The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, 2016 Western Michigan University

#### The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown

*Honors Theses*

*The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam *follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.

General Equations For Natural Selection Under Complete Dominance, 2016 New York University

#### General Equations For Natural Selection Under Complete Dominance, Kasthuri Kannan, Adriana Heguy

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Development Of Honesty In Repeated Signalling Games, 2016 University of North Carolina at Greensboro

#### Development Of Honesty In Repeated Signalling Games, Michael I. Leshowitz

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Extracting Biochemical Parameters From Protein Distributions Of Vascular Cells, 2016 Cleveland State University

#### Extracting Biochemical Parameters From Protein Distributions Of Vascular Cells, Partha Srinivasan

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Interdisciplinary Undergraduate Research In Biofluids, 2016 James Madison University

#### Interdisciplinary Undergraduate Research In Biofluids, Eva M. Strawbridge

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

A Survey Of Graphs Of Minimum Order With Given Automorphism Group, 2016 University of Texas at Tyler

#### A Survey Of Graphs Of Minimum Order With Given Automorphism Group, Jessica Alyse Woodruff

*Math Theses*

We survey vertex minimal graphs with prescribed automorphism group. Whenever possible, we also investigate the construction of such minimal graphs, confirm minimality, and prove a given graph has the correct automorphism group.

Definition Of A Method For The Formulation Of Problems To Be Solved With High Performance Computing, 2016 Kennesaw State University

#### Definition Of A Method For The Formulation Of Problems To Be Solved With High Performance Computing, Ramya Peruri

*Master of Science in Computer Science Theses*

Computational power made available by current technology has been continuously increasing, however today’s problems are larger and more complex and demand even more computational power. Interest in computational problems has also been increasing and is an important research area in computer science. These complex problems are solved with computational models that use an underlying mathematical model and are solved using computer resources, simulation, and are run with High Performance Computing. For such computations, parallel computing has been employed to achieve high performance. This thesis identifies families of problems that can best be solved using modelling and implementation techniques of ...

Applications Of Discrete Mathematics For Understanding Dynamics Of Synapses And Networks In Neuroscience, 2016 University of Nebraska - Lincoln

#### Applications Of Discrete Mathematics For Understanding Dynamics Of Synapses And Networks In Neuroscience, Caitlyn Parmelee

*Dissertations, Theses, and Student Research Papers in Mathematics*

Mathematical modeling has broad applications in neuroscience whether we are modeling the dynamics of a single synapse or the dynamics of an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better understand how visual information is processed. In Part II, we explore a simple model of neural networks with the goal of discovering how network structure shapes the behavior of the network.

Vision plays an important role in how we interact with our environments. To fully understand how visual information is processed requires an understanding of the way signals are ...

Newsvendor Models With Monte Carlo Sampling, 2016 East Tennessee State University

#### Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

*Electronic Theses and Dissertations*

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected proﬁt. Finally, this method will be used ...

An Algorithm For The Machine Calculation Of Minimal Paths, 2016 East Tennessee State University

#### An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

*Electronic Theses and Dissertations*

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R^{3}, but also to the general case of finding minimal functionals on hypersurfaces in R^{n} associated with an arbitrary metric.

Multilevel Models For Longitudinal Data, 2016 East Tennessee State University

#### Multilevel Models For Longitudinal Data, Aastha Khatiwada

*Electronic Theses and Dissertations*

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each ...

Hybrid Chebyshev Polynomial Scheme For The Numerical Solution Of Partial Differential Equations, 2016 University of Southern Mississippi

#### Hybrid Chebyshev Polynomial Scheme For The Numerical Solution Of Partial Differential Equations, Balaram Khatri Ghimire

*Dissertations*

In the numerical solution of partial differential equations (PDEs), it is common to find situations where the best choice is to use more than one method to arrive at an accurate solution. In this dissertation, hybrid Chebyshev polynomial scheme (HCPS) is proposed which is applied in two-step approach and one-step approach. In the two-step approach, first, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then, the resulting homogeneous equation is solved by boundary type methods including ...

Extension Theorems On Matrix Weighted Sobolev Spaces, 2016 University of Tennessee, Knoxville

#### Extension Theorems On Matrix Weighted Sobolev Spaces, Christopher Ryan Loga

*Doctoral Dissertations*

Let D a subset of R^{n} [R n] be a domain with Lipschitz boundary and 1 ≤ p < ∞ [1 less than or equal to p less than infinity]. Suppose for each x in R^{n} that W(x) is an m x m [m by m] positive definite matrix which satisfies the matrix A_{p} [A p] condition. For k = 0, 1, 2, 3;... define the matrix weighted, vector valued, Sobolev space [L p k of D,W] with

[the weighted L p k norm of vector valued f over D to the p power equals the sum over all alpha with order less than k of the integral over D of the the pth power ...

The Greatest Integer Function, 2016 Claremont Colleges

#### The Greatest Integer Function, Alanna Rae

*Journal of Humanistic Mathematics*

No abstract provided.

Octahedral Dice, 2016 Butler University

#### Octahedral Dice, Todd Estroff, Jeremiah Farrell

*Jeremiah Farrell*

All five Platonic solids have been used as random number generators in games involving chance with the cube being the most popular. Martin Gardenr, in his article on dice (MG 1977) remarks: "Why cubical?... It is the easiest to make, its six sides accomodate a set of numbers neither too large nor too small, and it rolls easily enough but not too easily."

Gardner adds that the octahedron has been the next most popular as a randomizer. We offer here several problems and games using octahedral dice. The first two are extensions from Gardner's article. All answers will be ...

The Most-Perfect 4*4 Puzzle Game, 2016 Butler University

#### The Most-Perfect 4*4 Puzzle Game, Jeremiah Farrell, Karen Farrell

*Jeremiah Farrell*

Draft of the 'Solution Page' for Jeremiah's puzzle "The Most Perfect 4*4 Puzzle Game", which was exchanged at the 2014 London International Puzzle Party. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exhange them. Includes e-mail correspondence with editor of the book.

Seven Roads To Roam: A Magical Journey, 2016 Butler University

#### Seven Roads To Roam: A Magical Journey, Jeremiah Farrell, Judith H. Morrel

*Jeremiah Farrell*

Farrell and Morrel's contribution to "Homage to a Pied Puzzler"

**Related Works: **

See "The ASTEROID Puzzle and Games" online at:

http://digitalcommons.butler.edu/facsch_papers/913/

The Magic Octagon, 2016 Butler University

#### The Magic Octagon, Jeremiah Farrell, Tom Rodgers

*Jeremiah Farrell*

The black nodes mark the corners of an octagon and each of these nodes in connected to four others by lines. The (rather hard) puzzle is to assign the sixteen numbers 0 through 15 to each of the sixteen lines so that each black node has a sum of 30 when the line numbers leading into it are added.

The word version of the puzzle was described in the article "Most-Perfect Word Magic", Oscar Thumpbindle, *Word Ways* Vol. 40(4). Nov. 2007.

Some Curious Cut-Ups, 2016 Butler University

#### Some Curious Cut-Ups, Jeremiah Farrell, Ivan Moscovich

*Jeremiah Farrell*

We have noticed a certain kind of n-gon dissection into triangles that has a wonderful property of interest to most puzzlists. Namely that any two triangles have at least one edge in common yet no two triangles need be congruent. In an informal poll of specialists at a recent convention, none of them saw immediately how this could be accomplished. But in fact it is very straightforward.

Farrell's Spider, 2016 Butler University

#### Farrell's Spider, Jeremiah Farrell, Ivan Moscovich

*Jeremiah Farrell*

Puzzle game featured in Ivan Moscovich's magnetic puzzle pack:

Place the 18 discs on the web so that the sum of the numbers on each of the three hexagons and on each of the three ribs equals 57.