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Filtering by: Creator Petsche, Clayton Remove constraint Creator: Petsche, Clayton Degree Name Honors Bachelor of Science (H.B.S.) Remove constraint Degree Name: Honors Bachelor of Science (H.B.S.)

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  • The Axiom of Choice and Homotopy Type Theory

    Creator:
    Schneider, Eric
    Abstract:
    In this work we introduce some basic concepts within homotopy type theory (HoTT), a proposed alternative mathematical foundation to classical set theory. In particular, our discussion revolves around the Axiom of Choice (AC). In Part I, we introduce the classical AC and some of its most important equivalents. In Part...
    Resource Type:
    Honors College Thesis
    Full Text:
    . APPROVED: David Wing, Mentor, representing Mathematics Clayton Petsche, Committee Member, representing

  • The geometry of the octonionic multiplication table

    Creator:
    Killgore, Peter Lloyd
    Abstract:
    We analyze some symmetries of the octonionic multiplication table, expressed in terms of the Fano plane. In particular, we count how many ways the Fano plane can be labeled as the octonionic multiplication table, all corresponding to a specified octonion algebra. We show that only 28 of these labelings of...
    Resource Type:
    Honors College Thesis
    Full Text:
    Corinne Manogue, Committee Member, representing Physics Clayton Petsche, Committee Member, representing