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Free Products Of Operator Spaces And Free Markov Processes, Mingchu Gao

Doctoral Dissertations

Certain (reduced) free product is introduced in the framework of operator spaces. Under the construction, the free product of preduals of von Neumann algebras agrees with the predual of the free product of von Neumann algebras. This answers a question asked by Effros affirmatively. An example is presented to show that the C*-algebra reduced free product of two C*-algebras may be contractively isomorphic to a proper subspace of the operator space reduced free product of the two C*-algebras.

Free Markov processes are also investigated in Voiculescu's free probability theory. This highly non-commutative notion generalizes that of free Brownian motion and …

Perceptions Of Eighth-Grade Mathematics Teachers Of The Impact Of The Maine Educational Assessment On Instructional Practices, Mary Christine Runge

Doctoral Dissertations

The purposes of this study are (a) to examine the perceptions of eighth grade mathematics teachers in the state of Maine concerning their classroom instructional and assessment practices and the influence on their students' scores in the MEA tests and (b) to determine if there is a relationship between community social/economic levels and student achievement on the Maine Educational Assessment (MEA) mathematics tests. The survey instrument consisting of a mailed questionnaire designed for this study contained 86 Likert scale items that measured teachers' beliefs regarding the following resource 1 indicators: awareness and use of MEA resources, content area knowledge, instructional …

Spectral Interpretation Of Zeros Of Zeta Functions, Tamas Waldhauser

Doctoral Dissertations

For every algebraic number field we construct an operator on a separable Hilbert space, whose eigenvalues are exactly the critical zeros of the Dedekind zeta function of the number field.

The Interplay Between Instructional Policy And Its Constituents: How Mathematics Teachers Interact With And Understand "Principles And Standards For School Mathematics", Dawn M. Berk

Doctoral Dissertations

Educational policies aimed at reforming school mathematics education have been disseminated at an increasing rate in recent years. The impact of such policies hinges on if and how constituents decide to implement the policy recommendations, and these decisions depend largely on constituents' interpretations of the policy. Investigating how classroom teachers make sense of policy recommendations is particularly important, for teachers are the ones who ultimately decide what mathematics students learn, and how they learn it. This research followed a group of teachers as they studied a particular instructional policy, Principles and Standards for School Mathematics (NCTM, 2000). Fourteen middle school …