) alot better.  Maybe you meant don't oversleep to the
    point of drowsiness.  The suggestion about reading the test over
    once at first and jotting down what comes to mind works really good
    for me.
      More advice about math is: don't think of it as reality, think of 
    it as a game/puzzle, where you are given a set of assumptions,
    and *based on those*, are expected to draw conclusions.  Just keep
    the assumptions in mind (rules) and combine those to get to the
    answer.
        	Linda

    in re .7
    
    Linda is correct about the good night's sleep.
    
    Behavior studies of people who stayed up all night studying and
    those that got a good night's sleep but didn't study as much
    found that the latter did better on tests.
    
    It turns out that sleeping on material that you've studied, as it
    were, actual improves your memory of it.
    
    Bonnie

    A couple   of   books   I'd   recommend:   Newman  "The  World  of
    Mathematics", Bell "Men of Mathematics" (it may be out of print).

    I really  liked  algebra  (groups,  fields,  and rings). It's very
    different  from  high  school  algebra,  and  is  one  of the more
    beautiful  parts  of  mathematics.  Number theory may be even more
    beautiful,  and  almost completely useless except for fun (and the
    cryptography  I'm  working  on  now).  Algebra is actually useful,
    which may or may not recommend it.

    I was  never  very  fond  of  calculus because most of the courses
    spend  too  much  time  on applications and not enough time on the
    theory and beauty.

--David

    
    oops, I made a typeO.  I meant get the sleep that you need, exactly.  
    Not too much, not too little.
    

    
    I loved math when I was in school.
    
    I always set in the front row and I always followed the professor
    lecture and asked questions right away (not afterwards) when I
    couldn't understand something.  I made sure I understood everything
    at class or at least note the things I didn't and tried to figure them
    out or get help later.
    
    I did all the homework on my own, I don't like group studies.
    (I have trouble understanding other's thought process..) I always did
    the homeowrk on the same day after class, so I could remember what
    the prof. said. 
    
    I always study a couple of days ahead of time. I would go over the
    theorems and then do all the execises at the end of the chapters.
    That would cover a good 90% of the questions you'll encounter in the
    test.  Try to work extra hard on your weak areas.
    
    Get a lot of sleep before the test. Check the calculator batteries,
    check lead in pencils, etc. 
    At the test, don't panic, take a deep breath. Don't panic and don't
    sepnd too much time on a question that you don't know. Finish all the
    ones you know first and come back to the hard ones later. With the
    hard one, try to figure out if you have seen something similar before.
    Take the best guess.I remember that even if the final answer is wrong,
    marks are given for the right equations and logic. So, always right
    down every single step. Try to answer all hard questions, don't put your
    eggs in one basket.
    
    I always re-did the test and re-did the numbers in case I punched them in
    wrong. Writing down every step helped to find any mistakes.
    
	Eva.
    
    ps. Also, believe in yourself. Good luck.

    	I was a double math and CS major in college as well.
    Basically my math major was because I enjoyed math and was good at
    it, so why not major in it!  Unfortunately, I haven't used any of
    what I learned since, but I mostly expected that.

    	I agree with a lot of the previous suggestions, especially
    ones made about how to take tests.  Read through the entire exam
    when you first get it, and do all the "easy" problems first.  Then
    go back and tackle the harder ones.  I started doing this on math
    exams and actually now use this technique on most applicable
    exams.

    	Jody's correct - the professor can make a *world* of
    difference.  Interestingly enough, when I look back on the math
    courses I didn't enjoy, I think part of the problem was the
    teacher.  I just finished a Stats course for my MBA - and had
    really worried cuz I know how dry Statistics can be.  But I had a
    good professor, and he really helped make the class both
    interesting and applicable to real-life situations.

    	Whoever had the idea to think of problems like puzzles or
    games was right...because sometimes there are definitely more ways
    to solve something, and if you can't do it one way, you may find
    another which is just as acceptable.  (And the professors I've
    seen often enjoy a solid alternative solution.)

    	My last semester I took a history of math course - what a
    blast that was!  Solving problems like Egyptians did, like the
    Greeks did, seeing how formulas developed...it seemed to me to be
    the perfect finale to my major.  (The text for the course was
    called "Classics of Mathematics" edited by Ronald Calinger.  It's
    a series of articles, extracts from texts by the mathematical
    greats like Euclid, Archimedes, Plato, Newton, etc., etc. right
    through the centuries - fascinating stuff!)

    	Another fun book to read, especially if you also like music
    and art, is "Godel, Escher, and Bach", by Douglas Hoffsteder.

    	Good luck,

    	amy

    Janice and I met in Honors Math at UCSD. She went on to get a double
    degree - Math and Linguistics - from U. C. Berkeley. (I dropped out...
    :-) I love math and so does Janice. Good Luck and Best Wishes! Some
    things I found helpful was hanging out with other people who were into
    Math and just talking about it, and reading a lot of "fun math" stuff
    like puzzles and games. Find some *fun* in Math and keep with that part.
    
    	-- Charles

    Wow!
    I've always felt I deserted/betrayed my first love because I 
    didn't take math in college my first year, and by the second
    I'd forgotten too much to go on..
    
    I still love math, and Amy, I've never finished GEB....but I've
    read bits of it almost as often as I've read Tolkein.
    
    nice to see another way we are alike! :-)
    
    Bonnie

    I'm somewhat  depressed  by  the  direction  much of this note has
    taken.  Take  math  for  the love and beauty of it. The tests will
    take  care of themselves. There's something very sad about someone
    saying  that  she  wants to study math and getting responses about
    how to get through tests.

    While I'm in a bad mood, I'll dissent from the Godel, Escher, Bach
    recomendation.  It's  an  interesting book, but I find that when I
    try  to go back to look up some point in it I find it tiresome. (I
    read  the whole thing just after it came out when I was bed ridden
    for  a week.) Somehow despite much analysis of the book and how it
    fits together, the ideas don't gell. There are lots of interesting
    ideas, but I wish he'd put them together.

    I will  recommend a Russian book called "Did you say Mathematics".
    It's  imported by Imported Publications which specializes in books
    from  Eastern Europe. It's an interesting book about where various
    bits of mathematics pop up in real world problems.

    Also, if  you're  interested  in  geometry,  read "Flatland" about
    2-dimensional   society   and  what  it  looks  like  from  a  3-d
    perspective. It will really help when you start to think about 4-d
    spaces.  It's also well written and fun to read, even if you don't
    care  about  the  math. I think the author is Abbott. I've seen an
    edition  (from  the  20s?)  that talks about some junior professor
    named   Einstein,   and  how  his  work  may  depend  on  multiple
    dimensions. I think the book was written in the 1880s or so.

    If you want a very heavy novella, Donald Knuth's "Surreal Numbers"
    is  a  novella  about  two  people on an island who develop number
    theory  from  set  theory.  It  can  be read as a novella, or as a
    fairly difficult math text.

--David

	David beat me to it.  I'll second the reccomendation for "Flatland".

Tracey

Let me second David's earlier recommendation for Newman's "The World
of Mathematics" -- it is not difficult reading (I read it in high-school)
but gives a very good perspective on mathematics.  It was written before
computers were anything other than a lab curiousity, which might make a
few bits seem outdated.

Bill Gates (CEO of Microsoft) thought enough of it that he commissioned
a re-printing -- it was originally published in the 1950's.

Martin.

    
    	RE: .15  David W.
    
    	Don't get depressed, David.  Remember, I've already studied
    	Math (I got all A's in Trig, and through semesters of Calculus.)
    	So it's not new to me.
    
    	The thing is, I'm doing it over (since I took it all in the mid
    	70s and feel it's worth doing over since I plan to minor in it
    	this time, which means I'll be taking it further than I did before.)
    
    	It occurred to me that I could do it better this time (no, I don't
    	regard all A's in Math as proof that I did it as well as I could
    	have.)  
    

    
    	Thanks to everyone for the wonderful responses!!!
    
    	You've all given me a new appreciation for Math!  I love it already,
    	but now I have a lot of great new ideas for getting more out of it
    	this time than I did last time!
    
    	Also, thanks for the tips on taking tests.  Although I do love Math
    	for the beauty of it, I do have to be somewhat practical when it
    	comes to grades.  I'm holding a 4.0 at school right now, so it
    	would be nice to keep it (or at least stay up there as close to it
    	as I can - for the sake of getting into a good school for my Masters.)
    
    	Again - thanks so much!!  I'd love to hear more!

    I loved "Flatland" when I was a kid; my mother had an old copy of it. 
    It came out in paperback a few years ago, and I have it someplace - it
    is still great fun!  I guess you have to like topology and stuff.  Some
    time ago, there was an article in `Scientific American' that had
    various Flatlander "machines" that would work in a two-dimensional
    universe - it was hilarious!
    
    /Charlotte

    I agree with some others who say "learn math for its own sake".
    It's the most beautiful experience when you formally learn
    the patterns in math and then see them happening all around you
    in the real world. To me, it's almost a universal language
    in which people can communicate the most intricate observations.
                     
    Ganesh. 

    One thing  I  found really helped me understand many kinds of math
    (algebra  in particular) was to read the problem set as soon as it
    was  handed  out  and  spend  the  week thinking about some of the
    problems.  By the end of the week I understood them well enough to
    simply  write out the answers, which I couldn't possibly have done
    when  I  first  read them. This assumes that the problems are well
    enough  stated  so  you can remember the whole problem easily (and
    most interesting math problems are.)

--David

A general reference, for DECies

$ VTX DLNCATALOG     [at least on some systems]
puts you in the DEC corp library catalog and you can hunt down a
book or videotape or whatever by title, author, search phrase...

The library has cassette tapes of all the "thank you" speches
of the Turing award winners. One of the winners, Dyksta (sp?)
talked about going into computers in the late 50s, and his
hesitation to enter a field that did not have a "literature."
I guess he made up for it; he helped write it. :) 

Anyway, when brownsing thru the Mill catalog, I noticed they
have a lot on cassette tape ... if you drive a lot, this might
make fun listening. Big universities have some great talks
on cassettes ... Alas, you have to hunt a bit. The audio 
card-catalogers seem to lack the skill or the book people.]

 Meigs

    
    
    Having taught math both at the high school and college level, I have to
    put my $0.02 worth in.  8-)
    
    When I was teaching, especially at the college level, I loved to try
    (didn't always succeed) to create innovative tests that really showed
    me whether my students had mastered the concepts or whether they had
    simply learned the "pattern" necessary to solve a certain type of
    problem.  My favorite course was always "Statistical Methods", a
    non-theoretical approach to probability and statistics usually taken by
    business majors (needed for their BA) and by other students (who needed
    it for their general mathematics credit).  I often handed out decks of
    cards (partial decks, not the full 52 cards) or packets of colored
    marbles, etc., and then had students "prove" (empirically) one or more
    of the "laws" which had been handed them during the previous unit. 
    
    I also, once, gave a test where I handed out one question at a time. 
    When a student finished the first question, they handed it in and
    received the second, etc.  There were 10 questions.  It was a 50 minute
    period.  All I told them at the beginning of the test was that there
    was 10 questions and that no question should take more than 10 minutes
    and that most questions would take no more than 3-5 minutes.  The
    results were, to put it mildly, interesting.  I found the students that
    were comfortable with the material didn't worry about which question
    they "thought" might be the 10 minute question -- they simply worked
    them through from beginning to end.  Those that worried more about
    which was the "hard" question tended to do poorly on all the questions
    because of not being able to think on the issue (question) at hand.
    This test probably wasn't the best tool for measuring the students'
    knowledge of probability, but it told me (I think) a lot about the
    students themselves.
    
    And, by the way, I was known for giving bitchy tests -- nobody ever got
    100% on one of my exams.  The high score was typically 80-85%.  I
    believe in "stretching" the student -- a test were 1/2 the class gets
    95% or more doesn't tell me a thing about how well the students were
    prepared, as a whole -- it only tells me I asked questions that
    everybody was able to answer.
    
    	Greg

Greg,

Sorry if this offends you, and I know it has not much to do with the
topic at hand, but you chose a topic I am *very* sensitive on, so I must
say that you are the type of professor that I considered to epitomize
the very worst things about professors.

>    This test probably wasn't the best tool for measuring the students'
>    knowledge of probability, but it told me (I think) a lot about the
>    students themselves.
 
And just what was the class about?  Students had to have a type of
personality you "approved of" to pass?  Why shouldn't knowledge of
mathematics be enough?  Why should students also be required to pass
tests of the what the *professor* feels should be their *personal*
skills????
 
For instance...
  
>    And, by the way, I was known for giving bitchy tests -- nobody ever got
>    100% on one of my exams.  The high score was typically 80-85%.  I
>    believe in "stretching" the student

Yah.  Right.  The math dept at RPI had a similar philosophy...they gave
*really* *hard* *tests* that would average around 30-40, and then "scale"
(curve) the results.  And it's all fair, right, since it was curved it
didn't matter whether you got a 90% or a 25%, as long as you were better
than some arbitrary number of other students?

Wrong.  The problem with the "curve = fair" application of statistics is
that it does not take psychology into account. What tests like that test
is *really* test-taking ability...NOT KNOWLEDGE OF THE SUJECT.  There are
a bunch of kids...they are handed a test that has four questions on it...
as they start to work on the problems, they realize that they haven't
a chance of finishing all four questions, and they will be lucky to finish
three...some kids are really suave and cool, they just keep working without
worrying about it.  Some kids are a little more tense...they panic...they
loose their ability to concentrate.  They don't finish *any* of the questions.
They fail, and the kids who were better test-takers pass.  A great method
for sorting out which kids are panicky, but it tells you *nothing* about
which kids knew the math better.

My very first test in college was in Calculus.  I left the test in tears,
positive I had failed, or at least done very poorly, and contemplated
suicide. I was so upset that I couldn't study at all for the Chemistry 
test the next day, so I did poorly on *that*.  Then I got the test in
Calc back - I had gotten a 65%, as bad a grade as I had thought.  but that
had been scaled to a B!!!  I had been on the verge of dropping out of
school my first month for a B!

*There* is you fair application of statistics. Yah.

> -- a test were 1/2 the class gets
>    95% or more doesn't tell me a thing about how well the students were
>    prepared, as a whole -- it only tells me I asked questions that
>    everybody was able to answer.

How do you know?  Maybe all the kids were equally well prepared.  What
if (*gasp* and *horrors*!!!!!) all the kids were smart, they had all
listened in class, had all studied well and (!!!!) all understood the
material?!?!?  If your tests don't give you information about whether
the kids know the material, the problem is with your tests.  You designed
them wrong.  Not too easy, just *wrong*.

The whole idea of a curve is based on the idea that someone *must*
fail.  That there must be competition among students.  That it is more
important to know how you compare to your peers than to know how well
you understand the subject being taught.  That being better than Jane
Schmoe is more important than understanding Calculus.

Bah.

D!

    Greg,
    
    as a former college teacher I have to agree with D! on this one. My
    ideal would be that I had taught so well that everyone could get
    at least a B on my exams.
    
    If the whole class gets a grade below 60% the test was a bad one
    and the teacher a poor one.
    
    When I used to take exams it would drive me nuts to have studied
    some topic in depth and then have *no* question on the material,
    no way to show what I'd learned.
    
    So when I was writing tests I tried to ask questions on everything
    that I had taught, and to ask enough extra questions so that the
    student had a degree of flexibility in the exam. For example. I
    would write a test with 100 multiple choice questions for the student
    to pick 70, 4 essays for the student to pick 2 and 2 diagrams for
    the student to pick one. The whole exam would add up to a total
    of 100 points. 
    
    The students had to *know* the material on the essays, and the material
    on the diagrams, and the multiple choice questions were quite technical
    (this was after all biology) so an A on my tests was not a gift. But
    I also felt (and so my students told me) that my tests were fair. In
    fact I was told that out of all the courses they had taken my tests
    best tested the mastery of the material presented.
    
    A teacher who gives 'trick' tests has no business being in the teaching
    business, in my opinion.  That is not the point of teaching.
    
    Bonnie

    .24 .25 .26,
    
    I taught freshmen Calculus for one semester and I say ya gotta have
    curves (and perfect bell curves for the statisticians).  How else are 
    we gonna asign grades?  Yea, sometime people go panic on hard tests, 
    but we ain't psychologists and this is college.  Ya also gotta understand 
    that we are a bunch of underpaid grad rats and sure ain't their mommies 
    and daddies.  Sometime, this kinda thing can have some possitive results.  
    When I took Real Analysis, I went panic on the first test.  I didn't get 
    to finish on any of the problems, and I was so worried that I didn't get 
    much sleep over the subsequent weekend.  But when the test result came 
    out, I got 89 and the average of the class was 15!  From then on I knew 
    I was all set and partied for the rest of the semester. 
    
    Jus some tongue in cheek ramble...
    
    Alf
                                                           

    in re .27
    
    horsefeathers!
    
    :-)
    
    Bonnie

    Suppose your salary and performance reviews were done on a bell-shaped
    curve? We'd have the following breakdown:
    
    Rating       Percent of employees        
                 getting this rating
    
    1           10 
    2           15
    3           50
    4           15 
    5           10
    
    Since Digital no longer uses a 4 rating, the bottom 25 percent would be
    rated as 5, and fired if they didn't show improvement. 
    
    It would solve the excess employee problem. After all, college should
    reflect real life. And vice versa. 
    
    Bruce

    re .29
    
    The 4 rating was reinstated during FY90
    
    
    Judi
    

    
    >>the bottom 25 percent would be
    >>rated as 5, and fired if they didn't show improvement.
    
    Not exactly...
    
    We've had reviews come through with a 5 rating and a pay
    *increase* attached to them!  Yes folks, truth is stranger than
    fiction.

    If nobody in the class gets above, say 40%, then the most likely cause
    has to be the teacher, no?  Unless by amazing coincidence it is an
    entire class of goof-offs.

Re: .24 
    
Greg, as a former student and teacher, I'm with Bonnie and D! on 
this one, too.


>    And, by the way, I was known for giving bitchy tests -- nobody ever got
>    100% on one of my exams.  The high score was typically 80-85%.  I
>    believe in "stretching" the student -- a test were 1/2 the class gets
>    95% or more doesn't tell me a thing about how well the students were
>    prepared, as a whole -- it only tells me I asked questions that
>    everybody was able to answer.


Maybe I missed something here.  If everybody was able to answer
the questions, doesn't that mean they were prepared?   If not, 
perhaps you could clarify the difference for me.

Maryellen

    .33 and others,
    
    A math test is not a Jeopardy game where you either know the answer or
    you don't.  Memorizing a bunch of theorems will help you very little in
    a math test.  Mathematicians often talk about "mathematical maturity"
    when they evaluate math students.  Math tests are geared at testing
    such "maturity".  As a matter of fact, many of the math tests I have
    taken are "open book", but the textbooks really offer very little help 
    during the test.
    
    And folks, the first few math classes, more often than not, are geared
    at finding out the talents in math, science and engineering, so the
    students who don't do well can switch to something else without wasting
    a lot of time.  Finally, although it is very important for students to
    work hard, universities aren't really in the business of rewarding hard
    work.  Discovering and nurturing talents is what it is all about.
    
    Alf

    
    I have to admit, I can certainly see both sides to this.
    
    I like math a lot more than the average person. I love word problems, I
    play with numbers, I can recall most of my geometry and trig theorems,
    etc.
    
    I can understand that to someone who loves math, a math test is testing
    your ability see work with mathematics for the sake of math. To use
    your mind to explore what can be done with mathematics, etc.
    
    On the other hand: to most non-math majors, math is the key to
    understanding physics and chemistry, etc, but is ONLY that: a tool. So,
    the most helpful and appropriate test is to determine whether you have
    learned enough about math to be able to apply it to what you're REALLY
    after.
    
    I would strongly suggest that Alf be given a class of math majors, most
    of whom would enjoy his exams, and his style. For the non-math majors
    who simply need to know how to use math to acheive an end, having to
    sit through a semester of Alf's tests seems unreasonable. In the case
    where Alf knows that his class is mixed, he should consider the needs
    of his students first, and his own love of math, second. The members of
    his class who also love math will still make themselves known, and he
    can encourage them after class...
    
    If Alf WAS teaching math majors, his style seems quite appropriate. If
    you aren't so in love with math that the "tricks" turn you on... find
    another field.

    .35,
    
    I mostly agree with you.  However, I really think at Freshmen Calculus
    level, there isn't much of a difference between the two.  These courses
    are really designed to re-orient a student's mind into a
    mathematical/scientific/engineering perspective, and the "tricks" you
    are talking about doesn't come in until junior level, but by then,
    there are different math courses for math and engineering students.
    
    Alf

    When I was attending MIT, it was common for the class average to be in 
    the 75-85% range.
    
    In my engineering classes, it was not uncommon for the class ave. to be
    about 60-70%.  I heard of cases in the Chem E. department of class ave
    being 35%.
    
    And we were paying $14000 in tuition every year.  The rational behind
    this is that if everyone gets 95% on the test, you weren't challenged,
    you didn't have to think.
    
    I think that there were far more people who convinced themselves that
    they couldn't do math, than there were people that really could not
    grasp the concept.  But then math has always come easy for me.
    Except for line integrals, which I can't do to this day.
    
    Lisa

    The question  is what, if anything, (raw) grades should mean. Does
    100%  mean that you know everything about the subject, or all that
    you  need  to  know to go on to something else? I prefer the first
    interpretation,  which  implies that almost nobody should ever get
    100% (In most of my classes, the highest mark on any test would be
    in  the  80-90%  range.) I liked it that way, as there were always
    interesting  problems  on  the  tests,  and my inevitable careless
    mistake didn't make it impossible for me to get the best grade.

    But it  really  doesn't matter what the raw scores are, as long as
    the  curve  is reasonable not only for the present class, but also
    compared  to  other  classes.  There are different styles, and the
    students should be able to understand that by the time they get to
    college.

--David

    .37,                                         
    
    I am not sure if this helps.  One way to look at line integral is to
    consider it as a generalization of the regular integral in the
    following way.
    
    The intuitive meaning of a regular integral is the "area under the
    curve" if we have a function that takes real numbers to real numbers.  
    Now if you take the straight line of X-axis and "curve" it in the X-Y plane
    then the same "area under the curve" becomes the result of the line 
    integral over a line in the X-Y plane.
    
    Alf 

    My problem with line integrals was that I would invariably get zero for
    my answer when I was supposed to get a non-zero quantity and vice
    versa.  This greatly impaired my study of conservative forces.
    
    One of these days I should splurge on the book "Div, Grad, Curl" and
    finally learn this stuff.
    
    I thought it was weird that I could get an "A" in Calc I, and an "A"
    in Diff Eq., yet do "C" level work in Calc II.  Could it have been my
    recitation instructor, an old fogey-stogey who told me from day 1 that
    I would fail the class?
    
    Hmmmmmm, I wonder.....I did do much better after I went up to the
    professor himself, told him my grades, told him that my TA said I was
    going to fail.....he looked at my work for about 3 seconds, and said "get a
    60 on the final and you'll get a C, in fact even if you get a 0 on the
    final you'll still pass".....
    
    The only time I ever did a line integral properly was on that final....
    DON'T ask me to do one today....
    
    Lisa

    .40,
    
    Hmm, I thought you were an EE major in MIT, but now I am beginning to
    believe that you were a CS major since I can't imaging anyone going
    through the E/M courses without line integral.
    
    Alf

    I had to take E/M second term my freshman year.  I did fine as long as
    I didn't have to figure out whether a forcewas conservative or not.
    (I did the best on RLC circuits)
    
    Oh, I was a Materials Science and Engineering major.  I mostly dealt
    with things related to chemistry.  I specialized in microelectronic
    processing.
    
    Lisa

    .42,
    
    That explains it.  Now you got my curiosity up.  In E/M, there are a
    lot of surface integrals, do you have problem with that too?
    
    Alf

    Any integral sign with a circle on it will strike fear into my heart.
    
    Lisa

    .44,
    
    Lisa, I just came up with an idea (well probably too late).  Any
    integral sign with a circle on it means you are either integrating over
    a close loop or a close surface, and there you can use the Stokes'
    theorem to tranform it into a direct integral problem.
    
    I think you just got a bad instructor or TA in this course.  Anyone who
    can handle things like surface of evolution should have no problem with
    line or surface integral.  I bet I can fix the problem in less than 3
    hours, but I guess the point is moot now.
    
    Alf