Browsing UT Electronic Theses and Dissertations by Department "Mathematics"
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Abelian ChernSimons theory with toral gauge group, modular tensor categories, and group categories
(200808)Classical and quantum ChernSimons with gauge group U(1)N were classified by Belov and Moore in [BM05]. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a correspondence ... 
About the largest subsolution for a free boundary problem in R²
(201012)We analyze the geometry and regularity of the largest subsolution of a Free Boundary Problem. We showed that the largest subsolution is a viscosity solution of (1) with Lipschitz and NonDegenerate properties under a very ... 
Adiabatic limits of the Hermitian YangMills equations on slicewise stable bundles
(2002)A formal limit of the Hermitian YangMills Equations on a SU(2) bundle over a product of two Riemann surfaces yields the Adiabatic Equations when the metric of the first surface is stretched ad infinitum. This thesis ... 
Agents' agreement and partial equilibrium pricing in incomplete markets
(200812)We consider two riskaverse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential ... 
Algebra readiness : building strong foundations through conceptual understanding
(201108)Algebra readiness has been a topic of much research and debate. This report summarizes findings pertaining to how researchers and experts in the field of mathematics education define the term algebra readiness. The Southern ... 
Alternative estimation approaches for some common Item Response Theory models
(201008)In this report we give a brief introduction to Item Response Theory models and multilevel models. The general assumptions of two classical Item Response Theory, 1PL and 2PL models are discussed. We follow the discussion ... 
An analogue of the KorkinZolotarev lattice reduction for vector spaces over number fields
(201008)We show the existence of a basis for a vector space over a number field with two key properties. First, the nth basis vector has a small twisted height which is bounded above by a quantity involving the nth successive ... 
Analysis of errors and improvements in numerical approximations and methods in secondary mathematics curriculum
(201308)This report discusses three topics relating to errors of numerical methods and to improvements of numerical approximations. The introduction connects these topics to the secondary mathematics curriculum. The three chapters ... 
Analysis of geometric flows, with applications to optimal homogeneous geometries
(201105)This dissertation considers several problems related to Ricci flow, including the existence and behavior of solutions. The first goal is to obtain explicit, coordinatebased descriptions of Ricci flow solutionsespecially ... 
Analysis of Ricci flow on noncompact manifolds
(201305)In this dissertation, we present some analysis of Ricci flow on complete noncompact manifolds. The first half of the dissertation concerns the formation of TypeII singularity in Ricci flow on [mathematical equation]. For ... 
Analysis of the real line
(201108)The purpose of this report is to describe the course, Analysis of the Real Line, taught at The University of Texas at Austin. Course materials are presented using the inquiry based learning method. Students work a series ... 
The AndréQuillen spectral sequence for prelogarithmic ring spectra
(201508)We discuss an AndréQuillen spectral sequence and an étale descent theorem for prelogarithmic ring spectra. 
An application of KAM theory to a model for particle channelling in crystals and some related numerical simulations
(201005)It has been seen in physical experiments as early as the 1960’s that when a positively charged particle is injected into a crystal in certain directions and with sufficiently high energy, the particle can penetrate into ... 
Applications of calculus : summary of Dr. Stephen McAdam’s summer course Mathematics Department at the University of Texas at Austin
(201008)The aim of this paper is to summarize Professor McAdam’s course on the applications of calculus by showing how calculus can be applied within mathematical situations by understanding concepts in physics. Aside from using ... 
Applications of prime numbers
(201208)This report explores the historical development of three areas of study regarding prime numbers. The attempt to find an efficient and useful function to generate primes could be a helpful tool in the improvement of encryption. ... 
Applying Classification and Regression Trees to manage financial risk
(201205)This goal of this project is to develop a set of business rules to mitigate risk related to a specific financial decision within the prepaid debit card industry. Under certain circumstances issuers of prepaid debit cards ... 
Approximation of the 2D complex eikonal equation : analysis and simulation
(201212)High frequency wave propagation is well described even at caustics by Gaussian beams and the complex eikonal equation. In contrast to the real eikonal equation, the complex eikonal equation is elliptic and not well posed ...