Off on a Tangent
|
A Fortnightly Electronic
Newsletter from the Hope
College Department of Mathematics
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Colloquium
speaker will connect mathematics and music
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Title:
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Frequency Modulation and Synthesizing Music
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Speaker:
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Prof. David Austin, GVSU |
Time:
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Thursday,
March 5 at 4:00 p.m.
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Place:
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VWF
104
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Abstract: Music and mathematics are deeply expressive
languages that reveal their mysteries through both pattern and
serendipity. This talk aims to expand the connection by
demonstrating some elegant mathematical ideas that explain how music
may be represented and even created by a computer.
We will look at the waveform
created when the G string on a guitar is picked and use this as a
starting point to understanding the nature of sound and what it takes
to recreate a sound like this.
I intend for this talk to be
accessible to undergraduates. In fact, I hope to make the ideas, which
include topics such as Fourier series and Bessel functions, very
concrete through the use of pictures and sound files.
Please join us for refreshments
in VWF 222 at 3:45 p.m.
Next
week's colloquium will focus on the Lanczos Derivative
|
Title:
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The Two Sides to the Lanczos Derivative
Story |
Speaker:
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Prof. Paul Fishback, GVSU |
Time:
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Tuesday,
March 10 at 4:00 p.m.
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| Place: |
VWF
104
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In his classic text
Applied Analysis, Cornelius Lanczos presented a technique in which one could "differentiate'' by integrating. On the
surface, Lanczos' derivative
formula bears little resemblance
to the usual derivative formula with which we are all familiar. However, a deeper investigation
leads to intriguing
connections between the Lanczos derivative and basic probability and orthogonal polynomials. These connections serve to
demonstrate that a common thread links the Lanczos Derivative to a wide class of derivative extensions and, most
importantly, to the usual derivative itself.
Note that this
colloquium will occur on Tuesday.
The
Lower Michigan Mathematics Competition
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| Contest Date: |
Saturday,
April 4 |
Location:
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Albion
College
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How to Register:
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Sign up on
the sheet on Prof. Cinzori's Door (VWF 216) or email him at
cinzori@hope.edu
|
| Registration Deadline: |
Wednesday,
March 25 |
The 33rd Annual Lower Michigan
Mathematics Competition will be held
at Albion College this year on Saturday, April 4. Students
from colleges and universities in Michigan will gather there to
challenge themselves on 10 interesting problems, working together in
teams of up to three people. The competition runs from 9:30 a.m. to
12:30 p.m. After the problem session in the morning, there will be a
break for lunch followed by a solutions session in the afternoon.
Sign-up information is shown
above. You may register as a team (of two or three) or
individually (and you will be placed on a team). Hope has a
history of strong showings at
the LMMC, including several
championships, and we'd like to regain the title this year and bring
the Klein Bottle Trophy back to Hope!
The
Problem of the Fortnight
|
An
n x n matrix is called a Latin square
if each of the integers 1, 2,
..., n occurs exactly once in
each row and each column. Find the
number of distinct 4 x 4 Latin squares.
Write
your solution (not just the answer!) on the back of a (correctly)
completed Sudoku puzzle -- which is a special kind of Latin square -- and
before you leave campus for spring break,
drop it off at Dr.
Pearson's office (VWF 212) by noon
on Thursday, March 12.
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. Ima
Square, Prof. Circular Logic, Math 111: Proving
Proofs).
Good luck, and have
fun!
Problem
Solvers of the Fortnight
|
The last problem of the fortnight was:
Maya
would like you to help her out. She needs to integrate the
following:
∫
[√(1
+ x) + √(1 - x) ] / [√(1 + x) - √(1 - x) ]
dx
Congratulations
to the following problem solvers of the fortnight: Zachary Mitchell, Katie Nelson, Laine Klopfensten, Kylie Topliff, Lucas Osterbur, Chris Jordan, Dan Waldo, Valerie Winton, Alyssa Shaler, Ryan McCall, Ryan Johnson and Scott DeClaire.
The solution is posted on the bulletin board.
Somebody just gave
me a shower radio. Thanks a lot. Do you really want music in the shower?
I guess there's no better place to dance than a slick surface
next to a glass door.
~Jerry
Seinfeld
The last problem of the fortnight was: