Physical Sciences and Mathematics Commons^™

On The Utility Of I = √-1, Adam J. Hammett

Science and Mathematics Faculty Presentations

No abstract provided.

Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin

All HMC Faculty Publications and Research

We present mentally efficient algorithms for mentally squaring and cubing 2-digit and 3-digit numbers and for finding cube roots of numbers with 2-digit or 3-digit answers.

A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh

Mathematics Faculty Publications

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …

Quantitative Characterization Of Microstructure Features For 1st Generation Advanced High Strength Steels, Margarita Vidrio, Ellen Liu, Donsheng Li, Kyoo Sil Choi, Xin Sun

STAR Program Research Presentations

The role of Advanced High Strength Steels (AHSS) in the automotive industry is important because of its affordability and excellent mechanical properties. The 1st generation of AHSS achieves its preferred combination of strength and ductility by embedding harder martensite grains into softer ferritic matrix. Ductility and strength of these steels are important to safety, formability, application, and life. However, a noticeable degree of inconsistent forming behaviors has been observed in the 1st generation AHSS in production, which seems to be related to the microstructure-level inhomogeneity. The objective of this project is to grain fundamental understandings on how different microstructure level …

Careers In Mathematics, Adam J. Hammett

Science and Mathematics Faculty Presentations

No abstract provided.

On The Sum Of Reciprocals Of Amicable Numbers, Jonathan Bayless, Dominic Klyve

Mathematics Faculty Scholarship

Two numbers m and n are considered amicable if the sum of their proper divisors,
s(n) and s(m), satisfy s(n) = m and s(m) = n. In 1981, Pomerance showed that
the sum of the reciprocals of all such numbers, P, is a constant. We obtain both a
lower and an upper bound on the value of P.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

A Multiple Regression Analysis Of Personality’S Impact On Actuarial Exam Performance, Matthew Ciaffone

Honors Projects in Mathematics

Existing literature indicates that there is some connection between personality and both academic and work-related performance. The author's intent for the research described herein is to explore this connection for students majoring in actuarial mathematics with regard to their performance on actuarial certification exams. Specifically, using the five-factor model of personality, the author seeks to predict the number of attempts required to pass the first two exams in the process (Exam 1/P - probability; Exam 2/FM - financial mathematics) using measures of the five dimensions of the five-factor model (openness to experience, conscientiousness, extraversion, agreeableness, and emotional stability) through regression …

Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction, Amanda Zagame

Honors Projects in Mathematics

This fall 2010 study of Bryant University students enrolled in freshman-level math courses considered factors related to college-level math performance, including gender, math self-efficacy, math anxiety, and utilization of professors’ office hours and/or tutoring center services. Female students at Bryant reported lower levels of math self-efficacy and higher levels of math anxiety, both of which research has shown to be negatively correlated with test scores. The use of one-on-one instruction was expected to provide a potential counterweight to this equation. Results from the 287 initial and 229 final surveys administered in this study did not support this hypothesis. This phenomenon …

A Census Of Vertices By Generations In Regular Tessellations Of The Plane, Alice Paul '12, Nicholas Pippenger

All HMC Faculty Publications and Research

We consider regular tessellations of the plane as infinite graphs in which q edges and q faces meet at each vertex, and in which p edges and p vertices surround each face. For 1/p + 1/q = 1/2, these are tilings of the Euclidean plane; for 1/p + 1/q < 1/2, they are tilings of the hyperbolic plane. We choose a vertex as the origin, and classify vertices into generations according to their distance (as measured by the number of edges in a shortest path) from the origin. For all p ≥ 3 and q ≥ 3 with 1/p + 1/q ≤ 1/2, we give simple combinatorial derivations of the rational generating functions for the number of vertices in each generation.

Teaching Statistics To Elementary Children: Using A Problem-Solving Approach To Enhance Learning, Kayla Lee Botelho

Honors Projects

When teaching statistics (or data analysis) to elementary children, it is beneficial to use a problem-solving approach that incorporates meaningful tasks to enhance the students' learning. This was determined through a careful review of literature, observations of elementary teachers, and the creation and instruction of data analysis unit. The unit required the students to collect data on heights, organize the data in charts, and display the data in line plots. In addition, the students analyzed the data to recalculate the average and other measures of central tendency and to answer questions that arose through the implementation of the lessons. In …

King, John (Sc 594), Manuscripts & Folklife Archives

MSS Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 594. Ciphering book of John King including mathematical exercises, numeration of money, simple and compound reduction, weights and measures, and word problems.

Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives

MSS Finding Aids

Finding aid and full text (click on "Additional Files" below) for Manuscripts Small Collection 966. Ciphering book (94 p.), focusing chiefly on surveying and navigating rules for solving problems as well as giving specific problems, of Spencer Curd, Logan County, Kentucky, with accompanying genealogical data.

Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko

Department of Math & Statistics Faculty Publications

Springer varieties are studied because their cohomology carries a natural action of the symmetric group S_n and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties X_n as subvarieties of the product of spheres (S²)ⁿ. We show that if X_n is embedded antipodally in (S²)ⁿ then the natural S_n-action on (S²)ⁿ induces an Sn-representation on the image of H_*(X_n). This representation is the Springer representation. Our construction admits an elementary (and geometrically …

Statistical Analysis Model Predicting Computer Use In Mathematics, Rebecca Hudson, Anne Porter, Mark Nelson

Faculty of Informatics - Papers (Archive)

This paper is a report of a doctoral thesis that investigated the factors that were associated with the use of computers in secondary mathematics teaching, the choices made by teachers and learning theories guiding their teaching. Mixed methods approaches were used to triangulate the results of the study. The study was divided into three stages, the first a questionnaire completed by 114 teachers, the second was examination of current accredited courses in teacher preparation for mathematics teaching to identify what learning theories were included in subjects, and the third were interviews with 8 teachers in training and 6 experienced teachers. …

Problems With And Without … Problems!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is addressed to College honor students, researchers, and professors. It contains 136 original problems published by the author in various scientific journals around the world. The problems could be used to preparing for courses, exams, and Olympiads in mathematics. Many of these have a generalized form. For each problem we provide a detailed solution.

I was a professeur coopérant between 1982-1984, teaching mathematics in French language at Lycée Sidi EL Hassan Lyoussi in Sefrou, Province de Fès, Morocco. I used many of these problems for selecting and training, together with other Moroccan professors, in Rabat city, of the …

Mathematics In The Age Of Technology: There Is A Place For Technology In The Mathematics Classroom, Helen Crompton

Teaching & Learning Faculty Publications

In today’s world of ubiquitous computing there are a number of technologies available to K-12 educators for teaching and learning mathematics. However, Koehler and Mishra (2008) have described how teaching and learning with such technologies presents a “wicked problem,” as it can involve a number of variables, independent of each other and contextually bound, that need to be brought together. This article highlights the advantages technology offers for mathematics education and looks at some of the reasons behind the poor uptake, such as teacher beliefs and lack of training. A number of solutions are offered to address these issues, including …