A Special Tribute To Martin Gardner, 2019 Butler University

#### A Special Tribute To Martin Gardner, Jeremiah Farrell

*Jeremiah Farrell*

There are exactly 12 different letters in the phrase GATHERING FOR MARTIN GARDNER. We use each of the 12 letters three times each in 18 different two-letter words that are to be placed on the nodes of the graph so adjoining nodes have a letter in common.

Inquiry In Inquiry: A Classification Of The Learning Theories Underlying Inquiry-Based Undergraduate Number Theory Texts, 2019 Seattle Pacific University

#### Inquiry In Inquiry: A Classification Of The Learning Theories Underlying Inquiry-Based Undergraduate Number Theory Texts, Rebecca L. Butler

*Honors Projects*

While undergraduate inquiry-based texts in number theory share similar approaches with respect to learning as the embodiment of professional practice, this does not entail that these texts all operate from the same fundamental understanding of what it means to learn mathematics. In this paper, the instructional design of several texts of the aforementioned types are analyzed to assess the theory of learning under which they operate. From this understanding of the different theories of learning employed in an inquiry-based mathematical setting, one can come to understand the popular model of what it is to learn number theory in a meaningful ...

Increasing C-Additive Processes, 2019 Department of Mathematical Sciences, University of Indianapolis, Indianapolis, IN 46627, USA

#### Increasing C-Additive Processes, Nadjib Bouzar

*Communications on Stochastic Analysis*

No abstract provided.

The Martingale Approach To Financial Mathematics, 2019 California Polytechnic State University, San Luis Obispo

#### The Martingale Approach To Financial Mathematics, Jordan M. Rowley

*Master's Theses and Project Reports*

In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure *Q*, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure *Q* also gives the arbitrage-free pricing formula for every asset on our market. In considering ...

Strong Convergence Rate In Averaging Principle For The Heat Equation Driven By A General Stochastic Measure, 2019 Department of Mathematical Analysis, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine

#### Strong Convergence Rate In Averaging Principle For The Heat Equation Driven By A General Stochastic Measure, Vadym Radchenko

*Communications on Stochastic Analysis*

No abstract provided.

Smoothing Parameters For Recursive Kernel Density Estimators Under Censoring, 2019 Univ. Poitiers, Lab. Math. et Appl., Futuroscope Chasseneuil, France

#### Smoothing Parameters For Recursive Kernel Density Estimators Under Censoring, Yousri Slaoui

*Communications on Stochastic Analysis*

No abstract provided.

Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, 2019 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

#### Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas, Philip J. Feinsilver

*Communications on Stochastic Analysis*

No abstract provided.

A Limiting Process To Invert The Gauss-Radon Transform, 2019 Department of Mathematics and Statistics, Stephen F. Austin State University, Nacogdoches, Texas 75962-3040, USA

#### A Limiting Process To Invert The Gauss-Radon Transform, Jeremy J. Becnel

*Communications on Stochastic Analysis*

No abstract provided.

Calculus Remediation As An Indicator For Success On The Calculus Ap Exam, 2019 California State University, San Bernardino

#### Calculus Remediation As An Indicator For Success On The Calculus Ap Exam, Ty Stockham

*Electronic Theses, Projects, and Dissertations*

This study investigates the effects of implementing a remediation program in a high school Advanced Placement Calculus AB course on student class grades and success in passing the AP Calculus AB exam.

A voluntary remediation program was designed to help students understand the key concepts and big ideas in beginning Calculus. Over a period of eight years the program was put into practice and data on student participation and achievement was collected. Students who participated in this program were given individualized recitation activities targeting their specific misunderstandings, and then given an opportunity to retest on chapter exams that they had ...

Tribonacci Convolution Triangle, 2019 California State University, San Bernardino

#### Tribonacci Convolution Triangle, Rosa Davila

*Electronic Theses, Projects, and Dissertations*

A lot has been said about the Fibonacci Convolution Triangle, but not much has been said about the Tribonacci Convolution Triangle. There are a few ways to generate the Fibonacci Convolution Triangle. Proven through generating functions, Koshy has discovered the Fibonacci Convolution Triangle in Pascal's Triangle, Pell numbers, and even Tribonacci numbers. The goal of this project is to find inspiration in the Fibonacci Convolution Triangle to prove patterns that we observe in the Tribonacci Convolution Triangle. We start this by bringing in all the information that will be useful in constructing and solving these convolution triangles and find ...

Analogues Between Leibniz's Harmonic Triangle And Pascal's Arithmetic Triangle, 2019 California State University - San Bernardino

#### Analogues Between Leibniz's Harmonic Triangle And Pascal's Arithmetic Triangle, Lacey Taylor James

*Electronic Theses, Projects, and Dissertations*

This paper will discuss the analogues between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle by utilizing mathematical proving techniques like partial sums, committees, telescoping, mathematical induction and applying George Polya's perspective. The topics presented in this paper will show that Pascal's triangle and Leibniz's triangle both have hockey stick type patterns, patterns of sums within shapes, and have the natural numbers, triangular numbers, tetrahedral numbers, and pentatope numbers hidden within. In addition, this paper will show how Pascal's Arithmetic Triangle can be used to construct Leibniz's Harmonic Triangle and show how both triangles ...

Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, 2019 California State University, San Bernardino

#### Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr.

*Electronic Theses, Projects, and Dissertations*

Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.

Taking Notes: Generating Twelve-Tone Music With Mathematics, 2019 East Tennessee State University

#### Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder

*Electronic Theses and Dissertations*

There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of diﬀerent musical notes, each of which has diﬀerent sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.

Median Energy Imaging Of Supernova Remnants With Chandra X-Ray Observatory, 2019 William & Mary

#### Median Energy Imaging Of Supernova Remnants With Chandra X-Ray Observatory, Anne Blackwell

*Undergraduate Honors Theses*

Supernova remnants (SNRs) play an important role in shaping the energy density, chemical enrichment, and interstellar medium (ISM) of galaxies, and in our understanding of stellar evolution. Due to the high plasma temperatures of SNRs, they primarily emit X-rays. Using data collected with the Chandra observatory, we study a novel statistical imaging analysis technique to probe the underlying structure and physical properties of DEM L71, a SNR in the Large Magellanic Cloud. We used the statistical properties of the photons within an image pixel, such as the median energy, to make images of the energetics across the SNR. We have ...

Totally Positive Completable Matrix Patterns And Expansion, 2019 William & Mary

#### Totally Positive Completable Matrix Patterns And Expansion, David Allen

*Undergraduate Honors Theses*

Though some special cases are now understood, the characterization of TP-completable patterns is far from complete. Here, a new idea is developed: the \underline{expansion} of a pattern. It is used to explain some recent results, such as border patterns. The effects of expansion on certain cases of non-completable and completable patterns is examined, as well as an attempt to characterize $3$-by-$n$ TP-completable patterns. While many TP-completable patterns remain so under expansion, a counterExample shows that this is not always so. In the process, some new results about TP-completability are given.

An Alternative Almost Sure Construction Of Gaussian Stochastic Processes In The L2([0,1]) Space, 2019 Bowdoin College

#### An Alternative Almost Sure Construction Of Gaussian Stochastic Processes In The L2([0,1]) Space, Kevin Chen

*Honors Projects*

No abstract provided.

Understanding The Impact Of Peer-Led Workshops On Student Learning, 2019 CUNY New York City College of Technology

#### Understanding The Impact Of Peer-Led Workshops On Student Learning, Afolabi Ibitoye, Armando Cosme, Nadia Kennedy

*Publications and Research*

As students we often wonder why some subjects are easy to understand and requires not much effort in terms of re-reading the material, for us to grasp what it entails. One subject seems to remain elusive and uneasy for a vast majority of learners at all levels of education; that subject is Mathematics, it is one subject that most learners finds difficult even after doubling the amount of time spent on studying the material. My intention is to explore ways to make Mathematics easier for other students using feedback from students enrolled in NSF mathematics peer leading workshops, and use ...

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, 2019 University of Lynchburg

#### Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

*Undergraduate Theses and Capstone Projects*

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic ...

A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, 2019 Chapman University

#### A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

The classical unconditional exact *p*-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact *p*-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate ...

Folding Mathematics: A Mathematical Approach To Origami, 2019 Louisiana Tech University

#### Folding Mathematics: A Mathematical Approach To Origami, Zachary Davis

*Mathematics Senior Capstone Papers*

From constructing a midpoint on a line to observing specific divisions of a plane, the art form of Origami borrows many mathematical tools in order to create complex, and often symmetrical, patterns in a paper medium known as a fold. For this project, the traditional fold known as the Origami Crane/Swan will be thoroughly examined as it contains the unique property to lie completely flat when complete. This phenomenon occurs because the vertices holding the fold together are not all considered to be flat folds. The different types of vertices interacting with each other create a natural locking mechanism ...