Digital Commons Network^™

What Is A Number?, Nicholas Radley

HON499 projects

This essay is, in essence, an attempt to make a case for mathematical platonism. That is to say, that we argue for the existence of mathematical objects independent of our perception of them. The essay includes a somewhat informal construction of number systems ranging from the natural numbers to the complex numbers.

The Theatre Of Math: The Stage As A Tool For Abstract Math Education, Blaine Hudak

Honors Projects

So often in the education of Mathematics does instruction solely consist of the lecture. While this can be an effective method of communicating the ideas of math, it leaves much to be desired in gathering the interest and intrigue of those who have not dedicated their lives to the study of the subject. Theatre, by contrast, is a tool that has been used in the past as means of teaching complicated and difficult to understand moral and emotional subjects. While Theatre and Mathematics have been used in combination many times in the past, it is most often done in the …

The Impact Of Virtual Learning Modalities On The Academic Success Of Students In One Arkansas School District, Diane F. Richards

ATU Theses and Dissertations 2021 - Present

The COVID-19 pandemic changed the way Arkansas public schools’ offered students an education. While moving through this pandemic, many Arkansas schools implemented optional methods of delivery for their students. Some schools tried to maintain face-to-face classes, while others offered completely online classes. Still, others offered a hybrid format where students attended some face-to-face classes and online classes. One Arkansas school district offered all three options. School districts need guidance as to which teaching methods worked well. The long-term effects of the educational impact of COVID-19 are not known at this time. Schools could benefit from a guide with useful strategies …

A Phenomenological Study Of The Lived Experiences Of African American Women In Undergraduate Stem Degree Programs, Vernon H. Smith

Theses and Dissertations

This applied dissertation was designed to provide a better understanding of the lived experiences of African American women in STEM undergraduate degree programs at a 4-year degree granting institution in the southernmost part of central Virginia. The central problem is that there is disparity between the number of African American women with STEM degrees and that of other races in the STEM job market. The existing literature has gaps in the research of African American women’s perception of undergraduate STEM programs. Further, the researcher posits there is a lack of consideration for diversity that is detrimental to the United States; …

Cognition Without Construction: Kant, Maimon, And The Transcendental Philosophy Of Mathematics, Nicholas A. J. Birmingham

Electronic Thesis and Dissertation Repository

In the Critique of Pure Reason, Immanuel Kant takes the ostensive constructions characteristic of Euclidean-style demonstrations to be the paradigm of both mathematical proofs and synthetic a priori cognition in general. However, the development of calculus included a number of techniques for representing infinite series of sums or differences, which could not be represented with the direct geometrical demonstrations of the past. Salomon Maimon’s Essay on Transcendental Philosophy addresses precisely this disparity. Maimon, owing much to G. W. Leibniz, proposes that differentials of sensation achieve what Kantian constructions could not. More importantly, Maimon develops a kind of symbolic cognition that …

Road To Regionals: A S.T.E.A.M. Team Novel, Erin Distefano

Children's Book Writing and Illustrating (MFA) Theses

This thesis is composed of two parts. First a full-length realistic fiction Middle Grade novel about a group of five girls who form a S.T.E.A.M. (science, technology, engineering, arts and mathematics) team at their school and compete in multiple tournaments. Through the story they learn not only about themselves, but about each other and help each other to succeed. The second part is a critical paper on how girls are treated in the S.T.E.A.M. world and how more S.T.E.A.M. literature (along with other things) can help to guide girls to more S.T.E.A.M. related fields later in life. It also discusses …

Non-Naturalism And Naturalism In Mathematics, Morality, And Epistemology, Nicholas Distefano

Honors Projects

No abstract provided.

Applied Temperament, Geoffrey D. Hershberger

Theses and Dissertations--Music

The following document was created in order to promote intonation consensus in ensembles and to better facilitate learning in educational settings. Non-keyboard instruments provide musicians an opportunity to make nearly infinitesimal adjustments to pitch while performing; this creates difficulties for students and challenges even the most seasoned professionals. Non-keyboard musicians struggle their whole lives to play in tune, and even when one knows exactly where they want to place a pitch, technical difficulties can foul any musician's performance. When performing solo, the musician must choose a tuning system that is suitable for the music being performed, and attempt to realize …

Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich

Williams Honors College, Honors Research Projects

The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.

Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit

Williams Honors College, Honors Research Projects

In this paper I discuss six philosophical theories of mathematics including logicism, intuitionism, formalism, platonism, structuralism, and moderate realism. I also discuss problems that arise within these theories and attempts to solve them. Finally, I attempt to harmonize the best features of moderate realism and structuralism, presenting a theory that I take to best describe current mathematical practice.

Explaining Participation : An Explanatory History Of Select Gender Patterns In Undergraduate Stem, Michael Pasquale Mastroianni

Legacy Theses & Dissertations (2009 - 2024)

This explanatory study examines three focal periods in undergraduate STEM as related to the gender gap. Social, economic, and more general historical data are used to develop a clear and powerful explanation of baccalaureate trends in biology and engineering. Specifically, historical accounts are offered for 1) a ten-year period in undergraduate biology in which the number of baccalaureates awarded to men decreased 44 percent, while the number of baccalaureates awarded to women decreased one percent; 2) the start of a twenty-year period in which the number of bachelor’s degrees awarded in the biological sciences increased 150 percent—from 36,068 degrees in …

Epistemology Of The Cartesian Image, Mikhail Pozdniakov

Electronic Thesis and Dissertation Repository

This study is an examination of the epistemological history of the image. Its first strands are to be found in the Christian concept of profanity, in the difference of the world to the divine. The highest form of intelligibility profanity could have, second only to theology, was mathematics. Derived from the problems surrounding this concept are the techniques of inquiry that eventually resulted in the development of analytic geometry by Descartes. The latter marked a new sensibility regarding the physical universe and its constitution, one that is coterminous with the development of exact procedures in science. Being that exactitude regards …

All At One Point: The New Physics Of Italo Calvino And Jorge Luis Borges, Mark Thomas Rinaldi

Dissertations, Theses, and Capstone Projects

This work of comparative literary criticism focuses on the presence of mathematical and scientific concepts and imagery in the works of Italo Calvino and Jorge Luis Borges, beginning with an historical overview of scientific philosophy and an introduction to the most significant scientific concepts of the last several centuries, before shifting to deep, scientifically-driven analyses of numerous individual fictions, and finally concluding with a meditation on the unexpectedly fictive aspects of science and mathematics. The close readings of these authors' fictions are contextualized with thorough explanations of the potential literary implications of theories from physics, mathematics, neuroscience and chaos theory. …

La Vie De Blaise Pascal Et Son Heritage Mathématique Et Philosophique, Katherine Weeks

Honors Theses

This paper will discuss the life of Blaise Pascal, his philosophy and mathematics. We will first study the life of Pascal, by looking at his family, the success of his family, and how he was educated. We will then move onto study the history of the arithmetic triangle, which eventually becomes known as Pascal’s Triangle. Finally we will look at Pascal’s Pensées. Finally we will conclude that Pascal is not only known for Pascal’s Triangle but also his legacy in the Philosophic world. It becomes clear that Pascal would not have been the mathematician he was without the philosophy, and …

A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson

Undergraduate Honors Thesis Collection

The idea for this thesis originated from my fascination with the studies of both music and mathematics throughout my entire life. As a triple major in Middle/Secondary Math Education, Mathematics, and Music, I have learned more than I thought possible of music and math. In proposing this thesis, I desired to use my knowledge of arithmetic and aesthetics to research how music and mathematics are intertwined. I am confident that the following three chapters have allowed me to develop as an academic in both music and mathematics. This thesis serves as a presentation of the connections of music and math …

Existence: An Unholy Trinity. An Account Of Indeterminate Existence, Salas Sanchez-Bennasar

Dissertations, Theses, and Capstone Projects

What is it for something to exist? This dissertation provides an answer to this question by giving a philosophical theory of existence in which the concept of existence in understood as a complex tri-partite notion. The account of existence defended here is arrived at by taking into consideration past philosophical theories of existence, the everyday and scientific uses of the notion, and also philosophical considerations about the nature of reality.

There are three conditions that are central to existence: spatiotemporality, mind-independence, and being a member of the quantificational domain of a true and complete scientific description about the world. To …

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.

Investigating The Status Of Early Numeracy Skills In Bilingual Dual Language Learner Latino Children Attending Head Start And The Association With Parent Demographic Characteristics, Chavely Lissette Iglesias

USF Tampa Graduate Theses and Dissertations

Research on mathematics achievement has become increasingly important with today's technological advances and demand for specialized knowledge. Though there is much literature regarding mathematics achievement in monolingual speakers, little is known regarding the mathematical abilities of Dual Language Learner (DLL) Latino children. This study examined the early numeracy skills in English and Spanish of 132 DLL Latino children attending Head Start programs in five counties across Florida. Relationships and differences among their performance in both languages were examined, along with the contribution of specific parent demographic variables to math achievement. Findings indicated that DLL Latino Head Start children's performance on …

The Calculus Of Variations, Erin Whitney

Honors Theses

The Calculus of Variations is a highly applicable and advancing field. My thesis has only scraped the top of the applications and theoretical work that is possible within this branch of mathematics. To summarize, we began by exploring a general problem common to this field, finding the geodesic be-tween two given points. We then went on to define and explore terms and concepts needed to further delve into the subject matter. In Chapter 2, we examined a special set of smooth functions, inspired by the Calabi extremal metric, and used some general theory of convex functions in order to de-termine …

An Investigation Of Melodic Musical Modeling Using Homogeneous And Non-Homogeneous Markov Chains, Eric Robert Sherman Buenger

Undergraduate Honors Thesis Collection

As an actuarial science student, my observations have a different focus than the other composers. In the industry, actuaries aren't interested in a probability model for its own sake. Rather, they "want to use the model to analyze the ... impact of the events being modeled" [Da]. This analysis focuses equally on the generation of the model as well as the results of the model. While other researchers have investigated many topics in the field of musical generation through mathematical means, no one has yet explored non-homogeneous and homogeneous models simultaneously. This study compares melodic material generated from both homogeneous …

An Investigation Of Air Resistance On Projectile Motion From Aristotle To Euler, Michael Edward Clayton

Theses Digitization Project

From antiquity until today, mathematicians have tried to develop a theory of projectile motion. The development of a theory of projectile motion began with just a basic observation of motion by the great Greek mathematician Aristotle and has evolved to become more than conjecture or hypothesis, but a well developed science of prediciting the flight and accuracy of a projectile in motion. This thesis traces the development of the theory of projectile motion from Greek antiquity to about the mid 1700's.

A General Look At Posets Rings And Lattices, Courtney A. Phillips

Honors Theses

A lattice is a type of structure that aims to organize certain relationships that exist between members of a set. This thesis seeks to define lattices, and demonstrate the different types. It will give examples of lattices, as well as various ways to describe and classify them.

Preservice Elementary Teachers‟ Pedagogical Content Knowledge Related To Area And Perimeter: A Teacher Development Experiment Investigating Anchored Instruction With Web-Based Microworlds, Matthew S. Kellogg

USF Tampa Graduate Theses and Dissertations

Practical concepts, such as area and perimeter, have an important part in today's school mathematics curricula. Research indicates that students and preservice teachers (PSTs) struggle with and harbor misconceptions regarding these topics. Researchers suggest that alternative instructional methods be investigated that enhance PSTs' conceptual understanding and encourage deeper student thinking. To address this need, this study examined and described what and how PSTs learn as they engage in anchored instruction involving web-based microworlds designed for exploring area and perimeter. Its focus was to examine the influences of a modified teacher development experiment (TDE) upon 12 elementary PSTs' content knowledge (CK) …

Women And Math Performance: The Effects Of Stereotype Threat, Math Identity, And Gender Identity, Felicia W. Chu

Seton Hall University Dissertations and Theses (ETDs)

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Form And Numbers: Mathematical Patterns And Ordering Elements In Design, Alison Marie Thom

USF Tampa Graduate Theses and Dissertations

In America, buildings are often constructed with the intent of being utile only 30-40 years. All over the world though, there are buildings that are hundreds of years old that are still very functional. Historically, architecture was a part of mathematics, and in many periods of the past, the two were indistinguishable. Architects were often required to be also mathematicians in ancient times. The idea of this thesis is to identify the relationship between mathematics and architecture and to reintroduce them in order to create a module for successful design .

Presence of mathematical boundaries help to attain visual consistency …

Everything Stems From Nothing, Daniel Theis

All Theses

In sixteenth century Europe, mathematics was undergoing a transformation. Prominently among these changes were the switch from roman numerals to arabic numerals and the implementation of the number zero. The number zero has two main functions: to stand on its own as a symbol of nothing and to function as a placeholder. Thus, zero can be a symbol of nothing as well as a number that dramatically increases the value of the others. The dual roles of zero led to much confusion in early modern people. Shakespeare uses the different roles of zero in his plays Richard III, Hamlet, and …

The Relationship Between Teaching Experience And Style And Primary Student Gains In Mathematics Using An Integrated Learning System, Marilyn N. Meub

USF Tampa Graduate Theses and Dissertations

The purpose of this mixed methods study was to ascertain using multiple tools and methods, the impact of teachers' interaction with primary students on mathematics performance using the Successmaker Integrated Learning System to determine effective teacher practices. The sample of nineteen primary teachers from an elementary school in southwest Florida included five first grade teachers, seven second grade teachers, and seven third grade teachers.

Data analysis included total years of teaching experience, years of experience in Florida schools, and years of experience at each grade. Both the total years of teaching and the years of teaching at the research site …

Lessons Learned About Boys’ And Girls’ Mathematical Problem Solving: The Solution Processes, Performance, Linguistic Explanations, Self-Efficacy, And Self-Assessment Of Fifth-Grade Students Of Varying Reading And Mathematics Abilities, Patricia D. Hunsader

USF Tampa Graduate Theses and Dissertations

The purpose of this non-experimental, causal-comparative study was to examine how gender, reading ability, and mathematics ability differentially moderated students’ mathematical problem-solving processes, linguistic explanations of those solution processes, achievement on a mathematical problem-solving test, self-efficacy on a self-reported rating scale, and selfassessment on a self-reported rating scale. The investigation addressed five research questions. First, to what extent are students’ mathematical problemsolving processes related to gender? Second, to what extent is children’s performance in mathematical problem solving related to gender, reading ability, and mathematics ability? Third, to what extent is the quality of students’ linguistic explanations of their problem-solving processes …

History Of Applied Geometry, Evelyn Jackson

Electronic Thesis and Dissertation

No abstract provided.