The results of a round robin tournament can be represented as a matrix of zeros and ones, by ordering the players and placing a one in the (i,j) position if player i beat player j, and zeros otherwise. These matrices, called tournament matrices, can be represented by graphs, called tournament graphs. They have been the subject of much research and study, yet there have been few attempts to give a wide exposition on the subject. Those that have been done tend to focus on the graph theoretical aspects of tournaments. S. Ree and Y. Koh did write a brief survey from the matrix viewpoint in 1998, but it was not complete and not published. This paper is an attempt to give an exposition on tournament matrices. Recent research will be presented, some new ideas and properties will be proposed, and a few applications of the material will be reviewed.

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Seismic hazard analysis aims to estimate human risk due to natural disasters such as earthquakes. To improve seismic hazard analysis, our group is focused on earthquake induced tsunamis and the use of statistical models to reconstruct historical earthquakes. Based on the estimated wave heights given in anecdotal historical descriptions, we created observational probability distributions to model the historically recorded observations and constructed a prior distribution on the relevant earthquake parameters based on known seismicity of a given region. Then we used the software package GeoClaw, and a Metropolis-Hastings sampler to obtain a posterior distribution of earthquake parameters that most closely matches the historically recorded tsunami. Our method was tested on two main events that occurred in 1820 and 1852 in central and eastern Indonesia respectively. The random walk Metropolis-Hastings sampler we employed appeared to recover the causal earthquake quite well, but the computational costs were prohibitive even though both scenarios we considered were relatively simple. To improve the sampling procedure, we have focused on advanced sampling techniques such as Hamiltonian Monte Carlo (HMC) where the gradient of the forward model (Geoclaw) is required. This is problematic however as this gradient is not available computationally. To mitigate this problem, we make use of a linearized adjoint solver for the shallow water equations, and exact gradient calculations for the Okada earthquake rupture model, yielding a surrogate gradient that leads to improved sampling.

Malaria is a vector borne disease that has been plaguing mankind since before recorded history. The disease is carried by three subspecies of mosquitoes Anopheles gambiae, Anopheles arabiensis and Anopheles funestu. These mosquitoes carry one of four type of Plasmodium specifically: P. falciparum, P. vivax, P. malariae or P. ovale. The disease is a killer; the World Health Organization (WHO) estimates that about 40% of the world's total populations live in areas where malaria is an endemic disease and as global warming occurs, endemic malaria will spread to more areas. The malaria parasite kills a child every 30 seconds. In Africa alone, as many as one million children die annually from malaria before they reach the age of 5. The World Health Organization has an estimate of 100-200 million victims annually. Malaria has many mathematical models and this paper will examine several different models in order to achieve a greater understanding of this disease.

Intense intervention is needed for students who have persistent math challenges and perform below grade level. In the classroom setting, teachers need to provide additional support for some students based on their specific needs. This correlational study was an examination of interventions' impact on student achievement in math. The sample comprised students enrolled in Algebra I during the 2021–2022 school year. The results of this study showed that interventions may have a positive impact on student performance, especially when carried out in the proper educational setting. The findings from the research showed that there is no significant statistical correlation between students who received the intervention and those who didn't, as observed through the Algebra 1 EOC. Further studies are required to determine the impact of the interventionist on the academic performance of the students.

Indiana University-Purdue University Indianapolis (IUPUI) / Music and math are related in that 1) they both rely on the basic understanding of numbers, proportions, intervals, measurements, and operations and 2) both require levels of abstract thinking and symbolic notation. Studies link music and math by examining, for example, how music may play a role in math performance. There are, however, few studies that examine how a musical curriculum may impact not only math performance, but math related variables including math anxiety, math self-efficacy, and math motivation. This study sought to develop and assess the feasibility of MuSciQ, a music technology-based curriculum, and explore how it might impact math anxiety, math selfefficacy, math motivation, and math performance in twelve fourth-grade students. Additionally, acceptability of the MuSciQ curriculum was assessed by students, a teacher, and a school administrator by using the Technology Acceptance Model. Participants experienced large, significant improvements in math anxiety scores and significant improvement in math motivation. Math performance and self-efficacy showed small, non-significant improvements. When split by gender, only math anxiety scores showed statistically significant improvement in males. As expected, there was a significant positive correlation between motivation and self-efficacy before and after the curriculum was introduced. There was also a significant positive correlation between technology acceptance and motivation. Surprisingly, although there were significant positive correlations between the pre- anxiety and motivation measures, there were no significant correlations after the curriculum was introduced. There were no significant correlations found between anxiety and technology acceptance. There was, however, a significant correlation between technology acceptance and self-efficacy. Technology acceptance and additional qualitative comments provided by students and administrators suggest MuSciQ is an easy and useful platform to promote music and math learning. These findings point to a need for further investigation into the influence of MuSciQ on math related variables.

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Say Yes Quickly is a manuscript of poetry.

The purposes of this study were to assess the effect of the initial and exiting attitudes toward mathematics and academic outcomes of students placed in the Developmental Mathematics Basic Arithmetic course at a community college in Maryland. Major research questions included were: (1) What is the difference, if any, between the pretest and posttest attitudes toward mathematics of students placed in Basic Arithmetic as measured by the Aiken Mathematics Attitude Survey? (2) What is the effect, if any, of the placement test for students enrolled in Basic Arithmetic on the final exam score, attitude pretest scores, and attitude change scores? (3) What is the difference between the achievers and nonachievers in Basic Arithmetic as measured by the Aiken Attitude Towards Mathematics Survey? (4) What is the difference between the achievers and nonachievers in Basic Arithmetic based on the demographic variables of age, gender, and ethnicity? The population consisted of 329 students placed in the developmental course DVM001 Basic Arithmetic. Data were collected by utilizing the Lewis R. Aiken Attitude Toward Mathematics Survey and the admissions and registration data. The analysis of variance and the Paired Samples Test were used to obtain the comparative and correlation analysis. Chi Square was utilized to determine the relationship between the final grade and the demographic variables. The results revealed: (a) No significant differences between the pretest and posttest attitudes toward mathematics; (b) The posttest shows a gain of 1.70 percent in the attitudes towards mathematics; (c) Attitude change based on gender showed a gain in the female score only; (d) Achievers and nonachievers have the same attitude towards mathematics; (e) There were statistically significant differences between the placement score and the final exam score, and (f) The demographic variables of age and gender were related to the final exam score. / Ed. D.