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  • A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem

    Creator:
    Rockwell, Daniel Luke
    Abstract:
    The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the...
    Resource Type:
    Dissertation
    Full Text:
    , and New Demonstrations of, the Borel Normal Number Theorem Abstract approved: Robert M. Burton The

  • Arithmetic dynamical questions with local rationality conditions

    Creator:
    Noytaptim, Chatchai
    Abstract:
    We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...
    Resource Type:
    Dissertation
    Full Text:
    algebraic number is totally real (respectively, totally p-adic) if its minimal polynomial over Q splits

  • On Small Heights of Totally p-adic Numbers

    Creator:
    Stacy, Emerald T.
    Abstract:
    The height of an algebraic number A is a measure of how arithmetically complicated A is. We say A is totally p-adic if the minimal polynomial of A splits completely over the field of p-adic numbers. In this paper, we investigate what can be said about the smallest nonzero height...
    Resource Type:
    Dissertation
    Full Text:
    number α is a measure of how arithmetically compli- cated α is. We say α is totally p-adic if the

  • Mahler's order functions and algebraic approximation of p-adic numbers

    Creator:
    Dietel, Brian Christopher
    Abstract:
    If P is an integer polynomial denote the degree of P by ∂(P) and let H(P) be the maximum of the absolute value of the coefficients of P. Define Λ(P)=2[superscript ∂(P)]H(P) and for a fixed prime p let C[subscript p] denote the completion of the algebraic closure of the p-adic...
    Resource Type:
    Dissertation
    Full Text:
    consider how well a given transcendental number can be approximated by algebraic numbers, or if there

  • The structure of E6

    Creator:
    Wangberg, Aaron D.
    Abstract:
    A fundamental question related to any Lie algebra is to know its subalgebras. This is particularly true in the case of E6, an algebra which seems just large enough to contain the algebras which describe the fundamental forces in the Standard Model of particle physics. In this situation, the question...
    Resource Type:
    Dissertation
    Full Text:
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.3 Lie Algebras

  • Zeros of Certain Combinations of Products of Eisenstein Series

    Creator:
    Klangwang, Jetjaroen
    Abstract:
    In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower...
    Resource Type:
    Dissertation
    Full Text:
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1 Statement of main result

  • The impact of the number of kinetochore microtubules on the rate of chromosome segregation

    Creator:
    Duan, Yunhan
    Abstract:
    Successful cell division requires proper chromosome movement, including accurate congression to the metaphase plate and proper segregation to spindle poles. Errors that occur in either event can cause chromosome aneuploidy in daughter cells, which may lead to cell death, genetic diseases and cancers (Matson and Stukenberg,2012, Compton, 2000). The force...
    Resource Type:
    Masters Thesis
    Full Text:
    . ©Copyright by Yunhan Duan December 12, 2013 All Rights Reserved The Impact of the Number of

  • Clinical Development for Paraprofessional Counselors : A 12 Session Protocol

    Creator:
    Sotelo, Dominique L.
    Abstract:
    Paraprofessional counselors comprise a significant sector of the mental health workforce (Buchbinder, 2003; Golden, 1991; Nieuwsma et al., 2014; Norcross, 2000). Professional counselors have offered both praise (Durlak, 1979) and criticism (Nietzel & Fisher, 1981) for paraprofessional counselors and the services that they provide. Paraprofessional counselors work under the guidance...
    Resource Type:
    Dissertation
    Full Text:
    : A 12 Session Protocol AN ABSTRACT OF THE DISSERTATION OF Dominique

  • Students' Understanding of Complex Numbers in Middle-Division Physics

    Creator:
    Smith, Emily M.
    Abstract:
    Mathematical sophistication increases rapidly as students transition from lower- to upper-division physics courses. Complex algebra is one of the mathematical tools that is not introduced or used in lower-division physics courses but is pervasive throughout upper-division courses. In this dissertation, I study middle-division physics students' developing fluency with complex number...
    Resource Type:
    Dissertation
    Full Text:
    physics students’ developing fluency with complex number algebra as they transition from lower- to upper

  • Publicly Funded, Privately Assisted : The Role of Giving in Oregon K-12 Education

    Creator:
    Sattem, Jennifer L.
    Abstract:
    In Oregon, property tax revolts and school equalization measures have led to increasingly unstable and more non-discretionary public funding for schools. As a result, public schools are turning to private donations to provide both basic and supplemental educational opportunities. Some schools and districts are raising hundreds of thousands of dollars,...
    Resource Type:
    Capstone Project
    Full Text:
    Oregon K-12 Education. Abstract approved