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ThesisSteidly, Carl W.This is a syllabus for a onesemester, eleventh grade, advanced mathematics course. Motivation for mathematics rigor is advocated by an emphasis on application and problem solving through the use of various mathematical models.

ThesisStewart, MaryIn this thesis, we study finite simple groups as well as the Classification Theorem, which classifies all such groups. We will see by the Classification Theorem that all simple groups are one of the following four types: cyclic of prime order, alterna . . .

ThesisVargas, BrianA search engine is intended to crawl the world wide web and retrieve a list of sites that match the user's search terms. Listing the search results in a proper order is crucial but it is far from being a trivial task. Prior to the rise of Google, sear . . .

ThesisWilson, Jason RA major part of topology is the study of properties of topological spaces that are invariant under homeomorphisms. Such properties allow us to classify spaces. Some basic examples are compactness and connectedness. Although quite useful, these propert . . .

ThesisDozal, Jared MichaelThis graduate project is submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics for Educational Careers. It is a compilation of five projects, each focusing on different fields of mathematics relevant t . . .

ThesisMabe, NicholasIn this work I propose several numerical algorithms to calculate the steady state solutions of the SaintVenant equations, a hyperbolic balance law commonly used to model shallow water flows. The main focus is on twolayer stratified flows distinguish . . .

ThesisRudin, Brenda I.This thesis is a study of "La geometria elementare istitutta sulle nozioni di 'punto' e 'sfera'" (Elementary geometry instituted on the notions of "point" and "sphere") by the Italian geometer Mario Pieri ( 1860 1913). It focuses on the importance of . . .

ThesisWei, YunAs a typical model to represent nonlinear pulse propagation, the complex GinzburgLandau equation (CGLE) with linear and nonlinear gain or loss possesses solitary wave, hole wave and shock wavesolutions. In this thesis, we investigate the existence . . .

ThesisSteidly, Carl W.This is a syllabus for a onesemester, eleventh grade, advanced mathematics course. Motivation for mathematics rigor is advocated by an emphasis on application and problem solving through the use of various mathematical models.

ThesisKaspar, HansThe transient solution of a parking lot problem with a finite number of parking spaces is considered when, in a given time interval, the number of cars arriving are Poisson distributed with identical parameters. If the parking lot is full, all arrivin . . .

ThesisHamilton, Ann EstherNonstandard analysis was developed by Abraham Robinson in 1961. It offers a new number system which can serve as an alternative to the real numbers. This new system, called R*, is an ordered field containing numbers larger and numbers smaller than an . . .

ThesisThomassin, Steven L.In late October of 1972, my father confronted me with a piece of paper containing a square grid of 64 cells (8X8) followed by the directions: "Take a pencil and darken eight of these 64 squares, making sure that no darkened square is on the same horiz . . .

ThesisBarbullushi, IngridThe Macroscopic Vicsek (MV) model describes a largescale limit of selfpropelled particle systems used to describe behavior in animal societies such as fish school or bird flocks. From a mathematical point of view the MV model presents a number of ch . . .

ThesisLiu, JunyuThe present work investigates the Korteweg de Vries equation, nonlinear Schrödinger equation (NLSE), Hirota equation, coupled Hirota equations, and the (2+1)dimensional fourthorder NLSE. The latter equation describes a Heisenbergferromagnetic spin . . .

ThesisLimbacher, JeffreyGas flows around highspeed high altitude aircraft and within rocket thrusters contain regions where the particle velocities deviates significantly from the Maxwellian distribution. The gas in these regions is said to be in noncontinuum and is best d . . .

ThesisJones, AimeIn their paper, Toward A Mathematical Analysis For Driftflux Multiphase Flow Models In Networks, Banda et. al,[2] investigate networks whose flow is governed by an isothermal noslip driftflux model. In this paper, we consider solving for the model . . .

ThesisMakaryan, MariyaNonlinear partial differential equations (NLPDEs) are extremely hard to solve analytically because no specific general algorithm exists for this task. As is well known, integrability of the NLPDEs plays an important role in soliton theory (when the so . . .

ThesisNguyen, Ngoc My NhiThe problem of statistical classification and pattern recognition with functional covariates has received considerable attention in recent years. In standard functional classification, the covariates are typically assumed to be fully observable. This . . .

ThesisPleet, Lawrence JosephThis paper is a survey of the theory of prime numbers. Historical as well as mathematical content has been included. Where appropriate, examples are given to illustrate the various topics. Also, tables are employed to c1arify and enhance the discussio . . .


ThesisKalia, PareenA new test statistic is proposed for the general multivariate twosample problem using an inverse probability weighted statistic involving the numbers of nearest neighbor comparisons in which observations and specified numbers of their neighbors belo . . .

ThesisPaesachov, SharonIn this thesis we start with some important classical results in noncommutative ring theory. Namely, we classify all semisimple Artinian rings in terms of matrices with entries from division rings. In the second chapter we start with some natural cons . . .

ThesisRandles, Evan D.Explicit Fermi coordinates are given for geodesic observers comoving with the Hubble flow in expanding RobertsonWalker spacetimes, along with exact expressions for the metric tensors in these coordinates. For the case of non inflationary cosmologies, . . .

ThesisAlsafri, AreejThe goal of this study is to investigate the conditions under which the Fokker Planck equation assumes closed form solutions. The FokkerPlanck equation arises in the study of fluctuations in physical and biological systems. This equation has been su . . .

ThesisHafid, AliMost real world physical systems are modeled by nonlinear partial differential equations (PDEs) chief among them is the nonlinear Schro\"odinger equation (NLSE). The present work investigates fifthorder focusing and defocusing NLSEs, all appearing in . . .

ThesisKnauer, Hedwig GertrudThis thesis deals with curves of constant width (rotors in a square), a topic which first appeared in 1780 in a treatise by Leonard Euler and reappeared intermittently in the late 19th and early 20th century in widely different mathematical contexts. . . .

ThesisLagerson, Sheila KathleenThe study of networks and flows is an area of linear programming. This thesis begins with an intuitive approach which later develops into a rigorous treatment of the ideas of networks, flows, cuts and maximum value of a flow. The concepts of feasibili . . .

ThesisDavidson, Kathleen LynnA study of the life of Pascal and an examination of the existence of the triangle prior to Pascal's work is an important preliminary to the discussion of Pascal's triangle itself. Not only does the history of the man and the triangle make for interest . . .

ThesisCholvin, RobertA considerable effort has been directed recently at the development of solvers for the Boltzmann equation that utilize nonuniform grids and adaptive grids in the velocity space. However, when used with discrete ordinate approaches, nonuniform grids . . .

ThesisKofmehl, John AlbertDiophantine analysis was named after the Greek Diophantus, of the third century, who proposed many indeterminate problems in his arithmetic. He was content with finding single rational solutions to his problems although they usually had an infinitude . . .

ThesisManley, KevinWe consider the problem of estimation of a density function in the presence of incomplete data and study the Hellinger distance between our proposed estimators and the true density function. Here the presence of incomplete data is handled by utilizing . . .

ThesisStewart, JaredNonlinear partial differential equations (NLPDE) are ubiquitous in the applied science. However, NLPDEs are generally not solvable analytically. Using the Lax pair as a litmus test for integrability, we explore various equations which are known to ana . . .

ThesisZelaya Eufemia, GerardoWorking toward a possible generalization to the PaynePolyaWeinberger conjecture for the complex projective space, we prove that for a geodesic ball in the ndimensional complex projective space of geodesic radius r, the first Dirichlet eigenvalue mu . . .

ThesisLund, Donald JamesThis paper discusses how to use orthogonal polynomials to find a polynomial least squares approximation of a function which is defined by experiment over a discrete set of points. After discussing the advantages of using orthogonal polynomials over th . . .

ThesisHolden, Robert C.The importance of the hypergeometric equation lies in the fact that under certain conditions, its solutions reduce to many of the special functions which are essential to most areas of physics and engineering. The objective of this study is to investi . . .

ThesisMilne, AndrewPhysical simulation of soft tissues such as skin, muscle and fat is increasingly used for characters in computer animation. However, such simulations remain computationally expensive and require large amounts of memory. In this thesis, we extend a met . . .

ThesisCollins, John StuartThis is a textbook for use in secondary education to introduce the history, development, concept and use of computers to students desitring a basic understanding of computers and their relationship to mathematics. The text is broken into four main par . . .

ThesisStanley, AlyssaWe study interval estimation for both parameters of the hypergeometric distribution: (i) the number of successes in a finite population and (ii) the size of the population. In contrast to traditional methods that specify intervals via a formula, our a . . .

ThesisTrumpis, Marilyn AnnIn past years, computers have made significant contributions to mathematics education both as problem solving tools and as tutors in computer assisted instruction programs (CAI). Both of these contributions have been student centered than teacher cent . . .

ThesisCope, Dryden WarrenThe continuum problem is the problem of evaluating the infinite product 2w0 The history of the continuum problem is briefly sketched. Forcing is a technique invented by Paul J. Cohen in 1963 for constructing models of ZermeloFraenkel set theory (ZF). . . .

ThesisHoover, Erwin Michael

ThesisWatson, Mary EllenThe theory of prime numbers contains several questions that remained unanswered for more than two thousand years. From the time that the concept of prime numbers was first developed until the early twentieth century, mathematicians were unable to find . . .

ThesisBaghumyan, AnzhelaIn this thesis I discuss two widely used models which are called CuckerSmale and Kuramoto. The CuckerSmale model is a prototype model for describing the emergence of organization in the systems of interacting agents. It applies to phenomena such as . . .

ThesisAsaad, SaifIn optical fibers, the role of multicomponent systems becomes quite important, since several physical phenomena require modeling waves with two or more components. Compared with the single component systems, multicomponent systems possess many addit . . .

ThesisThomas, Ronald P.This paper presents an elemetry study of difference equations. Difference equations are defined and their origin in the works of Brook Taylor and James Stirling, circa 1715, is viewed in the perspective of broad developments of mathematics to that tim . . .

DissertationFu, YiweiThe development of cervical cells from normal cells infected by human papillomavirus into invasive cancer cells can be modeled using population dynamics of the cells and free virus. Since the human papillomavirus can be separated into lowrisk types a . . .

ThesisKim, ChoomeeThe Zariski Topology in an interesting topic in algebraic geometry that combines commutative algebra and topology to deal with questions that are algebraic and geometrical in nature. Initially, it was about understanding the qualitative and quantitati . . .

ThesisNguyen, Ha NamWe study the analytic properties of twisted Dirichlet series associated to Bmultiplicative arithmetic functions. An example of such a function is the exponential of the sum of digits of an integer in the base. Twisting by additive characters, we can . . .

ThesisImhoff, Gregory B.The nth cyclotomic polynomial Phi_n(x)is the minimal polynomial of a primitive nth root of unity. The order of \Phi_n is the number of distinct odd prime factors of and the height of \Phi_n=\sum_ka_n(k)x^k$\ is A(n)=\max_ka_n(k), the maximum absolut . . .

ThesisBalas, KevinIn this thesis, we deal with problems involving finding the maximum area covered when packing rectangles into a bounding box, each containing a specified representative point. Given a set of n points in the unit square, U = [0, 1]^2, we choose n inter . . .