Mathematics, Department of
http://hdl.handle.net/2027.42/61172
2014-10-31T19:31:13ZMathematical Knowledge for Teaching High School Geometry
http://hdl.handle.net/2027.42/91279
Mathematical Knowledge for Teaching High School Geometry
Herbst, Patricio; Kosko, Karl W.
This paper documents efforts to develop an instrument to measure mathematical knowledge for teaching high school geometry (MKT-G). We report on the process of developing and piloting questions that purported to measure various domains of MKT-G. Scores on the final set of items had no statistical relationship with total years of experience teaching, but all domain scores were found to have statistically significant correlations with years of experience teaching high school geometry. We use this result to propose ways of conceptualizing how instruction-specific considerations might matter in the design of MKT items.
2012-05-28T00:00:00ZOn the Pythagorean hull of Q
http://hdl.handle.net/2027.42/61250
On the Pythagorean hull of Q
Pambuccian, Victor
1990-01-01T00:00:00ZSperner spaces and first-order logic
http://hdl.handle.net/2027.42/61173
Sperner spaces and first-order logic
Blass, Andreas; Pambuccian, Victor
We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of pointline incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even ℒ[sub]∞ω-axiomatizable. We also axiomatize the first-order theory of this class.
2003-01-27T00:00:00ZAsymptotics of rare events in birth–death processes bypassing the exact solutions
http://hdl.handle.net/2027.42/58127
Asymptotics of rare events in birth–death processes bypassing the exact solutions
Doering, Charles R.; Sargsyan, Khachik V.; Sander, Leonard M.; Vanden-Eijnden, Eric
We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth–death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining finite-difference equations alone. For the simple class of processes we consider here, exact closed-form solutions for the mean first passage time between any two states are available and the near-continuum expansion of these formulae defines the correct limiting behaviour and is used to check the results of asymptotic analysis of the difference equations. We find that in some cases the asymptotic approach does not lead unequivocally to the proper result.
2007-02-14T00:00:00Z