Physical Sciences and Mathematics Commons^™

Lack Of Quantitative Training Among Early-Career Ecologists: A Survey Of The Problem And Potential Solutions, F. Barraquand, T. G. Ezard, P. Søgaard Jørgensen, Naupaka B. Zimmerman, S. Chamberlain, R. Salguero-Gómez, T. J. Curran, T. Poisot

Biology Faculty Publications

Proficiency in mathematics and statistics is essential to modern ecological science, yet few studies have assessed the level of quantitative training received by ecologists. To do so, we conducted an online survey. The 937 respondents were mostly early-career scientists who studied biology as undergraduates. We found a clear self-perceived lack of quantitative training: 75% were not satisfied with their understanding of mathematical models; 75% felt that the level of mathematics was “too low” in their ecology classes; 90% wanted more mathematics classes for ecologists; and 95% more statistics classes. Respondents thought that 30% of classes in ecology-related degrees should be …

Existence Of Positive Solutions For A Superlinear Elliptic System With Neumann Boundary Condition, Alfonso Castro, Juan C. Cardeño

All HMC Faculty Publications and Research

We prove the existence of a positive solution for a class of nonlin- ear elliptic systems with Neumann boundary conditions. The proof combines extensive use of a priori estimates for elliptic problems with Neumann boundary condition and Krasnoselskii's compression-expansion theorem

How We Got From There To Here: A Story Of Real Analysis, Eugene Boman, Robert Rogers

Milne Open Textbooks

The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.

This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) …

The Mathematics Of Spot It, Marcus Heemstra

The Journal of Undergraduate Research

Spot It™ is a fun, fast paced game for people of all ages. The game appears to have a rich mathematical structure, which we investigated, using combinatorial analysis. We constructed some similar Spot It type games with a different number of cards, and displayed that some games are impossible to complete. In particular, the original Spot It game has eight objects on each card; however, it is impossible to construct a complete game (a game in which every object appears with every other object) in which every card has seven objects. We have investigated the mathematics behind the game.

Re-Analysis Of The World Data On The Emc Effect And Extrapolation To Nuclear Matter, Stacy E. Karthas

Honors Theses and Capstones

The EMC effect has been investigated by physicists over the past 30 years since it was discovered at CERN. This effect shows that the internal nucleon structure varies when in the nuclear medium. Data from SLAC E139 and JLab E03 103 were studied with the Coulomb correction and directly compared. The Coulomb distortion had a greater impact on the JLab data due to slightly lower energies and different kinematics. The EMC ratio was found to have a dependence on a kinematic variable, which was removed when Coulomb corrections were applied. The methodology was developed to apply Coulomb corrections, which had …

Bad Boundary Behavior In Star Invariant Subspaces I, William T. Ross, Andreas Hartmann

Department of Math & Statistics Faculty Publications

We discuss the boundary behavior of functions in star invariant subspaces (BH²)¹, where B is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of B where B does not admit a derivative in the sense of Carathéodory.

Markov Chain Theory With Applications To Baseball, Cal D. Thomay

Senior Independent Study Theses

The applications of Markov chains span a wide range of fields to which models have been designed and implemented to simulate random processes. Markov chains are stochastic processes that are characterized by their memoryless property, where the probability of the process being in the next state of the system depends only on the current state and not on any of the previous states. This property is known as the Markov property. This thesis paper will first introduce the theory of Markov chains, along with explaining two types of Markov chains that will be beneficial in creating a model for analyzing …

Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder

Senior Independent Study Theses

An option is a contract which gives the holder of the option the right, but not the obligation, to buy or sell a given security at a given price, which is called the strike price. For example, suppose Yahoo stock is currently trading at $10 per share. A person could buy an option that gives him or her the ability to purchase shares of Yahoo stock for $12 in one year. If the price of Yahoo stock is greater than $12 in one year, the holder of the option will make money. However, he or she will not use the …

The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen

Senior Independent Study Theses

The ability to make the right decision is an asset in many areas and lines of profession including social work, business, national economics, and international security. However, decision makers often have difficulty choosing the best option since they might not have a full understanding of their preferences, or lack a systematic approach to solve the decision making problems at hand. The Analytic Hierarchy Process (AHP) provides a mathematical model that helps the decision makers arrive at the most logical choice, based on their preferences. We investigate the theory of positive, reciprocal matrices, which provides the theoretical justification of the method …

Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer

Senior Independent Study Theses

No abstract provided.

Education And Women Mathematicians In The Middle East, Syeda Tooba Zahra

Legacy Theses & Dissertations (2009 - 2024)

Middle Eastern women have made important contributions in the field of Mathematics. The purpose of this thesis is to understand the educational background for women in the Middle East and look at the life and contribution of a sample of women mathematicians in representative Middle Eastern countries such as Turkey, Lebanon, Iran, and Pakistan.

Design Considerations For Visually-Aided Discussion Prompts: Emphasizing Mathematical Reasoning In Teacher Education, Anne Marie S. Marshall, Kadian M. Callahan

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

The availability and familiarity of online discussion tools create new instructional options that teacher educators can use to foster prospective teachers’ understanding of mathematics. In particular, online discussion blogs provide an avenue through which teacher educators can press prospective teachers to explore mathematical concepts and share their mathematical reasoning with peers. Furthermore, by incorporating visual stimulations as a design component of these discussion blogs, prospective teachers can make sense of and respond to others’ ideas about mathematical concepts with greater clarity. This paper shares preliminary findings of a research study that examined the extent to which the design of a …

A Twisted Dimer Model For Knots, Heather M. Russell, Moshe Cohen, Oliver Dasbach

Department of Math & Statistics Faculty Publications

We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.

A Reduced Set Of Moves On One-Vertex Ribbon Graphs Coming From Links, Heather M. Russell, Susan Abernathy, Cody Armond, Moshe Cohen, Oliver T. Dasbach, Hannah Manuel, Chris Penn, Neal W. Stoltzfus

Department of Math & Statistics Faculty Publications

Every link in R³ can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.

A Bayesian Model Of Fertility Decisions In Relationship To Female Labor Force Participation, Rebecca C. Wardrop

Senior Independent Study Theses

Due to the increasing number of women in the labor force, opportunity costs associated with labor force participation are becoming an important factor in fertility decisions. Further, these decisions are assumed to be dynamic as the opportunity costs change as a woman progresses through her career. A Bayesian statistical model , which allows the distribution of the likelihood of having children to be updated as information is gathered, lends itself to the dynamicity of the decision-making process. A generalized model for fertility decisions in terms of labor force participation is created. I also discuss potentials for implementation and furthering the …

Collected Papers, Vol. V, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

On Crittenden And Vanden Eynden's Conjecture, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It is possible to cover all (positive) integers with n geometrical progressions of integers? Find a necessary and sufficient condition for a general class of positive integer sequences such that, for a fixed n , there are n (distinct) sequences of this class which cover all integers.

Algebraic Structures On Real And Neutrosophic Semi Open Squares, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Here for the first time we introduce the semi open square using modulo integers. Authors introduce several algebraic structures on them. These squares under addition modulo ‘n’ is a group and however under product  this semi open square is only a semigroup as under  the square has infinite number of zero divisors. Apart from + and  we define min and max operation on this square. Under min and max operation this semi real open square is a semiring. It is interesting to note that this semi open square is not a ring under + and  since …

Neutrosophic Theory And Its Applications : Collected Papers - Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every entity tends to be …

Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.

Accelerating Computational Algorithms, Michael Risley

Theses and Dissertations

Mathematicians and computational scientists are often limited in their ability to model complex phenomena by the time it takes to run simulations. This thesis will inform interested researchers on how the development of highly parallel computer graphics hardware and the compiler frameworks to exploit it are expanding the range of algorithms that can be explored on affordable commodity hardware. We will discuss the complexities that have prevented researchers from exploiting advanced hardware as well as the obstacles that remain for the non-computer scientist.

Analysis Of Mathematical Models Of The Human Lung, Cooper Racheal

Theses and Dissertations

The processes of lung ventilation and perfusion, diffusion, and gas transport make up the system of breathing and tissue oxygenation. Here, we present several mathematical formulations of the essential processes that contribute to breathing. These models aid in our understanding and analysis of this complex system and can be used to form treatments for patients on ventilators. With the right analysis and treatment options, patients can be helped and money can be saved. We conclude with the formulation of a mathematical model for the exchange of gasses in the body based on basic reaction kinetics.

The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales

Dissertations

The use of standards-based grading in American public schools is increasing, offering students, parents, and teachers a new way of measuring and communicating about student achievement and performance. Parents indicate an appreciation for this method of grading, and students at the elementary grades (K-6) have improved standardized test scores in reading and math as a result of its implementation. This study seeks to determine whether standards-based grading has the same effect on students at the high school level (grades 9-12) by comparing end-of-course test scores and posttest scores of Algebra 2 students enrolled in a standards-based graded classroom with to …

The Kronecker-Weber Theorem: An Exposition, Amber Verser

Lawrence University Honors Projects

This paper is an investigation of the mathematics necessary to understand the Kronecker-Weber Theorem. Following an article by Greenberg, published in The American Mathematical Monthly in 1974, the presented proof does not use class field theory, as the most traditional treatments of the theorem do, but rather returns to more basic mathematics, like the original proofs of the theorem. This paper seeks to present the necessary mathematical background to understand the proof for a reader with a solid undergraduate background in abstract algebra. Its goal is to make what is usually an advanced topic in the study of algebraic number …

Testing And Assessment In Mathematics Via Web Applications, Stefanie Winkler, Carina Pöll, Andreas Körner, Niki Popper, Felix Breitenecker

UBT International Conference

This paper deals with the web interface Maple T.A. which is used for mathematical education at the Vienna University of Technology. Maple T.A. is based on the computer algebra system Maple. This fact offers the possibility to test and assess the students in easy but also complex mathematical matters in an uncomplicated way. This interface was first used only for the refresher course. This course takes place in the first 3 weeks of the semester and deals with the repetition of all the important themes of the school mathematics. Maple T.A. is also used for the basic and advanced mathematical …

On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera

Theses and Dissertations - UTB/UTPA

The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of …

Book Review: Encyclopedia Of Mathematics And Society, Gizem Karaali

Pomona Faculty Publications and Research

The Encyclopedia of Mathematics and Society is an impressive achievement of collective effort and serious thought, an amazing collection of delightful, unexpected essays, a sourcebook for students and teachers alike. The experience of reading the EMS was, for this encyclopedia enthusiast, enlightening and enjoyable.

If any librarians out there are still wondering, let me be clear: I strongly recommend this encyclopedia. For individuals, the expense might well be an initial turn-off; keeping in mind that the hard copy books come with online access to the same content might alleviate some of the pain.

As for me? I expect to enjoy …

Fully Coupled Fluid And Electrodynamic Modeling Of Plasmas: A Two-Fluid Isomorphism And A Strong Conservative Flux-Coupled Finite Volume Framework, Richard Joel Thompson

Doctoral Dissertations

Ideal and resistive magnetohydrodynamics (MHD) have long served as the incumbent framework for modeling plasmas of engineering interest. However, new applications, such as hypersonic flight and propulsion, plasma propulsion, plasma instability in engineering devices, charge separation effects and electromagnetic wave interaction effects may demand a higher-fidelity physical model. For these cases, the two-fluid plasma model or its limiting case of a single bulk fluid, which results in a single-fluid coupled system of the Navier-Stokes and Maxwell equations, is necessary and permits a deeper physical study than the MHD framework. At present, major challenges are imposed on solving these physical models …

Mathematics Libguide, Sandra Barclay

Sandra Barclay

Welcome to the Horace W. Sturgis Library and the Mathematics Libguide at Kennesaw State University! To get started with your math research, this is the place to go. We hope you will find this information helpful. Please let us know what other resources you could use.

Orienteering In Knowledge Spaces: The Hyperbolic Geometry Of Wikipedia Mathematics, Gregory Leibon, Daniel N. Rockmore

Dartmouth Scholarship

In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example …