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Upcoming Seminars
WEDNESDAY, January 23, 2008
COLLOQUIUM (FACULTY CANDIDATE) PSA 206 9:00 a.m.
Luis Saldanha, Portland State University
"Students Exploring Connections between Sampling
Distributions and Statistical Inference in the Context of
Instruction Involving Repeated Sampling"
ABSTRACT: Construing a collection of values of a sample
statistic as a distribution is central to developing a coherent
understanding of statistical inference. This talk discusses key
developments that unfolded over part of a classroom teaching
experiment designed to support a group of high school students
in developing such a construal. Instruction began by engaging
students in activities that focused their attention on the
variability among values of a common sample statistic. There
occurred a shift in students' attention and discourse away from
individual values of the statistic and toward a collection of
such values as a basis for inferring the value of a population
parameter. This was followed by their comparisons of such
collections and by the emergence and application of a rule for
deciding whether two such collections were similar. In the
repeated application of their decision rule students structured
these collections as distributions. We characterize aspects of
these developments in relation to students' classroom
engagement, and we explore evidence in students' written work
and classroom conversations that points to their reasoning and
the influence of instruction.
Refreshments will be served in PSA 206 at 8:45 a.m.
THURSDAY, January 24, 2008
DISCRETE MATH AND ALGORITHMS SEMINAR BYENG 210 1:00 p.m.
Christian Scheideler, Technical University of Munich
"An Adaptive Scheme for Redundant and Fair Storage in Dynamic
Heterogenous Storage Systems"
ABSTRACT: We consider the problem of designing an adaptive hash
table for redundant data storage in a system of storage devices
with arbitrary capacities. Ideally, such a hash table should
make sure that (a) a storage device with x% of the available
capacity should get x% of the data, (b) the copies of each data
item are distributed among the storage devices so that no two
copies are stored at the same device, and (c) only a near-
minimum amount of data replacements is necessary to preserve
(a) and (b) under any change in the system. Hash tables
satisfying (a) and (c) are already known, and it is not
difficult to construct hash tables satisfying (a) and (b).
However, no hash table is known so far that can satisfy all
three properties as long as this is in principle possible. We
present a strategy that solves this problem for the first time.
As long as (a) and (b) can in principle be satisfied, our
scheme preserves (a) for every storage device within a
(1 ± epsilon) factor, with high probability, where epsilon > 0
can be made arbitrarily small, guarantees (b) for every data
item, and only needs a constant factor more data replacements
than minimum possible in order to preserve (a) and (b).
COMPUTATIONAL AND APPLIED MATHEMATICS PROSEMINAR
GWC 487 3:15 p.m.
Mark Iwen, University of Michigan
"Faster Fourier Transforms via Compressed Sensing"
ABSTRACT: I will discuss a recently proposed Deterministic
sublinear-time Sparse Fourier Transform algorithm (hereafter
called DSFT). DSFT can exactly reconstruct the Fourier
transform (FT) of an N-bandwidth signal f, consisting of B << N
non-zero frequencies, using O(B^2 log^4(N)) time and
O(B^2 log^3(N)) f-samples. DSFT works by taking advantage of
natural aliasing phenomena to hash a frequency-sparse signal's
FT information modulo O(B log(N)) pairwise coprime numbers via
O(B log(N)) small Discrete Fourier Transforms. Number theoretic
arguments then guarantee the original DFT frequencies/
coefficients can be recovered via the Chinese Remainder
Theorem. DSFT's usage of primes makes its runtime and signal
sample requirements highly dependent on the sizes of sums and
products of small primes. Thus, we can use analytic number
theoretic techniques to generate (asymptotic) bounds for DSFT.
Applications, algorithmic improvements, and implementation
issues will also be discussed.
FRIDAY, January 25, 2008
COLLOQUIUM (FACULTY CANDIDATE) PSA 206 2:00 p.m.
Michelle Cirillo, Iowa State University
"On Becoming a Geometry Teacher: A Longitudinal Case Study of
One Teacher Learning to Teach Proof"
ABSTRACT: Currently, exposure to proof at the K-12 level is
mainly limited to a brief topic taught in the tenth-grade. In
addition, research has shown that students' beliefs about proof
are often unproductive and unsupportive of a positive
disposition toward writing proofs. Thus, the teacher and the
activities designed by the teacher are critical components to
students' understanding of proof. In this study, I look into
one novice teacher's classroom to understand how he cultivates
the notion of proof and proving in his high school geometry
class. I seek to explore how and why this teacher's proof-
related discourse practices changed across three years. In this
talk, I will first discuss some of the literature that I am
using to ground this work. Second, I will provide some context
to the study. Finally, I will discuss how I analyzed the data
and the findings of this study.
Refreshments will be served in PSA 206 at 1:45 p.m.
MATH BIO SEMINAR ECG G237 3:40 p.m.
Kailash C. Patidar, University of the Western Cape, South Africa
"On the Selection of Non-Standard Finite Difference Modeling
Rules"
ABSTRACT: The non-standard finite difference methods are
attracting many applied mathematicians. Because of their ease
in construction, even engineers have started using them (see,
e.g. K.C. Patidar, On the use of non-standard finite difference
methods, Journal of Difference Equations and Applications, 11
(2005), 735-758; for such works). In this talk, we will
consider a variety of ODEs and PDEs which involve one or more
parameters. We discuss the role of these parameters and
associated difficulties when these parameters take certain
values. A number of numerical methods will then be discussed
where the main emphasis will be on the role of some specific
non-standard modeling rules.
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