On The Conjugacy Problem For Automorphisms Of Trees, 2016 Boise State University

#### On The Conjugacy Problem For Automorphisms Of Trees, Kyle Douglas Beserra

*Boise State University Theses and Dissertations*

In this thesis we identify the complexity of the conjugacy problem of automorphisms of regular trees. We expand on the results of Kechris, Louveau, and Friedman on the complexities of the isomorphism problem of classes of countable trees. We see in nearly all cases that the complexity of isomorphism of subtrees of a given regular countable tree is the same as the complexity of conjugacy of automorphisms of the same tree, though we present an example for which this does not hold.

Counting Convex Sets On Products Of Totally Ordered Sets, 2015 Western Kentucky University

#### Counting Convex Sets On Products Of Totally Ordered Sets, Brandy Amanda Barnette

*Masters Theses & Specialist Projects*

The main purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the work presented in this thesis. Also, the definitions and notation used throughout the paper are introduced here The second chapter starts with examining the product spaces of the form {1; 2; : : : ;n} × {1; 2}. That is, we begin by analyzing a two-row by n-column ...

My Finite Field, 2015 Idaho State University

#### My Finite Field, Matthew Schroeder

*Journal of Humanistic Mathematics*

A love poem written in the language of mathematics.

Exploring A Generalized Partial Borda Count Voting System, 2015 Bard College

#### Exploring A Generalized Partial Borda Count Voting System, Christiane Koffi

*Senior Projects Spring 2015*

The main purpose of an election is to generate a fair end result in which everyone's opinion is gathered into a collective decision. This project focuses on Voting Theory, the mathematical study of voting systems. Because different voting systems yield different end results, the challenge begins with finding a voting system that will result in a fair election. Although there are many different voting systems, in this project we focus on the Partial Borda Count Voting System, which uses partially ordered sets (posets), instead of the linearly ordered ballots used in traditional elections, to rank its candidates. We introduce ...

On Some Min-Max Cardinals On Boolean Algebras, 2015 University of Colorado Boulder

#### On Some Min-Max Cardinals On Boolean Algebras, Kevin Selker

*Mathematics Graduate Theses & Dissertations*

This thesis is concerned with cardinal functions on Boolean Algebras (BAs) in general, and especially with min-max type functions on atomless BAs. The thesis is in two parts:

(1) We make use of a forcing technique for extending Boolean algebras.

elsewhere. Using and modifying a lemma of Koszmider, and using CH, we prove some general extension lemmas, and in particular obtain an atomless BA, *A* such that *f*(A) = s_{mm}(A) = *w* < *u*(A) = *w*_{1}.

(2) We investigate cardinal functions of min-max and max type and also spectrum functions on moderate products of Boolean algebras. We prove several ...

From Nonlinear Embedding To Graph Distances: A Spectral Perspective, 2015 University of Colorado Boulder

#### From Nonlinear Embedding To Graph Distances: A Spectral Perspective, Nathan D. Monnig

*Applied Mathematics Graduate Theses & Dissertations*

In this thesis, we explore applications of spectral graph theory to the analysis of complex datasets and networks. We consider spectral embeddings of general graphs, as well as data sampled from smooth manifolds in high dimension. We specifically focus on the development of algorithms that require minimal user input. Given the inherent difficulty in parameterizing these types of complex datasets, an ideal algorithm should avoid poorly-defined user-selected parameters.

A significant limitation of nonlinear dimensionality reduction embeddings computed from datasets is the absence of a mechanism to compute the inverse map. We address the problem of computing a stable inverse using ...

Morphological Operations Applied To Digital Art Restoration, 2014 University of Minnesota, Morris

#### Morphological Operations Applied To Digital Art Restoration, M. Kirbie Dramdahl

*Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal*

This paper provides an overview of the processes involved in detecting and removing cracks from digitized works of art. Speciﬁc attention is given to the crack detection phase as completed through the use of morphological operations. Mathematical morphology is an area of set theory applicable to image processing, and therefore lends itself eﬀectively to the digital art restoration process.

The Mathematics Of The Card Game Set, 2014 Rhode Island College

#### The Mathematics Of The Card Game Set, Paola Y. Reyes

*Honors Projects Overview*

SET is a card game of visual perception. The goal is to be the first to see a SET from the 12 cards laid face up on the table. Each card has four attributes, which can vary as follows: 1. Shape: oval, squiggle, or diamond 2. Color: red, green, or blue 3. Number: the number of copies of each symbol can be 1, 2, or 3 4. Filling: solid, unfilled, stripped Each card has a unique combination, for a total of 34 = 81 different cards in a deck. A SET consist of three cards for which each of the four ...

Axioms Of Set Theory And Equivalents Of Axiom Of Choice, 2014 Boise State University

#### Axioms Of Set Theory And Equivalents Of Axiom Of Choice, Farighon Abdul Rahim

*Mathematics Undergraduate Theses*

Sets are all around us. A bag of potato chips, for instance, is a set containing certain number of individual chip's that are its elements. University is another example of a set with students as its elements. By elements, we mean members. But sets should not be confused as to what they really are. A daughter of a blacksmith is an element of a set that contains her mother, father, and her siblings. Then this set is an element of a set that contains all the other families that live in the nearby town. So a set itself can ...

Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, 2014 East Tennessee State University

#### Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus

*Electronic Theses and Dissertations*

The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or a ...

An Introduction To Set Theory And Topology, 2014 Washington University in St. Louis

#### An Introduction To Set Theory And Topology, Ronald C. Freiwald

*Books and Monographs*

These notes are an introduction to set theory and topology. They are the result of teaching a two-semester course sequence on these topics for many years at Washington University in St. Louis. Typically the students were advanced undergraduate mathematics majors, a few beginning graduate students in mathematics, and some graduate students from other areas that included economics and engineering.

The usual background for the material is an introductory undergraduate analysis course, mostly because it provides a solid introduction to Euclidean space **R**^{n} and practice with rigorous arguments — in particular, about continuity. Strictly speaking, however, the material is mostly self-contained ...

An Explicit Construction Of Kleinian Groups With Small Limit Sets, 2014 Sacred Heart University

#### An Explicit Construction Of Kleinian Groups With Small Limit Sets, Andrew Lazowski

*Mathematics Faculty Publications*

This paper provides an explicit construction of Kleinian groups that have small Hausdorff dimension of their limit sets. It is known that such groups exist and they can be constructed by results of Patterson. The purpose here is to work out the methods of calculation.

A Systematic Martingale Construction With Applications To Permutation Inequalities, 2013 University of Pennsylvania

#### A Systematic Martingale Construction With Applications To Permutation Inequalities, Vladimir Pozdnyakov, John M. Steele

*Operations, Information and Decisions Papers*

We illustrate a process that constructs martingales with help from matrix products that arise naturally in the theory of sampling without replacement. The usefulness of the new martingales is illustrated by the development of maximal inequalities for permuted sequences of real numbers. Some of these inequalities are new and some are variations of classical inequalities like those introduced by A. Garsia in the study of rearrangement of orthogonal series.

Generalized Ordered Whist Tournaments For 6n+1 Players, 2013 Rhode Island College

#### Generalized Ordered Whist Tournaments For 6n+1 Players, Elyssa Cipriano

*Honors Projects Overview*

In this project, we worked to see if it would be possible to extend the idea of an ordered whist tournament to a generalized whist tournament on 6n or 6n + 1 players. We focused on tournaments where the players are divided into n games of size 6 each consisting of two teams of size 3. We aimed to balance the 3 occasions where the players meet as opponents.

Difference Sets In Non-Abelian Groups Of Order 256, 2013 University of Richmond

#### Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum

*Honors Theses*

This paper considers the problem of determining which of the 56092 groups of order 256 contain (256; 120; 56; 64) difference sets. John Dillon at the National Security Agency communicated 724 groups which were still open as of August 2012. In this paper, we present a construction method for groups containing a normal subgroup isomorphic to Z4 Z4 Z2 . This construction method was able to produce difference sets in 643 of the 649 unsolved groups with the correct normal subgroup. These constructions elimated approximately 90% of the open cases, leaving 81 remaining unsolved groups.

Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part Ii, 2012 Sacred Heart University

#### Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part Ii, Carol Jacoby, Peter Loth

*Mathematics Faculty Publications*

We consider abelian groups with partial decomposition bases in L^{δ}_{∞ω} for ordinals *δ*. Jacoby, Leistner, Loth and Str¨ungmann developed a numerical invariant deduced from the classical global Warfield invariant and proved that if two groups have identical modified Warfield invariants and Ulm-Kaplansky invariants up to *ωδ *for some ordinal *δ*, then they are equivalent in L^{δ}_{∞ω}. Here we prove that the modified Warfield invariant is expressible in L^{δ}_{∞ω} and hence the converse is true for appropriate *δ*.

Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part I, 2012 Sacred Heart University

#### Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part I, Carol Jacoby, Katrin Leistner, Peter Loth, Lutz Strungmann

*Mathematics Faculty Publications*

We consider the class of abelian groups possessing partial decomposition bases in *L ^{δ}*

_{∞ω}for

*δ*an ordinal. This class contains the class of Warfield groups which are direct summands of simply presented groups or, alternatively, are abelian groups possessing a nice decomposition basis with simply presented cokernel. We prove a classification theorem using numerical invariants that are deduced from the classical Ulm-Kaplansky and Warfield invariants. This extends earlier work by Barwise-Eklof, Göbel and the authors.

Distribution Of Prime Numbers,Twin Primes And Goldbach Conjecture, 2011 SelectedWorks

#### Distribution Of Prime Numbers,Twin Primes And Goldbach Conjecture, Subhajit Kumar Ganguly

*Subhajit Kumar Ganguly*

The following paper deals with the distribution of prime numbers, the twin prime numbers and the Goldbach conjecture. Starting from the simple assertion that prime numbers are never even, a rule for the distribution of primes is arrived at. Following the same approach, the twin prime conjecture and the Goldbach conjecture are found to be true.

The Mathematical Landscape, 2011 Claremont McKenna College

#### The Mathematical Landscape, Antonio Collazo

*CMC Senior Theses*

The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject. By no means is the following a complete formulation of any of the topics covered. I want to give the reader a tour of the mathematical landscape. There are plenty of further details to explore in each section, I have just touched the tip the iceberg. The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math. The first sections are a exposition into the mathematical objects and their ...

Morphogrammatics Of Reflection, 2010 ThinkArt Lab Glasgow

#### Morphogrammatics Of Reflection, Rudolf Kaehr

*Rudolf Kaehr*

Turning back from the studies of morphogrammatics to some open questions of reflectional programming, the recountered problematics might be put into a different light and new methods of handling formal aspects of reflection and reflectionality shall be introduced. Albeit the use of light-metaphors, morphogrammatic reflection is not sketched along the paradigm of optical metaphors. Morphograms are presenting neither propositions nor perceptions able for mirroring (representation). Exercises in defining morphogrammatic retro-grade recursion and reflection schemata are continued from the paper “Sketches to Morphogrammatic Programming”.