Mathematics Department Journal Articles

The Best Day of the Year to Invest in the Market

Robert Muksian — Thu, 25 Jan 2007 13:11:01 PST

In this study the author takes a look at specific dates of investments in the S&P 500 index to see which times are most opportune and also achievable by individual investors.

Internet Use Among Female and Male College Students

Patricia M. Odell et al. — Sun, 24 Sep 2006 17:59:49 PDT

A review of the recent literature concerning Internet usage among Americans reveals that the once stark gender gap is closing rapidly, but disparities remain in the purposes for which males and females use the Internet. Almost all of this research, however, is based on cross sections of American adults. Much less Internet research has focused on the college student population and, in particular, on female students; the few published studies show that female college students use the Internet less than males. However, even these recent studies may already be dated. This study, based on a large survey of college students from institutions of higher learning in Georgia, Hawaii, New Jersey, Massachusetts, and Rhode Island, considers these questions: (1) Has the gender gap in Internet use narrowed among college students to the same extent as it has in the general adult population? (2) Do female students differ from males in how they spend their time on the Internet? (3) Does family income, parental education or type of college influence female college students' use of the Internet? Results indicate that while the gender gap in use of the Internet has nearly closed, differences still remain in how male and female undergraduates use the Internet.

National Survey Results: Retention of Women in College Aviation

Mary Ann Turney et al. — Thu, 21 Sep 2006 17:02:43 PDT

Since the numbers of women pursuing technical careers in aviation continues to remain very low, a study on retention of women was undertaken by a team of university faculty from Embry Riddle Aeronautical University, Arizona State University, and Kent State University. The study was initiated to discover the factors that influence women once they have already selected an aviation career and to ascertain what could be done to support those women who have demonstrated a serious interest in an aviation career by enrolling in a collegiate aviation program.

This paper reports preliminary results of data collected in the first and second years of the study. The data was collected from surveys of 390 college students (195 women and 195 men) majoring in aviation programs in nine colleges and universities, representing widely varied geographic areas and including both two- and four-year institutions.

Results revealed significant areas of concern among women in pilot training. When queried about these concerns, differences were evident in the responses of the male and female groups. These differences were expected. However, a surprising finding was that women in early stages of pilot training responded differently from women in more experienced stages. These response differences did not occur among the men surveyed. The results, therefore, suggest that women in experienced stages of training may have gone through an adaptation process and reflect more male-like attitudes about a number of subjects, including social issues, confidence, family, and career.

Retaining Women in Collegiate Aviation by Implementing Learning Style Considerations

Merrill R. Karp et al. — Wed, 06 Sep 2006 19:12:02 PDT

Women are clearly underrepresented in aviation. Research must be accomplished to determine which factors influence women, once they have indicated a serious interest in an aviation career, to stay in collegiate aviation programs or to leave. Addressing the issue of women's retention in aviation is one way to help address the growing commercial pilot shortage, while moving toward gender equity in this critical, national industry. Projected shortages in the commercial pilot population, coupled with the low representation of women in career pilot positions, suggest that aviation education and training institutions should re-examine the structure and organization of the aviation knowledge transfer process. Classroom enhancements could improve education methods to make them more efficient from the perspectives of increased knowledge retention, improved application to broader subjects, and reduced loss to attrition of viable pilot candidates to enter the commercial pilot workforce. This study examines how aviation education can best serve the aviation student's learning style needs. The study looks at learning style theory, from the viewpoint of the wide diversity of aviation learners who are dominantly visual, auditory, or hands-on, tactile, or kinesthetic learners, and how women's learning styles are pivotal to their success and retention in collegiate aviation. By exploring how people learn best, and then providing those learners with the tools to maximize their dominant learning styles, the next generation of pilots, both women and men, should be better prepared to enter the aviation industry and help reduce the projected commercial pilot shortages.

A Collaborative Project to Increase the Participation of Women and Minorities in Higher Level Mathematics Courses

Kristin Kennedy et al. — Sat, 05 Aug 2006 10:02:03 PDT

In this article, the authors describe a program developed to encourage women and minorities to continue their study of mathematics in high schools until graduation. The 3-year program was a collaborative effort by professors and students from Bryant University, local businesses, and local high schools. During the 3 years, the program evolved from the development and presentation of reality-based mathematical modules taught in the high school classrooms to an interdisciplinary enrichment activity at Bryant University. The university students acted as mentors or tutors to the high school students. Throughout the program, the business representatives, university personnel, and high school teachers collaborated to bring mathematics alive to the students through real-world applications.

On the Trichotomy Character of

Esha Chatterjee et al. — Tue, 01 Aug 2006 18:14:06 PDT

We investigate the global stability, the periodic character, and the boundedness nature of the solutions of the difference equation...

Open Problems and Conjectures.

E. Camouzis et al. — Tue, 01 Aug 2006 17:25:50 PDT

This article presents information on some open problems and conjectures about some interesting types of difference equations. Solutions to questions are asked. One of the questions posed is when can the boundedness of all solutions of a rational equation be predicted from the characteristic roots of the linearized equation about its equilibrium? It is announced that an amount of $600 will be donated to the International Society of Difference Equations, if complete solutions of the open problems and conjectures presented in this article are provided.

Predicting Success for Actuarial Students in Undergraduate Mathematics Courses.

Richard Manning Smith et al. — Wed, 26 Jul 2006 14:15:10 PDT

A study of undergraduate actuarial graduates found that math SAT scores, verbal SAT scores, percentile rank in high school graduating class, and percentage score on a college mathematics placement exam had some relevance to forecasting the students' grade point averages in their major. For both males and females, percentile rank in high school class and math placement percentage were included in the best regression model. Verbal SAT score was significant for males and math SAT score was significant for females. For both males and females, a student's calculus average was found to be the single best predictor of a student's post-calculus grade point average. For males, high school percentile class rank is nearly as significant. The results are expected to improve the ability of teachers to advise prospective and beginning actuarial students as to their likelihood of success in this concentration.

The net cost of banning commercial foresting: a computable general equilibrium analysis for the Philippines.

Christian M. Dufournaud et al. — Wed, 26 Jul 2006 13:39:03 PDT

This paper examines logging policies in the Philippines through the use of an eleven-sector computable general equilibrium model. Several scenarios have been modeled based on a ban on commercial logging. The conclusion from the mathematical modeling is that a ban on commercial harvesting should be enforced in the Philippines.

The comparative efficacy of imputation methods for missing data in structural equation modeling.

Alan Olinsky et al. — Wed, 26 Jul 2006 13:17:30 PDT

Missing data is a problem that permeates much of the research being done today. Traditional techniques for replacing missing values may have serious limitations. Recent developments in computing allow more sophisticated techniques to be used. This paper compares the efficacy of five current, and promising, methods that can be used to deal with missing data. This efficacy will be judged by examining the percent of bias in estimating parameters. The focus of this paper is on structural equation modeling (SEM), a popular statistical technique, which subsumes many of the traditional statistical procedures. To make the comparison, this paper examines a full structural equation model that is generated by simulation in accord with previous research. The five techniques used for comparison are expectation maximization (EM), full information maximum likelihood (FIML), mean substitution (Mean), multiple imputation (MI), and regression imputation (Regression). All of these techniques, other than FIML, impute missing data and result in a complete dataset that can be used by researchers for other research. FIML, on the other hand, can still estimate the parameters of the model.

The study involves two levels of sample size (100 and 500) and seven levels of incomplete data (2%, 4%, 8%, 12%, 16%, 24%, and 32% missing completely at random). After extensive bootstrapping and simulation, the results indicate that FIML is a superior method in the estimation of most different types of parameters in a SEM format. Furthermore, MI is found to be superior in the estimation of standard errors. Multiple imputation (MI) also is an excellent estimator, with the exception of datasets with over 24% missing information. Considering the fact that FIML is a direct method and does not actually impute the missing data, whereas MI does, and can yield a complete set of data for the researcher to analyze, we conclude that MI, because of its theoretical and distributional underpinnings, is probably most promising for future applications in this field.

A genetic algorithm approach to nonlinear least squares estimation.

Alan Olinsky et al. — Wed, 26 Jul 2006 12:50:14 PDT

A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than global optimum. Genetic algorithms have been applied successfully to function optimization and therefore would be effective for nonlinear least squares estimation. This paper provides an illustration of a genetic algorithm applied to a simple nonlinear least squares example.

The Effect of Retirement Under Social Security at Age 62

Robert Muksian — Tue, 25 Jul 2006 15:54:28 PDT

The reduction in Social Security benefits due to early retirement at age 62 is greater than often realized. When calculating how much benefits will be reduced by retiring as early as age 62, observers often underestimate the reduction because they fail to account for the annual cost-of-living adjustments and make other incorrect assumptions relative to the reduction. The article explains how Social Security calculates a worker's "average indexed monthly wage" and how the primary insurance amount is in turn calculated from that, using "bend points." An accurate calculation of early retirement benefits is also key to spousal benefits, because a reduction of benefits for the primary worker may affect the amount of benefits the spouse receives both during the marriage and after the worker's death. A 62-year-old male has more than a 93% chance of living to normal retirement age, and a couple has more than a 99% chance that one of them will reach normal retirement age.

Calculating Break-Even Ages for Delaying Social Security Beyond Normal Retirement Age

Robert Muksian — Tue, 25 Jul 2006 15:44:47 PDT

Planners must frequently advise clients on the future economic effects of the timing of collecting Social Security benefits. The paper looks at three options for a worker who decides to continue working past normal retirement age, or has other adequate sources for retirement income, but takes the benefit at the normal retirement age: 1. always spend the after-tax amount, 2. always invest the after-tax amount, or 3. invest the after-tax benefits until age 70 and then make monthly withdrawals from the accumulated fund. Under the first option, most workers with normal life expectancy would be better off financially to delay taking the benefits. The second option of investing the money is investigated under different after-tax-return scenarios. Under the third option, building an accumulating fund until age 70, then to be depleted monthly, will produce a shortfall if the worker lives beyond the break-even age.

The Progress Report on Boundedness Character of Third Order Rational Equations.

Esha Chatterjee et al. — Sun, 23 Jul 2006 13:01:08 PDT

Presents a progress report on the boundedness character of third-order rational equations. Emphasis on the boundedness character of solutions of all special cases of equation; Determination of the region of parameters where every solution of the equation is bounded; Confirmation of the boundedness of 11 more special cases.

Measuring the Importance of Recent Airport Security Interventions

James C. Bishop et al. — Sun, 23 Jul 2006 11:18:25 PDT

Given the economic impact of airport delays, in particular the impact on business travelers and potential revenue from this source, it is imperative that authorities and regulators consider the outcomes and effectiveness of implementing security measures, such as armed pilots, secured cockpits, baggage matching, electronic scanning, passenger searches, and sniffer devices. Significant changes in security measures have been ongoing at major airports in the United States over the past year. Some of these changes represent knee-jerk reactions to 9/11. Other changes had long been planned for implementation as technology has advanced. This study queried flight crews and cabin crews to determine their perceptions about the relative importance of security measures. A survey was developed through a focus group of crew members whose work enabled them to observe and interact with security measures on a daily or regular basis. Results of the nearly 100 responses indicate some significant concerns about the importance of several security devices and measures.

Academic attributes of college freshmen that lead to success in actuarial studies in a business college

Richard Manning Smith et al. — Thu, 29 Jun 2006 07:18:14 PDT

The authors studied beginning undergraduate actuarial concentrators in a business college. They identified four variables (math Scholastic Aptitude Test [SAT] score, verbal SAT score, percentile rank in high school graduating class, and percentage score on a college mathematics placement exam) that were available for entering college students that distinguished freshman actuarial majors who completed the major from those who changed concentrations at some point before completing the major. In addition, the authors developed a logistic regression model using the same variables that predicted the probability of a student being a member of the actuarial graduates or the actuarial dropouts. This information is expected to improve the ability of teachers to advise prospective and beginning actuarial students as to their likelihood of completing this challenging concentration and, thereby, qualifying for an entry-level position in the actuarial field.