Off on a Tangent
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A Fortnightly Electronic
Newsletter from the Hope
College Department of Mathematics
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This
week's colloquium is a puzzler
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Title:
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Counting RSK Puzzles |
Speaker:
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Prof. David Murphy, Hillsdale College
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Time:
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Thursday,
April 9 at 4:00 p.m.
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Place:
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VWF
104
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Abstract: Logic puzzles such as Sudoku and Kakuro, in which
numbers are placed in arrays subject to certain conditions, have
recently become popular. In this talk, I will discuss a new
family of puzzles, which I call RSK puzzles, based on the
Robinson-Schensted-Knuth correspondence in combinatorics. My goal
is to count the number of solutions for a given RSK puzzle, as this
number has applications in combinatorics, algebraic geometry and
representation theory.
Please join us for refreshments
in VWF 222 at 3:45 p.m.
Dogs
might know calculus, do you?
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Title:
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Do Dogs Know
Calculus
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Speaker:
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Prof. Tim Pennings |
Time:
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Wednesday, April 15
at 8:00 p.m.
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| Place: |
VWF
104
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Abstract: A standard
calculus problem is to find the quickest path from a point on shore to
a point in the lake, given that running speed is greater than swimming
speed. Elvis, my Welsh Corgi, has never had a calculus
course. But, when we play “fetch” at Lake Michigan, he appears to
choose paths close to the calculus answer. In this talk we reveal
what was found when we experimentally tested this ability.
Elvis will be available for follow-up
questions.
Student
Research Colloquium
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Title:
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Necklaces,
Symmetry
and Irreducible Representations of Wreath Products
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Speakers:
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Sarah Cobb, Wheaton College, and Josh
Kinder, Hope College |
Time:
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Friday,
April 17 at 4:00 p.m.
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| Place: |
TBA -- watch for the
flyers advertising the talk!
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Abstract:
The problem of
finding a complete set of
irreducible representations of wreath products of cyclic groups can be
solved
using necklaces. Each necklace in the
set of k-bead, n-color necklaces that
is distinct under rotation can be used to
form a degree-k representation of Ck
wr Cn. If a necklace has
some nontrivial s-fold rotational symmetry, then the
degree-k representation formed from that
necklace will reduce into s nonequivalent
irreducible representations of degree k/s. After reducing representations that come from
necklaces with nontrivial rotational symmetry, the set of distinct k-bead, n-color necklaces gives each
irreducible representation of Ck wr Cn
exactly
once.
Note the nontypical
day and time for this colloquium
Students
participate in Research Celebration
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Hope’s mathematics department was well
represented in the 8th Annual Celebration of Undergraduate Research and
Creative Performance on March 27. Poster presentations were given
by four groups of students.
Kathryn Johnson and Zachary Mitchell presented “Turning out the
Lights.” They studied a generalization of the game Lights Out and
used graph theory to determine which graphs in certain families were
winnable. Drs. Stephanie Edwards and Darin Stephenson were their
mentors.
Joshua Kinder’s research was titled,
“Necklaces, Symmetry, and Irreducible Representations of Wreath
Products.” Working with mentor Dr. Mark Pearson, Josh’s research
in algebra used necklaces to find a complete set of irreducible
representations of wreath products of cyclic groups.
Dan Lithio and Forrest Gordon worked with Dr. Tim Pennings on
“Pseudo-Orbit Shadowing in Continuous Decreasing Functions on the Unit
Interval.” They found conditions for a decreasing continuous
function on the unit interval to have a shadowing property.
Brian McLellan’s statistical research looked at “Incorporating
Duplicate Genotype Data into Linear Trend Tests of Genetic Association:
Methods and Cost-effectiveness.” He studied a method of including
duplicate genotype data in linear trend tests of genetic association
that yielded increased power. Brian's mentors were Drs. Nathan
Tintle and Airat Bekmetjev.
Students
join Pi Mu Epsilon
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Fifteen students were
recently inducted into the Michigan Delta chapter
of Pi Mu Epsilon. The purpose of this national mathematics
honor society is to promote scholarly activity in mathematics among the
students in academic institutions. Students were invited to join
based on their gpa in their mathematics courses as well as their
overall gpa. The induction ceremony was
held Wednesday, April 1. After the short ceremony everyone
enjoyed our tradition of eating pie.
The new members of Pi Mu Epsilon are Daryl Andresen, Lydia Benish, Joel
Blok, Kelsey Bos, Andrea Eddy, Terra Fox, John McNutt, Jeffrey
Minkus, Zachary Mitchell, Megan Pearson, Christopher Ploch,
Alexander Schwiebert, Kylie Topliff, Blair Williams, and Valerie Winton.
Students
compete in the LMMC
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The 33rd Annual Lower Michigan
Mathematics Competition was held
at Albion College last Saturday, April 4. Working in teams,
students
from colleges and universities in Michigan gathered to
challenge themselves on 10 interesting problems.
Hope sent 2 vans of 6 teams and an undetermined number of donuts to the
competition. Judging from the photograph below, a good time was
had by all. (The photo of these smiling faces was taken before
they stopped for Plainwell Ice Cream!)
Front
row, left to right: Terra Fox, Kim Klask, Heather Thompson, Colin
Rathbun, Danelle Koetje, Nathaniel Martin.
Second row: Kristian
Cunningham, David Boothe, Chris Jordan, Ryan
Johnson, Bruce Kraay, Jessalyn Bolkema, Eric Hallquist, Laura
Petraskey, Zach Mitchell, Aaron Cinzori
Top: Scott DeClaire
Two
mathematics professors receive awards
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Two mathematics professors were honored
earlier this semester with awards. Last month
Dr. Mark Pearson received the
"Dean's Science Division Mentoring/ Advising/ Teaching Award."
This award recognizes a faculty member who has gone beyond the call of
duty in
being an exceptional mentor, advisor and teacher to students, and the
winner is selected by a panel of students.
In January, Prof. Todd Swanson
received the "Janet L. Andersen Excellence in Teaching Award."
This award is presented to
faculty members who have been teaching at Hope for at least seven years
and who have demonstrated recognizable excellence in specific
activities or aspects of teaching.
The
Problem of the Fortnight
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The last
Problem of the Fortnight for the 2008 - 09 academic year:
Determine the last two digits of
220,000,009
+ 620,000,009 + 720,000,009
Write
your solution (not just the answer!) on the back of your final exam
schedule (keep a copy for yourself -- you'll need
it!) and drop
it off at Dr.
Pearson's office (VWF 212) by noon
on Friday, April 17.
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. Ben
Werken, Professor Ben Graydon).
Good luck, and have
fun!
Problem
Solvers of the Fortnight
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The last problem of the fortnight was:
1. Which of the five numbers 2007, 2008, 2009, 2010, and 2011 has
the largest number of
factors, and which one has the fewest
number of factors?
2.
Determine the total
number of factors for the number
N
= (2007)(2008)(2009)(2010)(2011).
For example, 21
has 4 factors (1, 3, 7, 21) and 20 has 6 factors (1, 2,
4, 5, 10, 20).
Congratulations
to the following problem solvers of the fortnight, who determined that
2010 has the largest number of factors and 2011 the fewest, and that N
has 3840 factors: Zach Mobley, Zachary
Mitchell, Jeff Minkus, Jessica Clouse, Kyle Gibson, Cori Schild, Kelly
Shugart, Dan Waldo, Eric Lunderberg, Morgan Willming, Brian McLellan,
Cameron Evans, Lydia Rau, and Evan Ormiston.
All
I really need is love, but a little chocolate now and then doesn't hurt!
~ Charles Schulz via Lucy Van Pelt
The last problem of the fortnight was: