Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Mathematics (1815)
- Arts and Humanities (831)
- Education (436)
- Science and Mathematics Education (311)
- Social and Behavioral Sciences (240)
-
- Applied Mathematics (226)
- Physics (215)
- Environmental Sciences (205)
- Computer Sciences (187)
- Life Sciences (135)
- Creative Writing (130)
- Discrete Mathematics and Combinatorics (118)
- Statistics and Probability (108)
- Poetry (104)
- Algebra (95)
- Higher Education (93)
- Philosophy (90)
- History (89)
- Other Mathematics (84)
- Curriculum and Instruction (79)
- Scholarship of Teaching and Learning (70)
- Sustainability (67)
- Chemistry (66)
- Engineering (64)
- Geometry and Topology (62)
- Teacher Education and Professional Development (62)
- Earth Sciences (60)
- Medicine and Health Sciences (59)
- Logic and Foundations of Mathematics (58)
- Keyword
-
- Mathematics (102)
- Poetry (43)
- Combinatorics (38)
- Physics (33)
- Education (31)
-
- Mathematics education (25)
- Statistics (25)
- Art (24)
- STEAM (23)
- Sustainability (23)
- STEM (21)
- Teaching (20)
- Caves (18)
- Algebra (17)
- Math (17)
- Geometry (16)
- Heights (16)
- Pedagogy (16)
- Creativity (15)
- Differential equations (15)
- Motherhood (15)
- Probability (15)
- Dirichlet problem (14)
- Machine Learning (14)
- Mathematical modeling (14)
- Algebra rings (13)
- Complex symmetric operator (13)
- Environment (13)
- Ethics (13)
- Fibonacci numbers (13)
- Publication Year
- Publication
-
- Journal of Humanistic Mathematics (612)
- All HMC Faculty Publications and Research (564)
- Humanistic Mathematics Network Journal (415)
- Pomona Faculty Publications and Research (192)
- HMC Senior Theses (138)
-
- CMC Senior Theses (113)
- CMC Faculty Publications and Research (95)
- Pomona Senior Theses (79)
- Scripps Senior Theses (76)
- The STEAM Journal (58)
- CODEE Journal (56)
- CGU Theses & Dissertations (50)
- CGU Faculty Publications and Research (48)
- WM Keck Science Faculty Papers (46)
- EnviroLab Asia (27)
- Pitzer Faculty Publications and Research (27)
- Pitzer Senior Theses (22)
- Claremont-UC Undergraduate Research Conference on the European Union (5)
- Pomona Economics (5)
- Environmental Analysis Program Mellon Student Summer Research Reports (3)
- KGI Theses and Dissertations (2)
- All Faculty Publications (1)
- Eastern Sierra History Journal (1)
- Environmental Analysis Program Senior Projects (1)
- Interface Compendium of Student Work (1)
- KGI Faculty Publications and Research (1)
- Library Staff Publications and Research (1)
- Scripps Faculty Publications and Research (1)
- Publication Type
- File Type
Articles 451 - 480 of 2640
Full-Text Articles in Physical Sciences and Mathematics
The Complexity Of Symmetry, Matthew Lemay
The Complexity Of Symmetry, Matthew Lemay
HMC Senior Theses
One of the main goals of theoretical computer science is to prove limits on how efficiently certain Boolean functions can be computed. The study of the algebraic complexity of polynomials provides an indirect approach to exploring these questions, which may prove fruitful since much is known about polynomials already from the field of algebra. This paper explores current research in establishing lower bounds on invariant rings and polynomial families. It explains the construction of an invariant ring for whom a succinct encoding would imply that NP is in P/poly. It then states a theorem about the circuit complexity partial …
The Slice Rank Polynomial Method, Thomas C. Martinez
The Slice Rank Polynomial Method, Thomas C. Martinez
HMC Senior Theses
Suppose you wanted to bound the maximum size of a set in which every k-tuple of elements satisfied a specific condition. How would you go about this? Introduced in 2016 by Terence Tao, the slice rank polynomial method is a recently developed approach to solving problems in extremal combinatorics using linear algebraic tools. We provide the necessary background to understand this method, as well as some applications. Finally, we investigate a generalization of the slice rank, the partition rank introduced by Eric Naslund in 2020, along with various discussions on the intuition behind the slice rank polynomial method and …
Tiling Representations Of Zeckendorf Decompositions, John Lentfer
Tiling Representations Of Zeckendorf Decompositions, John Lentfer
HMC Senior Theses
Zeckendorf’s theorem states that every positive integer can be decomposed uniquely into a sum of non-consecutive Fibonacci numbers (where f1 = 1 and f2 = 2). Previous work by Grabner and Tichy (1990) and Miller and Wang (2012) has found a generalization of Zeckendorf’s theorem to a larger class of recurrent sequences, called Positive Linear Recurrence Sequences (PLRS’s). We apply well-known tiling interpretations of recurrence sequences from Benjamin and Quinn (2003) to PLRS’s. We exploit that tiling interpretation to create a new tiling interpretation specific to PLRS’s that captures the behavior of the generalized Zeckendorf’s theorem.
On The Tropicalization Of Lines Onto Tropical Quadrics, Natasha Crepeau
On The Tropicalization Of Lines Onto Tropical Quadrics, Natasha Crepeau
HMC Senior Theses
Tropical geometry uses the minimum and addition operations to consider tropical versions of the curves, surfaces, and more generally the zero set of polynomials, called varieties, that are the objects of study in classical algebraic geometry. One known result in classical geometry is that smooth quadric surfaces in three-dimensional projective space, $\mathbb{P}^3$, are doubly ruled, and those rulings form a disjoint union of conics in $\mathbb{P}^5$. We wish to see if the same result holds for smooth tropical quadrics. We use the Fundamental Theorem of Tropical Algebraic Geometry to outline an approach to studying how lines lift onto a tropical …
Going Meta On The Minimum Circuit Size Problem: How Hard Is It To Show How Hard Showing Hardness Is?, Zoë Bell
Going Meta On The Minimum Circuit Size Problem: How Hard Is It To Show How Hard Showing Hardness Is?, Zoë Bell
HMC Senior Theses
The Minimum Circuit Size Problem (MCSP) is a problem with a long history in computational complexity theory which has recently experienced a resurgence in attention. MCSP takes as input the description of a Boolean function f as a truth table as well as a size parameter s, and outputs whether there is a circuit that computes f of size ≤ s. It is of great interest whether MCSP is NP-complete, but there have been shown to be many technical obstacles to proving that it is. Most of these results come in the following form: If MCSP is NP-complete …
On Rank-Two And Affine Cluster Algebras, Feiyang Lin
On Rank-Two And Affine Cluster Algebras, Feiyang Lin
HMC Senior Theses
Motivated by existing results about the Kronecker cluster algebra, this thesis is concerned with two families of cluster algebras, which are two different ways of generalizing the Kronecker case: rank-two cluster algebras, and cluster algebras of type An,1. Regarding rank-two cluster algebras, our main result is a conjectural bijection that would prove the equivalence of two combinatorial formulas for cluster variables of rank-two skew-symmetric cluster algebras. We identify a technical result that implies the bijection and make partial progress towards its proof. We then shift gears to study certain power series which arise as limits of ratios of …
Towards Tropical Psi Classes, Jawahar Madan
Towards Tropical Psi Classes, Jawahar Madan
HMC Senior Theses
To help the interested reader get their initial bearings, I present a survey of prerequisite topics for understanding the budding field of tropical Gromov-Witten theory. These include the language and methods of enumerative geometry, an introduction to tropical geometry and its relation to classical geometry, an exposition of toric varieties and their correspondence to polyhedral fans, an intuitive picture of bundles and Euler classes, and finally an introduction to the moduli spaces of n-pointed stable rational curves and their tropical counterparts.
Exploring Winning Strategies For The Game Of Cycles, Kailee Lin
Exploring Winning Strategies For The Game Of Cycles, Kailee Lin
HMC Senior Theses
This report details my adventures exploring the Game of Cycles in search of winning strategies. I started by studying combinatorial game theory with hopes to use the Sprague-Grundy Theorem and the structure of Nimbers to gain insight for the Game of Cycles. In the second semester, I pivoted to studying specific types of boards instead. In this thesis I show that variations of the mirror-reverse strategy developed by Alvarado et al. in the original Game of Cycles paper can be used to win on additional game boards with special structure, such as lollipops, steering wheel locks, and 3-spoke trees. Additionally …
Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez
Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez
HMC Senior Theses
Many biological systems form structured swarms, for instance in locusts, whose swarms are known as hopper bands. There is growing interest in applying mathematical models to understand the emergence and dynamics of these biological and social systems. We model the locusts of a hopper band as point particles interacting through repulsive and attractive social "forces" on a one dimensional periodic domain. The primary goal of this work is to modify this well studied modelling framework to be more biological by restricting repulsion to act locally between near neighbors, while attraction acts globally between all individuals. This is a biologically motivated …
On The Inverse Hull Of A One-Sided Shift Of Finite Type, Aria Beaupre
On The Inverse Hull Of A One-Sided Shift Of Finite Type, Aria Beaupre
HMC Senior Theses
Let S be the semigroup constructed from a one-sided shift of finite type. In this thesis, we will provide the construction of H(S), the inverse hull of S, explore the properties of H(S), and begin to characterize the structure of H(S). We will also focus on a kind of one-sided shift of finite type, Markov shifts, and prove an invariant on isomorphic inverse hulls of Markov shifts.
Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes
Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes
HMC Senior Theses
Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.
Environmental Controls On The Spatial Distribution Of Greenfin Darters And Biodiversity In The Blue Ridge Mountains, Dri Tattersfield
Environmental Controls On The Spatial Distribution Of Greenfin Darters And Biodiversity In The Blue Ridge Mountains, Dri Tattersfield
CMC Senior Theses
Disproportionate concentrations of biodiversity in mountains worldwide suggest linkages between geologic processes and biodiversity that are not yet well understood. The Tennessee River Basin in the Blue Ridge Mountains of the southeastern U.S. is a global hotspot for freshwater fish biodiversity. To investigate drivers of biodiversity in the Tennessee River Basin, and explore links to geologic processes, I study the Greenfin Darter (Nothonotus chlorobranchius), a small fish endemic to the upper Tennessee River Basin. I use generalized linear models (GLMs) to evaluate the influence of topography, lithology, climate and land use on the distribution of the Greenfin Darter, …
Molecular Spectroscopy For Innovative Physics: Alcl & Baf, Alex Preston
Molecular Spectroscopy For Innovative Physics: Alcl & Baf, Alex Preston
Pomona Senior Theses
This thesis is inspired by recent developments in the realm of fundamental physics. Spectroscopic studies on diatomic molecules are at the forefront of such endeavors. High-precision microwave spectroscopy probing the rotational energy level transitions of the molecules AlCl and BaF are analyzed at length in this work. The frequency data for these molecules are evaluated using the programs SPFIT and SPCAT in order to develop a “global fit” numerical model of the rotational, vibrational, nuclear, and hyperfine parameters characterizing the systems. Born-Oppenheimer breakdown terms used to amend inconsistencies in the spectral coefficients are determined for both systems. Previously published data …
Heat Stress During Larval Stages On Coral Survivorship For M. Capitata, Sarah Woo
Heat Stress During Larval Stages On Coral Survivorship For M. Capitata, Sarah Woo
Pitzer Senior Theses
Very little is known about how heat stress during larvae stages effect larvae survivorship, early coral recruit settlement, and later stage coral survivorship. We focused on determining how heat stress during larvae stages effected Montipora capitata survivorship over time. After thermally stressing larvae, we asked how many larvae survived the treatment, how the treatment affected settlement, how many larvae survived the heat treatment but did not settle, and later stage coral survivorship experienced residual effects from the heat stress treatment. We exposed coral larvae to ambient seawater temperatures at 30°C and heated seawater temperatures to 34°C for an hour and …
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Pitzer Senior Theses
This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …
Measuring Machine Learning Model Uncertainty With Applications To Aerial Segmentation, Kevin James Cotton
Measuring Machine Learning Model Uncertainty With Applications To Aerial Segmentation, Kevin James Cotton
CGU Theses & Dissertations
Machine learning model performance on both validation data and new data can be better measured and understood by leveraging uncertainty metrics at the time of prediction. These metrics can improve the model training process by indicating which training data need to be corrected and what part of the domain needs further annotation. The methods described have yet to reach mainstream adoption, and show great potential. Here, we survey the field of uncertainty metrics and provide a robust framework for its application to aerial segmentation. Uncertainty is divided into two types: aleatoric and epistemic. Aleatoric uncertainty arises from variations in training …
Centering The Arts In Stem, Fay Cobb Payton
Centering The Arts In Stem, Fay Cobb Payton
The STEAM Journal
A reflection on a STEAM initiative: NC State University Alumni and their children attended free STEAM (Science, Technology, Engineering, Arts, and Math) family workshops at D.H. Hill Library. This program was a collaboration between Dr. Fay Cobb Payton, professor of Information Systems/Technology and University Faculty Scholar at NC State, the NCSU Libraries, and Arts NC State
Evolution Of Island, Dominique Kongsli
Evolution Of Island, Dominique Kongsli
The STEAM Journal
Evolution of Island emerged from the depths of an ocean of blue paint. My process involves observation of nature: I remember scuba diving in Thailand in the Andaman Sea and having a spiritual experience underwater while observing Christmas-tree worms pop in and out of the coral.
The Beautiful Math Of Everything And You Included, E. Ozie
The Beautiful Math Of Everything And You Included, E. Ozie
The STEAM Journal
This a reflection on how there is beautiful math to everything. An author's interpretation of matrices and mechanics in its relationship to someone's identity.
Drawing Parallels In Art Science For Collaborative Learning: A Case Study, Karen Westland
Drawing Parallels In Art Science For Collaborative Learning: A Case Study, Karen Westland
The STEAM Journal
This research paper explores drawing as a tool to facilitate interdisciplinary practice. Outlined is the personal experience of PhD researcher [name removed] in their physics/craft research project, combined with thoughts and opinions from collaborators gathered through group discursive interviews. Interdisciplinary projects face interpersonal and conceptually ambiguous challenges which can be addressed through adopting drawing techniques for educational purposes. Findings highlight that drawing can assist across a breadth of applications as a learning tool for everyone, regardless of drawing ability, to improve the functionality of collaborative projects. Specifically, drawing combined with other communication techniques develops a performative communicative approach that enriches …
Visual Arts Enhance Instruction In Observation And Analysis Of Microscopic Forms In Developmental And Cell Biology, Max Ezin, Christina Noravian, Amira Mahomed, Adam Lyle, Aveleen Gill, Tamira Elul
Visual Arts Enhance Instruction In Observation And Analysis Of Microscopic Forms In Developmental And Cell Biology, Max Ezin, Christina Noravian, Amira Mahomed, Adam Lyle, Aveleen Gill, Tamira Elul
The STEAM Journal
Two important skills for scientists in developmental and cell biology, as well as in fields such as neurobiology, histology and pathology, are: 1) observation of features and details in microscopic images of cells, and 2) quantification of cellular features observed in microscopic images. However, current training in developmental and cell biology does not emphasize observation and quantitative analysis of microscopic images, and it is unclear how best to teach students these skills. Here, we describe our experiences applying visual artistic approaches to instruct undergraduate and graduate students in how to observe and analyze cellular forms in microscopic images. At Loyola …
Jack Of All Trades, Master Of Scifi, Scott Coon
Jack Of All Trades, Master Of Scifi, Scott Coon
The STEAM Journal
This is a reflection on skills and science fiction
Modeling Residence Time Distribution Of Chromatographic Perfusion Resin For Large Biopharmaceutical Molecules: A Computational Fluid Dynamic Study, Kevin Vehar
KGI Theses and Dissertations
The need for production processes of large biotherapeutic particles, such as virus-based particles and extracellular vesicles, has risen due to increased demand in the development of vaccinations, gene therapies, and cancer treatments. Liquid chromatography plays a significant role in the purification process and is routinely used with therapeutic protein production. However, performance with larger macromolecules is often inconsistent, and parameter estimation for process development can be extremely time- and resource-intensive. This thesis aimed to utilize advances in computational fluid dynamic (CFD) modeling to generate a first-principle model of the chromatographic process while minimizing model parameter estimation's physical resource demand. Specifically, …
Extending Power Series Methods For The Hodgkin-Huxley Equations, Including Sensitive Dependence, James S. Sochacki
Extending Power Series Methods For The Hodgkin-Huxley Equations, Including Sensitive Dependence, James S. Sochacki
CODEE Journal
A neural cell or neuron is the basic building block of the brain and transmits information to other neurons. This paper demonstrates the complicated dynamics of the neuron through a numerical study of the Hodgkin-Huxley differential equations that model the ionic mechanisms of the neuron: slight changes in parameter values and inputted electrical impulses can lead to very different (unexpected) results. The methods and ideas developed for the ordinary differential equations are extended to partial differential equations for Hodgkin-Huxley networks of neurons in one, two and three dimensions.
Quantifying Controllability In Temporal Networks With Uncertainty, James C. Boerkoel Jr., Lindsay Popowski, Michael Gao, Hemeng Li, Savana Ammons, Shyan Akmal
Quantifying Controllability In Temporal Networks With Uncertainty, James C. Boerkoel Jr., Lindsay Popowski, Michael Gao, Hemeng Li, Savana Ammons, Shyan Akmal
All HMC Faculty Publications and Research
Controllability for Simple Temporal Networks with Uncertainty (STNUs) has thus far been limited to three levels: strong, dynamic, and weak. Because of this, there is currently no systematic way for an agent to assess just how far from being controllable an uncontrollable STNU is. We provide new insights inspired by a geometric interpretation of STNUs to introduce the degrees of strong and dynamic controllability - continuous metrics that measure how far a network is from being controllable. We utilize these metrics to approximate the probabilities that an STNU can be dispatched successfully offline and online respectively. We introduce new methods …
Specifications-Based Grading Reduces Anxiety For Students Of Ordinary Differential Equations, Mel Henriksen, Jakob Kotas, Mami Wentworth
Specifications-Based Grading Reduces Anxiety For Students Of Ordinary Differential Equations, Mel Henriksen, Jakob Kotas, Mami Wentworth
CODEE Journal
Specifications-based grading (SBG) is an assessment scheme in which student grades are based on demonstrated understanding of known specifications which are tied to course learning outcomes. Typically with SBG, students are given multiple opportunities to demonstrate such understanding. In undergraduate-level introductory ordinary differential equations courses at two institutions, SBG has been found to markedly decrease students’ self-reported anxiety related to the course as compared to traditionally graded courses.
The International Conference On Creative Mathematical Sciences Communication: Online Event (Cmsc'20) And Cmsc'21, Frances Rosamond
The International Conference On Creative Mathematical Sciences Communication: Online Event (Cmsc'20) And Cmsc'21, Frances Rosamond
Journal of Humanistic Mathematics
You are warmly invited to register now for the 5th International Conference on Creative Mathematical Sciences Communication (CMSC’21) which will be held at Adam Mickiewicz University in Poznań, Poland, 2–6 July, 2021.
The International Conference on Creative Mathematical Sciences Communication (CMSC) is a unique gathering of computer scientists and mathematicians, teachers, musicians, dancers, dramatists, game designers, educators and communicators of all sorts.
Due to the pandemic, the in-person event scheduled for 2020 has been post- poned and a short CMSC Online Event was organized as a “teaser” or trailer in order to feel the spirit of the full 5th CMSC …
Numberlines: The Evil Triplets, Egan J. Chernoff, Nat Banting, Jay Wilson
Numberlines: The Evil Triplets, Egan J. Chernoff, Nat Banting, Jay Wilson
Journal of Humanistic Mathematics
The purpose of this article is to further the recent introduction of numberlines. Number lines, still, yes, are a pictorial abstraction of the real numbers; numberlines, however, are hockey line nicknames based on jersey numbers. A discussion of numberlines, the recent playoff woes of the Tampa Bay Lightning, and the binary expansions of the jersey numbers worn by “The Triplets” (who play for The Bolts) culminates with a new nickname more befitting such a transcendent trio.
How To Measure A Coastline, Nora E. Culik
How To Measure A Coastline, Nora E. Culik
Journal of Humanistic Mathematics
The infinite shoreline of Lake Superior is embedded in the mathematical imagination, the memory of its stony beaches, and in the unifying consciousness that holds them all, just as the lake itself lies cradled in the land. The narrator of these paradoxes finds the lake, its border, and the calculi strewn along its shore a place a space between worlds where we rediscover that we can’t measure what we can’t locate, and can’t locate what we can’t measure, even the versions of ourselves.
Changes And Deltas, Jim Wolper
Changes And Deltas, Jim Wolper
Journal of Humanistic Mathematics
Lecturing about Mathematics is like playing Jazz.