Mathematics Commons^™

Use Of Standardized Patient Simulations To Assess Impact Of Motivational Interviewing Training On Social--Emotional Development, Suzanne M. Galal, Deepti Vyas, John Mayberry, Ed Rogan

College of the Pacific Faculty Articles

The objective of this study was to assess the impact of motivational interviewing (MI) training on students’ social–emotional development. Two simulations using standardized patients (SP) were conducted within a smoking cessation module. Students first completed a 4 h self-study module focused on smoking cessation tools and general counseling techniques. Faculty then administered a 15-item rubric focused on students’ self-assessment of their verbal/non-verbal communication, social–emotional competence and MI skills. Students then participated in a smoking cessation counseling session with an SP. SPs used the same rubric to assess student performance. Teaching assistants (TAs) observed and assessed the students using the same …

The Circles Of Apollonius, Christopher D. Goff

College of the Pacific Faculty Presentations

After creating an eye-catching logo for the San Joaquin Math Teachers’ Circle, we decided to spend a session studying it. Our investigation evolved into a journey covering over 2000 years of mathematics history, beginning with a lost work created by Apollonius, moving to a problem posed by a princess, and arriving in the strange world of fractals.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

The Ebb And Flow Of Official Calls In Water Polo, James Graham, John Mayberry

College of the Pacific Faculty Articles

Defensive fouls play an important role in elite men’s water polo generating over half of all goals. Despite their importance, little is known about the relationship between foul calling patterns and other game-state variables in the sport. Here we apply a sequence of hierarchical mixed logistic regression models on data from major tournaments in 2012–2014 to study such relationships and find a number of significant biases in foul calling rates. Offensive teams who are winning/tied are about 31% less likely to draw a defensive foul and 32% more likely to get called for an offensive foul than teams who are …

Alan Turing: The Man Behind The Machine, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

How Does The Structure Of A College Chemistry Examination Affect Pedagogy, Rajeev R. Pandey, John Mayberry, Jace Hargis

College of the Pacific Faculty Articles

This study examines variations of assessment and connections to active learning methods, which may enhance both the accuracy of assessment, engagement and retention. Correlation data relating instruction and assessment in a multiple dimensions are presented. Multiple choice (MC) and free response (FR) exams were provided and students were also given the option to provide FR answers to the MC items. This study suggests there is little overall difference in mean or median student scores on the MC vs. FR portions of the exam, but that there is some evidence to believe that student scores on MC portions are more variable …

Participation In The Virtual Environment Of Blended College Courses: An Activity Study Of Student Performance, Cathy Cavanaugh, Jace Hargis, John Mayberry

College of the Pacific Faculty Articles

This paper describes a study of success factors in the introductory semester of liberal studies blended courses offered at the bachelor of science level. The influence of student participation in the online course environment was examined, as measured by the number of times students logged into the learning management system (LMS) and average session length. These measures were correlated with final course grades to increase understanding of the participation patterns of successful students. The resulting patterns and their implications are identified. We observe that students with an intermediate number of logins and average session length tended to exhibit the optimal …

Fusion Algebras & Accidental Trigonometry, Christopher D. Goff

College of the Pacific Faculty Presentations

Have you ever been working in one area of math, and another area arises unexpectedly? While working on a problem in 2008, we inadvertently discovered some trigonometric identities. This talk will explain fusion algebras, which are relatively simple algebraic objects that demonstrate nice algebraic applications of linear algebra. Then we will see how trigonometry can arise in even this most algebraic of settings.

Sexually Dimorphic Gene Expression In The Lateral Eyes Of Euphilomedes Carcharodonta (Ostracoda, Pancrustacea), Andrea Sajuthi, Brenna Carrillo-Zazueta, Briana Hu, Anita Wang, Logan Brodnansky, John Mayberry, Ajna S. Rivera

College of the Pacific Faculty Articles

Background: The evolution and development of sexual dimorphism illuminates a central question in biology: How do similar genomes produce different phenotypes? In an XX/XO system especially the state of a sexually dimorphic trait is determined by differences in gene expression, as there are no additional genetic loci in either sex. Here, we examine the XX/XO ostracod crustacean species Euphilomedes carcharodonta. This species exhibits radical sexual dimorphism of their lateral eyes, females have only a tiny simple lateral eye while males have elaborate ommatidial eyes. Results: We find that males express three of nine eye-development gene homologs at significantly higher levels …

Euler's Multiple Solutions To A Diophantine Problem, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Measures Of Tactical Efficiency In Water Polo, James Graham, John Mayberry

College of the Pacific Faculty Articles

We present a notational analysis of offensive tactics commonly employed in elite men's water polo and address three questions related to this objective: which tactics are most effective?, which tactical performance indicators best classify the winning team?, and how accurate are predictive models based on these performance indicators? We define a new statistic, Efficiency Rating, which quantifies the importance of a tactic via a weighted average of direct and indirect goals generated by its use. By this measure, direct shot is the most efficient even strategy despite being employed far less frequently than centre or perimeter tactics. We address our …

Dynkin Diagrams And Fusion Algebras, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Euler’S Algebraic Creativity And Undergraduate Math, Christopher D. Goff

College of the Pacific Faculty Presentations

This talk will describe the author’s work translating a paper of Euler on number theory, and how researching the history of this paper led back to Lagrange, Fermat, and ultimately to a geometry problem of Diophantus. We will investigate Euler’s algebraic creativity and Lagrange’s explanation of his own method, inspired by Fermat. Moreover, we will demonstrate one way in which this paper of Euler’s has been used as part of a project in an undergraduate history of mathematics course. We will even investigate the continuation of Euler’s work.

Diophantine Geometry, Eulerian Number Theory, And Undergraduates, Christopher D. Goff

College of the Pacific Faculty Presentations

This talk will tell the story of how a geometry problem of Diophantus led all the way to a paper of Euler on number theory. Then we will describe how translating this work of Euler led ultimately to an undergraduate project in a History of Mathematics course last spring.

Traveling Waves Of Selective Sweeps, Rick Durrett, John Mayberry

College of the Pacific Faculty Articles

The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps in an exponentially growing population. To better understand this process, Beerenwinkel et al. [PLoS Comput. Biol. 3 (2007) 2239- 2246] consider a Wright-Fisher model in which cells from an exponentially growing population accumulate advantageous mutations. Simulations show a traveling wave in which the time of the first k-fold mutant, Tk, is approximately linear in k and heuristics are used to obtain formulas for ETk. …

Evolution Of Ligand Specificity In Vertebrate Corticosteroid Receptors, Adam S. Arterbery, Daniel J. Fergus, Elizabeth A. Fogarty, John Mayberry, David L. Deitcher, W. L. Kraus, Andrew H. Bass

College of the Pacific Faculty Articles

Background. Corticosteroid receptors include mineralocorticoid (MR) and glucocorticoid (GR) receptors. Teleost fishes have a single MR and duplicate GRs that show variable sensitivities to mineralocorticoids and glucocorticoids. How these receptors compare functionally to tetrapod MR and GR, and the evolutionary significance of maintaining two GRs, remains unclear. Results. We used up to seven steroids (including aldosterone, cortisol and 11-deoxycorticosterone [DOC]) to compare the ligand specificity of the ligand binding domains of corticosteroid receptors between a mammal (Mus musculus) and the midshipman fish (Porichthys notatus), a teleost model for steroid regulation of neural and behavioral plasticity. Variation in mineralocorticoid sensitivity was …

Generalized Twisted Quantum Doubles And The Mckay Correspondence, Christopher D. Goff, Geoffrey Mason

College of the Pacific Faculty Articles

We consider a class of quasiHopf algebras which we call generalized twisted quantum doubles. They are abelian extensions H=C[G¯]∗⋈C[G] (G is a finite group, G¯ a homomorphic image, and * denotes the dual algebra), possibly twisted by a 3-cocycle, and are a natural generalization of the twisted quantum double construction of Dijkgraaf, Pasquier and Roche. We show that if G is a subgroup of SU₂(C) then H exhibits an orbifold McKay Correspondence: certain fusion rules of H define a graph with connected components indexed by conjugacy classes of G¯, each connected component being an extended affine Diagram of …

Fusion Algebras & Accidental Trigonometry, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Gaussian Perturbations Of Circle Maps: A Spectral Approach, John Mayberry

College of the Pacific Faculty Articles

In this work, we examine spectral properties of Markov transition operators corresponding to Gaussian perturbations of discrete time dynamical systems on the circle. We develop a method for calculating asymptotic expressions for eigenvalues (in the zero noise limit) and show that changes to the number or period of stable orbits for the deterministic system correspond to changes in the number of limiting modulus 1 eigenvalues of the transition operator for the perturbed process. We call this phenomenon a λ-bifurcation. Asymptotic expressions for the corresponding eigenfunctions and eigenmeasures are also derived and are related to Hermite functions. © Institute of Mathematical …

An Isomorphism Between The Fusion Algebras Of Vl+ And Type D(1) Level 2, Michael Cuntz, Christopher D. Goff

College of the Pacific Faculty Presentations

This talk will show that the fusion algebra of the vertex operator algebra V_L⁺ (where L is a rank 1 even lattice) is isomorphic to the fusion algebra of the affine Kac-Moody Lie algebra of type D⁽¹⁾ at level 2.

Characterization Of Digraphs With Equal Domination Graphs And Underlying Graphs, Kim A. S. Factor, Larry L. Langley

College of the Pacific Faculty Articles

A domination graph of a digraph D, dom(D), is created using the vertex set of D and edge {u,v}∈E[dom(D)] whenever (u,z)∈A(D) or (v,z)∈A(D) for every other vertex z∈V(D). The underlying graph of a digraph D, UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, UG(D)=dom(D). The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given.

Does Spelling Count? Reflections On Writing In The Mathematics Classroom, Christopher D. Goff

College of the Pacific Faculty Presentations

The written word is scarce in the stereotypical mathematics course, which instead emphasizes the routine solving of problems. But having students explain their solutions in writing can pave the way to more critical mathematical thinking. This talk will examine the use of writing as a tool to learn mathematics. We will reflect on: reasons to incorporate writing in a mathematics class; which courses lend themselves to writing assignments; what types of assignments to use; samples of student work; and whether using writing can actually improve student learning. Depending on the assignments, writing can also incorporate several “Basic Principles” of AMATYC’s …

Movie Math: Mathematical Talent = Mental Illness, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

A Beautiful Mind, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Is Hollywood Good For Mathematics? (A Brief Discussion)., Christopher D. Goff

College of the Pacific Faculty Presentations

Mathematics has played a role in many recent films, such as Good Will Hunting, A Beautiful Mind, and Proof. But how exactly is mathematics being portrayed? What ramifications does this portrayal have on our ”students,” broadly defined? In Good Will Hunting, mathematics is Will’s ticket out of his lower-class life and into a prestigious existence. In A Beautiful Mind, mathematical talent and schizophrenia are identified, at least in part. In Proof, mathematics not only links a daughter to her late father, but it also provides a backdrop for much of the story’s conflict. In this discussion, we will begin by …

How (West) Hollywood Adds Up: A Queer Theoretical View Of Mathematics And Mathematicians In Film, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Using Composition Techniques To Improve Classroom Instruction And Students’ Understanding Of Proof, Christopher D. Goff

College of the Pacific Faculty Articles

This paper describes an effort to incorporate standard composition exercises into a sophomore-level discrete mathematics class. It provides an example of how peer review can be integrated with a mathematical curriculum through the writing of proofs.

Ethnomathematics: Challenging Traditional Notions Of Mathematical Authority, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Projective And Non-Projective Systems Of First Order Nonlinear Differential Equations, Riad A. Rejoub

University of the Pacific Theses and Dissertations

It is well established that many physical and chemical phenomena such as those in chemical reaction kinetics, laser cavities, rotating fluids, and in plasmas and in solid state physics are governed by nonlinear differential equations whose solutions are of variable character and even may lack regularities. Such systems are usually first studied qualitatively by examining their temporal behavior near singular points of their phase portrait.

In this work we will be concerned with systems governed by the time evolution equations [see PDF for mathematical formulas]

The x_i may generally be considered to be concentrations of species in a chemical …