Date of Award
Master of Science (MS)
Mathematics and Statistics
Anxiety and mathematics come hand in hand for many individuals. This is due, in
part, to the fact that the only experience they have with mathematics is what some
mathematics educators refer to as "schoolmath," which uses a somewhat different
language than real mathematics. The language of schoolmath can cause individu-
als to have confusion and develop misconceptions related to several mathematical
concepts. One such concept is a fraction. In chapter one of this report, one possible
reason for this is discussed and a possible solution is purposed.
In chapter three of this report, genus-two curves admitting an elliptic involution
are related to pairs of genus-one curves. This classical work dates back to early 20th
century and is known as Jacobi reduction. Jacobians of genus-two curves can be
used to construct complex two-dimensional complex projective manifolds known
as Kummer surfaces. On the other hand, the defining coordinates and parameters of
elliptic curves and Kummer surfaces can be related to Jacobi θ-functions and Siegel
θ-functions, respectively. This result goes back to the seminal work of Mumford in
the 1980s. We use a geometric relation between elliptic curves and Kummer surfaces
to derive functional relations between θ-functions.
Spatig, Shantel, "Recognizing and Reducing Ambiguity in Mathematics Curriculum and Relations of θ-Functions in Genus One and Two: A Geometric Perspective" (2022). All Graduate Plan B and other Reports. 1667.
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