Tuesday, November 16, 2010
MGB Officer Nominations
The election of new officers is only two weeks away! If you have been nominated for an office, please contact Andrew or Alina to accept/decline the nomination. Office descriptions are available at http://math.uiowa.edu/MathGraduateBoard/index_files/officerinfo.html
GAUSS: The Shadowing Property onn the Unit Interval
Our GAUSS speaker this week is first year math graduate Alex Berrian,
and the title of his talk is "The Shadowing Property on the Unit
Interval." Check the bottom of this e-mail for his abstract. The
main point is this: Alex is going to be talking about analysis
research he did as an undergrad in an REU (Research Experience for
Undergraduates) program, but he would also like to spend some time
talking about REU programs. If you are an undergrad math major then
you should come to GAUSS today to learn about REU programs. We would
like to get you excited about these excellent opportunities to
Experience real mathematics Research. If you are one of the many math
grads who at one point was in an REU or involved in an REU, you are
welcome to come join in the conversation. The final category of
people who should attend are people who like analysis. Snacks will be
provided.
Check http://math.uiowa.edu/~
GAUSS-related news. If you have any questions, comments, suggestions
concerning GAUSS feel free to e-mail me or Trent.
Your GAUSS co-organizers,
Ross and Trent
Speaker: Alex Berrian
Title: The Shadowing Property on the Unit Interval
Date time and location: Tuesday, November 16, 4:30 PM, 118 MLH
Abstract:
Try this with your TI-83 or similar calculator: Punch in .9 and hit
ENTER. Hit the Cosine button, and then hit ENTER. You get cos(.9),
which is about .62. Hit ENTER again, and you get cos(cos(.9)), which
is about .81. Now hit ENTER a whole lot of times. Eventually you'll
get a number close to .74. We call this process an iteration of the
function cos(x). Try doing this again, but start with .1 instead.
Guess what? After a while, you get the same number! Do this with any
number between 0 and 1 and you will arrive at the same result. Cool,
right? But wait - the calculator must truncate its answer each time in
order to do its calculations. How do you know that the calculator's
result for the nth iteration of cos(x) is close to the actual value?
One way of characterizing the accuracy of such an iteration is called
the shadowing property, which cos(x) happens to satisfy on the closed
unit interval [0,1], but which some functions do not. I'll explain
research I did during a summer NSF REU program with two other students
that gives a condition for certain functions to satisfy the shadowing
property on [0,1]. Undergraduates who want to know what REU programs
are like, as well as people who enjoy Analysis like me, are very much
encouraged to attend!
and the title of his talk is "The Shadowing Property on the Unit
Interval." Check the bottom of this e-mail for his abstract. The
main point is this: Alex is going to be talking about analysis
research he did as an undergrad in an REU (Research Experience for
Undergraduates) program, but he would also like to spend some time
talking about REU programs. If you are an undergrad math major then
you should come to GAUSS today to learn about REU programs. We would
like to get you excited about these excellent opportunities to
Experience real mathematics Research. If you are one of the many math
grads who at one point was in an REU or involved in an REU, you are
welcome to come join in the conversation. The final category of
people who should attend are people who like analysis. Snacks will be
provided.
Check http://math.uiowa.edu/~
GAUSS-related news. If you have any questions, comments, suggestions
concerning GAUSS feel free to e-mail me or Trent.
Your GAUSS co-organizers,
Ross and Trent
Speaker: Alex Berrian
Title: The Shadowing Property on the Unit Interval
Date time and location: Tuesday, November 16, 4:30 PM, 118 MLH
Abstract:
Try this with your TI-83 or similar calculator: Punch in .9 and hit
ENTER. Hit the Cosine button, and then hit ENTER. You get cos(.9),
which is about .62. Hit ENTER again, and you get cos(cos(.9)), which
is about .81. Now hit ENTER a whole lot of times. Eventually you'll
get a number close to .74. We call this process an iteration of the
function cos(x). Try doing this again, but start with .1 instead.
Guess what? After a while, you get the same number! Do this with any
number between 0 and 1 and you will arrive at the same result. Cool,
right? But wait - the calculator must truncate its answer each time in
order to do its calculations. How do you know that the calculator's
result for the nth iteration of cos(x) is close to the actual value?
One way of characterizing the accuracy of such an iteration is called
the shadowing property, which cos(x) happens to satisfy on the closed
unit interval [0,1], but which some functions do not. I'll explain
research I did during a summer NSF REU program with two other students
that gives a condition for certain functions to satisfy the shadowing
property on [0,1]. Undergraduates who want to know what REU programs
are like, as well as people who enjoy Analysis like me, are very much
encouraged to attend!
Tuesday, November 2, 2010
Pizza on Wednesday
Due to the success of last week's pizza fundraiser (we raised
$25!), I will be in the Muhly lounge this Wednesday between noon and
1pm again distributing pizza slices and beverages and collecting your
$2.50 contributions.
MGB has recently made a commitment to raise funds. These monies could
be used for mathematical events organized by us such as SK Day, the
math modelling competition and the AMS Central Section meeting to be
held here in the spring. We hope you will join us this Wednesday for
a slice (or two) !
$25!), I will be in the Muhly lounge this Wednesday between noon and
1pm again distributing pizza slices and beverages and collecting your
$2.50 contributions.
MGB has recently made a commitment to raise funds. These monies could
be used for mathematical events organized by us such as SK Day, the
math modelling competition and the AMS Central Section meeting to be
held here in the spring. We hope you will join us this Wednesday for
a slice (or two) !
MGB Meeting this Wednesday
Come to the MGB meeting this Wednesday (November 3, 2010) at 4:30 in the Muhly Lounge to nominate candidates for next year's Math Graduate Board officers. The offices are described at http://math.uiowa.edu/MathGraduateBoard/index_files/officers.html We will also discuss the recent departmental review, a hot chocolate fundraiser in December, math t-shirts, and coffee in MacLean hall.
We hope to see you there!
We hope to see you there!
GAUSS: A Look at the ABC Conjecture via Elliptic Curves
Hi everyone,
The GAUSS speaker today is Gerard Koffi. He's going to be talking
about "A Look at the ABC Conjecture via Elliptic Curves: An Algebraic
Approach." All are welcome to attend, and snacks will be provided.
I'll paste his abstract at the bottom of this message.
If you'd like to keep up to date on what is happening in GAUSS, our
website is http://math.uiowa.edu/~
any questions or comments about GAUSS e-mail either me or Trent, or
talk to us in person, or write one of us a personal letter.
Finally, if you haven't voted already today is the day.
Your GAUSS co-organizers,
Trent and Ross
Speaker: Gerard Koffi
Title: A Look at the ABC Conjecture via Elliptic Curves: An Algebraic Approach
When and where: Tuesday, November 2, 2010, 4:30 P.M., 118 MLH
Abstract:
The ABC conjecture is a central open problem in number theory. It was
formulated in 1985 by Joseph Oesterle and David Masser, who worked
separately but eventually proposed equivalent conjectures. Consistent
with many problems in number theory, the ABC conjecture can be stated
in relatively simple, understandable terms. However, there are several
profound implications of the ABC conjecture. Fermat's Last Theorem is
one such implication. We study the connection between elliptic curves
and ABC triples. Two important results are proved. The first gives a
method for finding new ABC triples. The second result states
conditions under which the power of the new ABC triple increases or
decreases. Finally and if time permit, we present two algorithms
stemming from these two results.
The GAUSS speaker today is Gerard Koffi. He's going to be talking
about "A Look at the ABC Conjecture via Elliptic Curves: An Algebraic
Approach." All are welcome to attend, and snacks will be provided.
I'll paste his abstract at the bottom of this message.
If you'd like to keep up to date on what is happening in GAUSS, our
website is http://math.uiowa.edu/~
any questions or comments about GAUSS e-mail either me or Trent, or
talk to us in person, or write one of us a personal letter.
Finally, if you haven't voted already today is the day.
Your GAUSS co-organizers,
Trent and Ross
Speaker: Gerard Koffi
Title: A Look at the ABC Conjecture via Elliptic Curves: An Algebraic Approach
When and where: Tuesday, November 2, 2010, 4:30 P.M., 118 MLH
Abstract:
The ABC conjecture is a central open problem in number theory. It was
formulated in 1985 by Joseph Oesterle and David Masser, who worked
separately but eventually proposed equivalent conjectures. Consistent
with many problems in number theory, the ABC conjecture can be stated
in relatively simple, understandable terms. However, there are several
profound implications of the ABC conjecture. Fermat's Last Theorem is
one such implication. We study the connection between elliptic curves
and ABC triples. Two important results are proved. The first gives a
method for finding new ABC triples. The second result states
conditions under which the power of the new ABC triple increases or
decreases. Finally and if time permit, we present two algorithms
stemming from these two results.
Tuesday, October 26, 2010
Gauss: What to do with 120 dodecahedra
Dear grads, undergrads, and faculty,
Our GAUSS speaker today is David Gay. He'll be giving a talk titled,
"What to do with 120 dodecahedra." Note that this is information is
not the same as in the seminar announcement. His abstract will be
provided at the bottom of this e-mail.
This is where I usually type something like, "as always, snacks will
be provided." Often those snacks are store-bought cookies. However,
this week we at GAUSS have the distinct pleasure of announcing that
the snacks are being home-baked by our very own MT Padberg. So
whether you like cookies or you like dodecahedra, there are a plethora
of reasons to attend GAUSS today.
If you have any questions, comments, suggestions, etc. feel free to
contact one of your GAUSS co-organizers. We reserve the right to
ignore you, but you shouldn't let that stop you. Have a wonderful week.
Your GAUSS co-organizers,
Trent and Ross
Speaker: David Gay
Title: What to do with 120 dodecahedra.
Date, time, location: Tuesday, October 26, 4:30 PM, 118 MLH
Abstract:
You'll also need an extra dimension to make this work. I'll describe a
way to glue 120 dodecahedra together in 4-dimensional space to make a
closed 4-dimensional version of a polyhedron. BTW, a dodecahedron is a
3-dimensional polyhedron built by gluing 12 pentagons together in
3-dimensional space. I'll also show you how to draw a dodecahedron, a
skill which might come in handy some day. And, BTW, a pentagon is a
2-dimensional polygon built by gluing 5 line segments together in
2-dimensional space. And a line segment is a 1-dimensional ...?
Our GAUSS speaker today is David Gay. He'll be giving a talk titled,
"What to do with 120 dodecahedra." Note that this is information is
not the same as in the seminar announcement. His abstract will be
provided at the bottom of this e-mail.
This is where I usually type something like, "as always, snacks will
be provided." Often those snacks are store-bought cookies. However,
this week we at GAUSS have the distinct pleasure of announcing that
the snacks are being home-baked by our very own MT Padberg. So
whether you like cookies or you like dodecahedra, there are a plethora
of reasons to attend GAUSS today.
If you have any questions, comments, suggestions, etc. feel free to
contact one of your GAUSS co-organizers. We reserve the right to
ignore you, but you shouldn't let that stop you. Have a wonderful week.
Your GAUSS co-organizers,
Trent and Ross
Speaker: David Gay
Title: What to do with 120 dodecahedra.
Date, time, location: Tuesday, October 26, 4:30 PM, 118 MLH
Abstract:
You'll also need an extra dimension to make this work. I'll describe a
way to glue 120 dodecahedra together in 4-dimensional space to make a
closed 4-dimensional version of a polyhedron. BTW, a dodecahedron is a
3-dimensional polyhedron built by gluing 12 pentagons together in
3-dimensional space. I'll also show you how to draw a dodecahedron, a
skill which might come in handy some day. And, BTW, a pentagon is a
2-dimensional polygon built by gluing 5 line segments together in
2-dimensional space. And a line segment is a 1-dimensional ...?
Tuesday, October 19, 2010
GAUSS
The GAUSS speaker today is Alex Zupan, and he is giving a talk titled:
"The Hausdorff metric: the magic and the mystery." From the looks of
that title one could get the impression that Alex is a mathemagician.
His abstract will appear below.
GAUSS occurs today, Tuesday October 19, at 4:30 P.M. in 118 MLH.
Snacks will be provided and everyone is welcome to attend. We are
always looking for ways to improve GAUSS, so if you have suggestions
feel free to e-mail or talk to either Trent or me.
Your GAUSS co-organizers,
Ross and Trent
ASTRACT: Everyone learns how to find the distance between two points in
a standard precalculus class, but what about the distance between two
sets? For any two points in Euclidean space, there exists a unique
point at a given location between them. However, in the geometry of
the Hausdorff metric, intuitive facts from the realm of Euclidean
geometry are no longer valid. In this talk, we provide a glimpse into
the strange world of the Hausdorff metric. Think graph theory won't
be involved? Think again!
"The Hausdorff metric: the magic and the mystery." From the looks of
that title one could get the impression that Alex is a mathemagician.
His abstract will appear below.
GAUSS occurs today, Tuesday October 19, at 4:30 P.M. in 118 MLH.
Snacks will be provided and everyone is welcome to attend. We are
always looking for ways to improve GAUSS, so if you have suggestions
feel free to e-mail or talk to either Trent or me.
Your GAUSS co-organizers,
Ross and Trent
ASTRACT: Everyone learns how to find the distance between two points in
a standard precalculus class, but what about the distance between two
sets? For any two points in Euclidean space, there exists a unique
point at a given location between them. However, in the geometry of
the Hausdorff metric, intuitive facts from the realm of Euclidean
geometry are no longer valid. In this talk, we provide a glimpse into
the strange world of the Hausdorff metric. Think graph theory won't
be involved? Think again!
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