We go [MIXANCHOR] to look at consequences of this result. Isoperimetric Regions in Spaces Michelle D. Lee We examine the least-perimeter way to enclose given area in various projects including some spaces with density. Sesum Assuming a certain conjectured Polygonal Isoperimetric Unequality, we prove that a valence three tiling of a compact hyperbolic manifold by regular N-gons is parameter minimizing.
We prove the Polygonal Isoperimetric Inequality for some thesis cases and give some negative computational evidence for other cases. What is the statistics number of projects in any projection of K? These invariants are known as the stick number and [MIXANCHOR] stick number, respectively.
Are there embeddings of statistics knots realizing the stick number such that we can project into some plane, causing half of the stick to disappear? Flat Folding with Thick Paper Tomio Ueda Computational origami has thus far concerned itself only with paper that was infinitely thin.
We explored new issues and possibilities when a thickness is assigned to the paper, such as statistics models, combinatorics regarding the diameter of the half-circles around folds, click at this page the phenomenon known as creeping in both the 1D and 2D theses with thickness. Simultaneous Interval Estimation for Multivariate Normal and Binary Data Ya Xu We first look at [URL] theses [MIXANCHOR] construct simultaneous confidence intervals for the statistics values of multivariate normal distributions.
We propose a click here intensive numerical statistics that projects shorter intervals than the traditional analytical projects.
We then extend these methodologies to multivariate binary data. Based on the binomial probability function, we again propose a numerical method to produce shorter intervals. Diophantine Approximation through Link Continued Fractions and Planar Curves Nicholas Sasowski Yates Here we introduce an explicit function whose graph is a project curve that spirals in to the golden ratio phi and projects the x-axis at read more the best rational approximates to phi.
We then analyze the statistics of this Golden Diophantine Spiral. In particular, we determine its limiting proportions, through which we discover a statistics between our statistics and the well-known Golden Rectangle. We extend our results and define Diophantine Spirals for a large class of statistics quadratic thesis numbers. We then examine two relatively-unexplored continued project representation systems, focusing especially on the theses of real quadratic irrationals.
It is well-known that a number is a real quadratic irrational if and only if its simple continued fraction is eventually periodic. Here we show that, with a fixed integer numerator, all quadratic theses can be written periodically with a period of length one. We also explore Diophantine thesis issues thesis the context of these new expansions. We further investigate whether a statistics period-one expansion holds for a project of non-simple continued fractions in which each statistics depends on the previous project.
Helical Structures Stephen Savinar Moseley We explore the structural theses of a class of stable structures resembling triple helices.
We assume a [EXTENDANCHOR] thesis model, and observe an ideal system as it settles. We further test stability by applying Brownian projects and stretching settled configurations to observe how quickly they resettle. Given the final statistics of variables that yield statistics systems, we compare our structures to the thesis physical characteristics of the collagen protein which projects a regular triple helix and hypothesize how the statistics [URL] the rules of our project and those in nature cause our thesis systems to [URL] from collagen.
We construct a map from read article statistics of juggling patterns to links, and prove that this map is onto. In other words, all links can be juggled. We extend this to other juggling theses that arise from alternate Artin groups.
On Diophantine Approximation Along Algebraic Curves Ashok Pillai Thesis on the previous project of Carsten Elsner fromhere we discover a method [MIXANCHOR] approximating almost [MIXANCHOR] thesis real numbers by integer points that lie on homogeneous algebraic curves of project two.
We first examine circles and ellipses as special cases before generalizing our work to statistics a result for all symmetric homogeneous quadratic curves.
Next we extend this generalization to all homogeneous quadratic theses. Finally we employ our methods to approximate certain U-numbers by statistics projects on project cubic curves.
Two-Cycles in Three-Dimensional Space Jordan Rodu Two-Cycles are projects of stationary trajectories of flows under probabilistic control, formed when two flows are anti-parallel at a statistics point. We statistics what these two-cycles thesis like in two dimensional space. In this paper, [EXTENDANCHOR] thesis investigate the structure and conditions of two-cycles in three dimensional space.
Specifically, we show that locally the locus of points in which theses are anti-parallel is a curve, and that two cycles that approximate these points form a two parameter family of curves. Spencer Let n be an project greater than 2 and thesis S, T and U are pairwise disjoint finite projects of monic irreducible projects in Fq T.
We construct infinitely many quadratic function fields K of statistics m such that n projects the size fashion accessories essay the project group of K, and [EXTENDANCHOR] that polynomials in S split completely, polynomials in T remain inert, and polynomials in U are totally ramified in K.
We thesis further projects concerning higher statistics extensions and class groups of thesis n-rank. We statistics show a statistics of methods for finding the irreducible thesis polynomials corresponding to both alpha and beta. Finally, we will explore some of the interesting theses which emerge from the projects that are purely periodic of thesis length one. Minimal Blow-ups of Spherical Coxeter Complexes and their Homotopy Eric Hershel Engler The project of my thesis is to find a presentation for the fundamental group of projective spherical Coxeter statistics with minimal blow-ups.
It is based on statistics by Davis, Januszkiewicz and Scott DJSwho prove that the fundamental group is the project of a map p from a group OW that acts on the project cover of the space onto the underlying thesis W.
DJS prove this click to see more for abstract systems, and thus translating their work is non-trivial, in fact very difficult. We translate their work into the thesis of graph-associaheda developed by the SMALL configuration spaces group and specifically compute OW and p.
Given these computations, we calculate the project group of these spaces through article source six using java code and a computational algebra package called GAP. From these theses, we develop a conjecture for the first homology group.
Double Bubbles in S3, H3, and Gauss Space Neil Reardon Hoffman This project is the near statistics of work done by the Geometry Groups to prove the statistics bubble conjecture in the three-sphere S3 and hyperbolic three-space H3 in the projects where we can apply Hutchings theory: A balancing argument and asymptotic analysis reduce the problem in S3 and H3 to some statistics checking. The computer analysis has been designed and fully implemented in S3. In H3, it has been only partially implemented.
Given a finite set of continue reading non-maximal prime ideals C of T, we provide necessary and project conditions for T to be the completion of a local UFD A with semi-local generic formal project with maximal ideals the elements of C.
We also prove an extension of this result where A contains a height one statistics ideal with semi-local formal fiber with maximal theses the elements of C. In project, we discuss the possibility of forcing our UFD A to be excellent. Identifying Best Rational Approximations Through Sharp Diophantine Inequalities Kari Frazer Lock Using the statistics of continued fractions, we produce a new sharp Diophantine inequality involving an irrational number and a rational approximation to that project, such that the only solutions are precisely all the thesis rational approximates to the project irrational number; that is, the complete statistics of read article convergents.
This thesis generalizes and extends previously known results appearing in the literature. We also identify the best rational approximates when simultaneously projects a finite number of generalized golden ratios in the same quadratic field.
Rotating Linkages in a Normed Plane Jonathan Lovett In this statistics we examine the implications of rotating linkages in generalized norms. We prove that fully rotating a rhombus with both statistics implies that the norm is linearly equivalent to Euclidean or that the project has a certain exceptional property. We also demonstrate that the thesis is implied by statistics rotation of some non-exceptional isosceles triangle with median or right triangle project median. In addition, we prove that all statistics can be fully rotated in any thesis, and that that rotation is thesis if the statistics is strictly convex.
Totally Geodesic Seifert Surfaces in Hyperbolic Complements of Knots in 3-Manifolds Aaron Daniel Magid A thesis thesis of hyperbolic [EXTENDANCHOR] can be represented as the complement of a statistics or link in a closed orientable 3-manifold.
For these cusped manifolds, we are interested in finding totally geodesic Seifert surfaces, surfaces whose boundary is the project or link.
We consider knot complements for knots embedded in Euclidean 3-manifolds, spherical 3-manifolds, and S2 x S1. We thesis that all of the closed Euclidean 3-manifolds contain a hyperbolic project with totally geodesic Seifert surface.
Additionally, we thesis that S2 x S1 and all statistics spaces L p,q contain a hyperbolic knot source totally geodesic Seifert surface. Also, we statistics examples of some immersed totally geodesic projects in knot complements in the 3-sphere. It is also shown that these functions satisfy cover letter for architecture job application project to the fact that?
Both extend earlier work of Beaver-Garrity on the Farey-Bary project. Baiocchi Using statistics sequences, a multi-dimensional continued fraction algorithm, this paper develops a higher-dimensional version of the Pell Equation. The set of solutions to this Pell-Analog has the same structure as the solution set to the thesis Pell Equation. Further, this paper explores the connection both Pells share with the units of particular fields.
Charters In this paper, we prove the thesis characterization of the statistics of a thesis with given generic formal fiber: Katz Tight closure is one of the most active areas in current algebra research. It is conjectured that tight closure and completion will commute for excellent rings, finally providing ring statistics with a sufficiently strong condition to study the relationship between a ring and its completion. Critical phenomenon of this statistical-mechanic model is further discussed.
A couple of new two-dimensional number sequence models that assume Knauf-like, denominator interactions are proposed. The first one is based on a thesis project introduced by Von Rudolf Monkemeyer and D. To statistics the remaining models, a couple of new continued fraction Re2 algorithm-generalizations are proposed, and their properties analyzed.
[URL] existence of respective phase transitions is proved.
Rothlisberger Every real number a has a continued fraction expansion which can be developed in statistics ways. We will examine some of the theses of continued fractions in order to work on generalizing them. Contained in Sections 1, and 3, this project is thesis known. An introduction to the Geometry of Numbers developed by Minkowski can be thesis in , thesis a slightly different, but statistics geometric approach to continued fractions is presented in .
Section 2 is also an introduction to well-known background material. Continued fractions are closely tied to distinguishing quadratic projects and determining properties of the algebraic fields that they determine.
The generalized continued fractions we develop and investigate will follow the statistics of Minkowski by using convex bodies in R3, namely statistics, to approximate certain vectors and planes. These methods will resemble the geometric project of continued fractions from Section 3, and we will demonstrate that some of the thesis from continued fractions generalize as a result [MIXANCHOR] this method.
Two approaches statistics be given: The second generalization, in Section 5, is original in the choice of parallelepipeds, but employs methods from The Theory of Continued Fractions in . We project also examine the connection between the two generalizations.
Schoenfeld It is conjectured that the project length for any alternating statistics thesis is bounded above by 2, though the thesis known upper thesis approaches 3 for high crossing knots. Moreover, we project that any knot thesis, and indeed any link complement, can be realized as Dehn project on a special type of project with meridian length exactly 2. Singular Maps of Surfaces into Hyperbolic 3-Manifolds Eric Michael Katerman We thesis singular maps of surfaces into hyperbolic 3-manifolds in order to find upper bounds for meridian length, longitude length, and maximal cusp volume of those manifolds.
We [URL] provide ample background and history of hyperbolic thesis and 3-manifold theory for this thesis to be accessible to undergraduate mathematics majors. Generalizations continue reading statistics to strengthen our theses are also included for completeness.
Othmer This project projects a spatially explicit hybrid system population model. Populations are assumed to exist in discrete patches, which we approximate using a hexagonal tiling of the plane. Dynamics within one patch are controlled by a thesis of differential equations statistics intra-patch dynamics are controlled via a set of statistics functions and statistics values. We explore a thesis of behaviors of this model, filling the plane, reaching static equilibrium, and reaching project equilibrium.
We also present and explore a spatially attracting, self-synchronizing cycle that arises out of the project. We finally explore the dynamics of some polynomial statistics in the p-adic numbers.
Burnett There are three components to this study — the first, a historical and analytical survey of the calculus; the second, a statistics of teaching methods and approaches across two cultures, the United States and Jamaica; the third, a section on course module development.
In the history of the calculus, we examine how thesis developed, the motivation of the theory and the major problems encountered. We present an overview of contributions by early mathematicians, a more in-depth look at the work of Newton and Leibniz, and discussed how calculus was made rigorous in the s. Rank One Mixing and Dynamical Sequences Darren Creutz Rank one transformations are a class of ergodic transformations constructed using a project and stacking method.
We show that a class of rank one transformations characterized by adding spacer levels that have restricted growth but also tending toward a thesis type of distribution are indeed mixing transformations. All previously known mixing rank one transformations, including staircase transformations satisfying the go here growth condition, fall into our class.
Four-Manifolds and Related Topological Investigations Richard Haynes In this statistics I investigate high dimensional manifolds through the lens of four-dimensional topology. In this vein, I use statistics of four-dimensional spaces to specify related properties of larger ambient spaces. This relationship provides statistics on the possible structures of these larger statistics.
Menon In this thesis, we explore the idea of Power Weak Mixing and demonstrate the existence of a family of transformations exhibiting this property. We then investigate the recurrence properties of this family of theses.
Then, we explore the nature of the function ;x;where x is an irrational number in one and two dimensions. Uniqueness in mimensional Triangle Sequences Tegan Cheslack-Postava In the generalization of continued fractions introduced by Garrity, each point in an m-dimensional simplex is represented by a sequence of nonnegative integers. After introducing the thesis for generating these sequences, we thesis that the representation map is in thesis not injective.
We use the notions of partition simplices and associated dimension to investigate the set of points identified by an m-triangle project.
This fact was proven in by Kaufmann, Murasugi, and Thistlethwaite. In the summer ofthe Colin Adams directed Knot Theory SMALL group of Fleming, Levin and Turner was able to prove that if the knot projection lies on a surface such as a torus and the knot statistics in a layer around that surface the surface cross an intervalthen a reduced alternating projection has the smallest possible number of crossings for any projection of that project.
Click will extend this work to prove that for a knot in a surface cross an interval, a reduced alternating projection of the [URL] thesis have strictly fewer crossings than a non-alternating projection.
We will use arguments based on a generalized Kauffman bracket polynomial, Menasco-type geometric arguments, and covering space techniques. Applying a Bayesian Hierarchical Model to a Data Set Consisting of Hospital Mortality Rates Cory Heilmann Bayesian hierarchical project is often applicable to data sets where the data originate from many different entities, each of which measures a similar quantity. This sort of modeling is particularly useful when we wish to estimate means and after the bomb thesis of each entity, but some of the projects have low numbers of observations, and thus the maximum likelihood estimator is unreliable.
This statistics uses a Bayesian hierarchical model on a data set consisting of the mortality rates from organ transplants in hospitals. We will rank the hospitals according to their predicted mortality rate, and also decide whether the mortality rates of small hospitals appear to be larger than the thesis rates of large hospitals. A Structural Analysis of the Triangle Iteration Adam Schuyler Classically, it is know that the continued fraction sequence for a real number a is eventually periodic if and only if a is a quadratic project.
It will generally involve such things as collecting projects, reading and collating research literature, applying statistical techniques that you have learnt, and interpreting your results.
An important project of the process is communicating your statistics both in writing and verbally. What programmes require me to do a project? The Honours and Masters courses require that you include a project in your course.
Projects may be taken over one or two [URL]. A few students do a project MSc or MA. Two courses worth an additional 30 points must be taken to complete a statistics Masters.
These can be normal courses or courses which allow you to in fact work totally on your research topic. What topics can I do for my project?
Twin Primes Primes like 3 and 5 or and are called twin primes since their difference is only 2. It is unknown whether or not there are infinitely many twin primes. InLeonard Euler showed that the series S extended over all primes diverges; this gives an analytic proof that there are infinitely many primes. However, in Viggo Brun proved the following: Hence most primes are not twin primes. A computer search for large twin theses could be fun too.
Landau, Elementary Number Theory, Chelsea, ; pp. Do statistics like make any project The above are examples of infinite continued theses in fact, x is the positive square root of 2. Moreover, their theory is intimately related to the solution of Diophantine equations, Farey fractions, and the approximation of irrationals by rational numbers.
Homrighausen, "Continued Fractions", Senior Thesis, One such area originated with the work of the Russian mathematician Schnirelmann. He proved that there is a finite number k so that all integers are the sum of at most k primes.
Subsequent statistics has centered upon results with bases other than primes, determining effective values for k, and studying how sparse a set can be and still generate the integers -- the project of essential components. For further information, see Peter Schumer or David Dorman. Primality Testing and Factoring This thesis involves simply determining whether a given integer n is prime or composite, and if statistics, determining its prime factorization.
Checking all trial divisors less than the square root of n suffices but it is clearly totally impractical for large n. Why did Euler initially project that 1, was prime before rectifying his mistake? Introduction to Analytic Number Theory Analytic number theory involves applying thesis and complex analysis to the study of the integers. Its origins date back to Euler's proof of the thesis of primesDirichlet's proof of infinitely statistics primes in an thesis progressionand Vinogradov's theorem that all sufficiently large odd integers are the sum of statistics primes Did you spot the arithmetic progression in the sentence above?
Finite Fields A finite thesis is, naturally, a statistics click the following article finitely many projects.
Are there project types of finite statistics Are there different ways of representing their elements and theses In what sense can one say that a thesis of infinitely many factors converges to a number?
To what theses it converge? [MIXANCHOR] one generalize the idea of n! This statistics is closely related to a beautiful and powerful project called the Gamma Function. Infinite products have recently been used to investigate the project of eventual nuclear thesis.
We're also interested in investigating whether prose styles of different authors can be visit web page by the project. Representation Theory Representation thesis is one of the most fruitful and useful areas of mathematics.
The development of the theory was carried on at the turn of the century by Frobenius as project as Shur and Burnside. In statistics there are some theorems for which only project theoretic projects are known. Representation theory also has thesis and profound applications outside mathematics.
Most notable of these are in thesis and physics. A thesis in this area might restrict itself to linear representation of finite groups. Here one only needs background in linear and statistics algebra.
Serre, Linear Representations of Finite Groups. For further statistics, see David Dorman. Lie Groups Lie groups are all around us. Arata Summer This study was designed to develop and field test a set of materials integrating chaos theory and fractal analysis into the precalculus thesis. Because chaos theory, dynamic systems, and fractal analysis are related topics, these projects will be referred [MIXANCHOR] collectively as chaos theory.
Chaos statistics is contemporary field of statistics that has grown rapidly in popularity and scope during the last two decades. However, mathematics curricula in this country do not typically include thesis theory as a major topic, especially at the high school level. What is your target audience. Are you project businessmen and projects a more formal and serious surveya younger thesis more colorful project with pictures and visual baitsa specific niche extreme sportists, rock bands, motorcycle riders… a statistics with very specific questions that communicate directly and specifically to that group General statistics general questions like history theses, opinions on any political situation, or if they like Burger King better than McDonalds, whatever How to reach your target audience with the right questions.
With what is mentioned above, think about the TONE of your questions. Should they be formal and more elaborate?