Off on a Tangent
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A Fortnightly Electronic
Newsletter from the Hope
College Department of Mathematics
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Colloquium
speaker will present his favorite calculus problem
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Title:
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My Favorite Calculus Problem |
Speaker:
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Prof. Charles Hampton, Calvin College
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Time:
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Thursday,
February 19 at 4:00 p.m.
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Place:
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VWF
104
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Abstract: For more than a decade I
have used on problem from the history of calculus to challenge (and
perhaps exasperate) my calculus students. Bernoulli first solved
it in the early 18th century. We will examine how he (and my
students) do it.
Please join us for refreshments
in VWF 222 at 3:45 p.m.
Students
are on their way to becoming actuaries
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Congratulations go out to
Kelsey Bos and Kylie Topliff. They both passed the first
actuarial exam
recently after completing Math 361: Introduction to Probability with
Prof. Bekmetjev.
If you are interested in learning what an actuary
is or what an actuary does visit http://www.beanactuary.org.
To find out more about the Hope actuarial
preparation program visit http://math.hope.edu/tintle/actuarial_program.html or come talk to Prof. Tintle .
At 4:00 a.m. on January 30, Terra Fox,
Kimberly Klask, Thao Le, Andrea Eddy,
Professor Edwards, and her daughter Maya embarked on
a ten hour trip to
Lincoln, Nebraska for the Nebraska Conference for Undergraduate
Women in
Mathematics. There they attended several talks and panel
discussions, and were able
to explore the exciting downtown Lincoln area.
The students were able
to learn about and discuss future graduate school and career options,
as well as attend short talks about REU projects that other
research that undergraduate women have accomplished. The presentations
ranged from the use of wavelets to the mathematics of the menstrual
cycle to mathematical literature to in classrooms. The panelists
gave
advice about graduate school, summer research, jobs, challenges, and
balancing career and home life. Any woman considering a career
in
math would gain a plethora of knowledge from the conference.
Information about next year's conference can be found at http://www.math.unl.edu/~ncuwm/12thAnnual.
A picture of those attending the
conference can be found here. Can you
find any Hope students in the crowd?
The
eighth edition of Probability
and Statistical Inference, co-written by Professor Emeritus
Elliot Tanis, was released
earlier this
semester by Prentice-Hall
Inc. First published in 1977, Probability
and Statistical Inference
is an introductory
calculus-based text geared toward
college juniors
and seniors. Dr. Tanis, who retired from teaching at Hope in
2000,
co-wrote the book with Dr. Robert Hogg of the University of Iowa.
Manhole covers are usually circular so
they can't fall in the hole. If manhole covers were square, for
example, they might fall in the hole when not set in properly.
Circles are, however, the only curves with a constant width. A
Reuleaux triangle also has a constant width. This type of
triangle can be constructed by starting out with an equilateral
triangle and making circular arcs on the sides by using the opposite
vertex as the center. For more information on Reuleaux triangles
visit http://en.wikipedia.org/wiki/Reuleaux_triangle.
Have you seen some mathematics professors
standing a little taller lately? (Or perhaps a bit more
relaxed.) If so, it could be because the board of trustees of
Hope College recently granted promotions to three mathematics
professors. Professors Bekmetjev and Pearson were granted tenure
and promoted
to the rank of associate professor. Prof. Stephenson was promoted
to the rank of
professor. Congratulations goes out to each of them on their
accomplishments.
The
Problem of the Fortnight
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Maya
would like you to help her out. She needs to integrate the
following.
∫
[√(1
+ x) + √(1 - x) ] / [√(1 + x) - √(1 - x) ]
dx
Be
sure to show all
your work. You may use a computer algebra program to check your
answer, but you must solve the integral by hand; computer solutions
will not be accepted.
Write
your solution (not just the answer!) on a graph of your favorite
function
-- between the x-axis and the curve, of
course -- and
drop it by Dr.
Pearson's office (VWF 212) by noon
on Friday, February 27.
As always, be sure
to write your name, the name(s) of your
professor(s), and your math class(es) on your solution (e.g. N.T.
Grate, Prof. M.T. Set, Math 172).
Good luck, and have
fun!
Problem
Solvers of the Fortnight
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The last problem of the fortnight was:
Integrate ∫
e 3√x dx, where 3√x denotes the cube
root of
x. Be sure to
show all
your work.
Congratulations
to the following problem solvers of the fortnight, who used
substitution and integration by parts (twice) to compute the
integral: Jared Wabeke, Eric Dulmes, Joshua Roberts, Amy
Speelman, Kylie Topliff, Blair Williams, Jonathan Winne, Joel Blok,
Kelsey Bos, Scott DeClaire, David Jenkins, Kyle McLellan, Patrick Lutz,
Eric Lunderberg, Lute Olson, Andrea Eddy, Lucas Johnson, Zachary
Mitchell, Elena Caruthers, Drew Reyelts, Ashley Wortelboer, Jordan
Ritsema, Stephen Burgett, Jon Wielenga, Kaily Gumpper, Kristian
Cunningham, Elizabeth Weidenhaft, Benjamin Strong, Ryan Converse, and
Mark Gilmore. Mark Gilmore's integral use of integration by parts
is displayed in his solution on the bulletin board.
Pure
mathematics is the world's best game. It is more absorbing than
chess,
more of a gamble than poker, and lasts longer than Monopoly. It's
free. It can be played anywhere - Archimedes did it in a
bathtub.
~Richard
J. Trudeau, Dots and Lines
The last problem of the fortnight was: