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Agent of Change: NSF Sponsored Mathematics Curriculum Development
(NCSM Journal of Mathematics Education Leadership, 2007)
these factors is the lack of consensus of state standards on what and when certain topics in mathematics should be addressed. The variability of grade placement of key mathematics learning goals across different state standards results in excessive repetition...
What is the Focus and Emphasis on Calculators in State-Level K-8 Mathematics Curriculum Standards Documents?
(NCSM Journal of Mathematics Education Leadership, 2006)
We conducted our own analysis of official state mathematics curriculum standards documents so that we might understand and describe the extent to which states support use of calculators in elementary and middle school mathematics classes...
Examination of the levels of Cogitive Demand Required by Probability Tasks in Middle Grades Mathematics Textbooks
(Statistics Education Research Journal (SERJ), 2007-11)
We analyze probability content within middle grades (6, 7, and 8) mathematics
textbooks from a historical perspective. Two series, one popular and the other
alternative, from four recent eras of mathematics education ...
Average Normalisations of Elliptic Curves
(Australian Mathematical Society, 2002)
Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field Fp is isomorphic to a curve y2 = x3 +ax+b
with a and b of size O(p3/4). In this paper, we show that almost all elliptic curves ...
On the norm of an idempotent Schur multiplier on the Schatten class
(American Mathematical Society, 2004)
We show that if the norm of an idempotent Schur multiplier on the Schatten class Sp lies sufficiently close to 1, then it is necessarily equal to 1. We also give a simple characterization of those idempotent Schur multipliers ...
Determining and Responding to Teacher Professional Development Needs
(2008)
professional development for teachers was not the only necessary component for moving school organizations forward. As a result, the initial premise of the ALM project was based on the idea that revitalizing school mathematics programs required full, systemic...
The vanishing of Tor_1^R(R^+,k) implies that R is regular
(2003)
Let (R,m,k) be an excellent local ring of positive prime characteristic. We show that if Tor_1^R(R^+,k) = 0 then R is regular. This improves a result of Schoutens, in which the additional hypothesis that R was an isolated ...
The Application of a Simple Method for the Verification of Weather Forecasts and Seasonal Variations in Forecast Accuracy
(American Meteorological Society, 2002-08)
) National Weather Service (NWS) Office for mid-Missouri over a period of 416 days with the goal of demonstrating the utility of this method. Zone forecasts were chosen because these forecasts are typically what the public will receive either directly...
Some unusual identities for special values of the Riemann zeta function
(2001)
In this paper, we use elementary methods to derive some new identities for special values of the Riemann zeta function.
The F-signature and strong F-regularity
(2002)
We show that the F-signature of a local ring of characteristic p, defined by Huneke and Leuschke, is positive if and only if the ring is strongly F-regular.
Holonomy and gravitomagnetism
(American Institute of Physics, 2002)
We analyse parallel transport of a vector field around an equatorial orbit in the Kerr and stationary axisymmetric spacetimes that are reflection symmetric about their equatorial planes. As in the Schwarzschild spacetime, ...
Number Theoretic Designs for Directed Regular Graphs of Small Diameter
(Society for Industrial and Applied Mathematics, 2004)
In 1989, F. R. K. Chung gave a construction for certain directed h-regular graphs of small diameter. Her construction is based on finite fields, and the upper bound on the diameter
of these graphs is derived from bounds ...
Nonaliquots and Robbins Numbers
(Polish Academy of Sciences, Institute of Mathematics, 2005)
Let '(•) and _(•) denote the Euler function and the sum of divisors function, respectively. In this paper, we give a lower bound for the number of m ≤ x for which the equation m = _(n)−n has no solution. We also show that ...
Let the Market Decide
(Education Next, 2001)
By thoroughly standardizing teacher pay, the single salary schedule suffers from a major flaw: It deprives the managers of public schools of the authority to adjust an individual teacher's pay to reflect both his performance and market realities...
Towards Faster Cryptosystems, II
(American Mathematical Society, 2005)
We discuss three cryptosystems, NTRU, SPIFI , and ENROOT, that are based on the use of polynomials with restricted coefficients.
When does the F-signature exist?
(2005)
We show that the F-signature of an F-finite local ring R of characteristic p > 0 exists when R is either the localization of an N-graded ring at its irrelevant ideal or
Q-Gorenstein on its punctured spectrum. This extends ...
Non-residues and primitive roots in Beatty sequences
(Australian Mathematical Society, 2006)
We study multiplicative character sums taken on the values of a non-homogeneous Beatty sequence Bα,β = {⌊αn + β⌋ : n = 1,2,3,…}, where α,β ∈ R, and α is irrational. In particular, our bounds imply that for every fixed ε > ...
Ubiquity of simplices in subsets of vector spaces over finite fields
(2007)
We prove that a sufficiently large subset of the $d$-dimensional vector space over a finite field with $q$ elements, $ {\Bbb F}_q^d$, contains a copy of every $k$-simplex. Fourier analytic methods, Kloosterman sums, and ...
Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies
(Wiley, 2009)
We derive an explicit Lorentz-invariant solution of the Einstein and null geodesic equations for data processing of the time delay and ranging experiments in the gravitational field of moving gravitating bodies of the Solar ...
Prime divisors of palindromes
(Springer Verlag, 2005)
In this paper, we study some divisibility properties of palindromic numbers in a fixed base g ≥ 2. In particular, if PL denotes the set of palindromes with precisely L digits, we show that for any sufficiently large value ...