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Since joining Bennett College in 2008, Dr. Oh has directed 17 undergraduate students’ research projects in applied mathematics. The National Science Foundation (NSF) awarded Dr. Oh grants from the Historically Black Colleges and Universities – Undergraduate Program (HBCU-UP). The grants allowed her to mentor eight mathematics majors/minors in summer research for four years (2009–2012). Based on the four years of successful undergraduate research (UGR) experiences, she, together with Dr. Jan Rychtar from the University of North Carolina at Greensboro (UNCG), received funding for two summers National Research Experience for Undergraduates (NREUP), an activity of Mathematical Association of America (MAA), funded by the NSF in 2013 and 2014. During the six years of funded UGR, Bennett students made 33 presentations at regional, state, and national conferences; two teams won the outstanding student presentation award and first place for presentation. Three papers were published; two of them by Dr. Oh and one of them with a UGR coauthor. Three projects resulted in manuscripts. As a result of the UGR experiences in 2015, Dr. Oh received three more grants: the MAA NREUP, the NSF’s Center for Undergraduate Research in Mathematics (CURM), and the NSF’s Preparation for Industrial Careers in Mathematical Sciences (PIC Math) program awarded grants. A grant was also submitted to HBC-UP-Targeted Infusion Projects: Computational Mathematics at Bennett College.

Overall, the six years of UGR at Bennett College attained the three goals of: (1) enhancing the quality of undergraduate STEM education and research for a deeper appreciation in those disciplines; (2) supporting increased graduation rates in STEM undergraduate education of females; and (3) broadening participation in the nation’s STEM workforce as well as enrollments in graduate schools.

In this chapter, the interplay between the development of the discipline, the development of the field of study, and the emergence of professional fields is examined using the example of mathematics. In connection with the formation of the modern research university, mathematics has emerged as an independent scientific discipline and as an independent field of study. In the process, mathematics attains a high degree of formalization and internal coherence. This is the basis for the penetration of mathematicians into more and more professional fields, even outside science. Real problems or real facts are reduced to aspects that are amenable to mathematical modeling by treating them as quantifiable parameters. As mathematics expands as a field of study, more and more professional sectors become applications of mathematical models. As a consequence, more mathematical fields of study are differentiating themselves, specializing in these application fields. This chapter analyzes this dynamic and its preconditions.

Flipped classroom approaches (FCA) are an educational innovation that could increase students' learning outcomes in, and their enjoyment of, mathematics or STEM education. To integrate FCA into education sustainably, professional teacher development (PTD) is a promising tool. The research aim is to explore which aspects should be considered when developing and implementing professional mathematics or STEM teacher development for flipped approaches.

A total of 20 expert interviews were conducted and analysed according to a synthesis of grounded theory approaches and qualitative interview study principles.

Evaluating the interview data indicates that the characteristics of different teacher types in PTD, learning activities in PTD and the DSE model derived in this study could be vital elements in professional mathematics or STEM teacher development for flipped approaches.

Evaluating the interview data indicates that the characteristics of different teacher types in PTD, learning activities in PTD and the DSE model derived in this study could be vital elements in professional mathematics or STEM teacher development for flipped approaches.

Attempts to throw some light on the sensible use of mathematics in economic theory. Argues that mathematics is a valuable and useful tool which economists should and must apply as long as its use is economically sensible. The dangers of going beyond the “frontier” of what is economically sensible occur when economists depart from the actual (empirical) subject matter because of the applied mathematical instruments, when the underlying value judgements are not, or only insufficiently, taken into consideration, when the recording and measurement of empirical magnitudes as an economic problem is underestimated or is even subordinate under the requirements of the formal language, and when the process of mathematization is considered as a substitute for the process of Verstehen. Concludes that although mathematical reasoning is one way of logical deduction, which secures a style of logical consistency in reasoning, it is a fallacy to believe that mathematical reasoning alone can secure logical, consistent reasoning. Mathematization for the sake of mathematization is useless.

The years of 1977–78 have seen more fuzzy sets and ill‐posed problems come along in mathematics in addition to sturdy statistics and robust estimations. Fortunately there has also appeared a modest number of titles to help the reference librarian sort out mathematics, pure and applied. And although a computerized data base with online access is still awaited, its blur on the horizon is becoming more distinct. For now it remains necessary for the librarian to keep informed and assist other information seekers primarily by means of the printed word.

This paper aims to provide a well-behaved nonlinear scheme and accelerating iteration for the nonlinear convection diffusion equation with fundamental properties illustrated.

A nonlinear finite difference scheme is studied with fully implicit (FI) discretization used to acquire accurate simulation. A Picard–Newton (PN) iteration with a quadratic convergent ratio is designed to realize fast solution. Theoretical analysis is performed using the discrete function analysis technique. By adopting a novel induction hypothesis reasoning technique, the L^∞ (H¹) convergence of the scheme is proved despite the difficulty because of the combination of conservative diffusion and convection operator. Other properties are established consequently. Furthermore, the algorithm is extended from first-order temporal accuracy to second-order temporal accuracy.

Theoretical analysis shows that each of the two FI schemes is stable, its solution exists uniquely and has second-order spatial and first/second-order temporal accuracy. The corresponding PN iteration has the same order of accuracy and quadratic convergent speed. Numerical tests verify the conclusions and demonstrate the high accuracy and efficiency of the algorithms. Remarkable acceleration is gained.

The numerical method provides theoretical and technical support to accelerate resolving convection diffusion, non-equilibrium radiation diffusion and radiation transport problems.

The FI schemes and iterations for the convection diffusion problem are proposed with their properties rigorously analyzed. The induction hypothesis reasoning method here differs with those for linearization schemes and is applicable to other nonlinear problems.

The Bryant University Mathematics Department has been collecting math placement scores and admissions data for all incoming freshmen for many years. In the past, the authors have used these data mainly for placement in first-year classes and more recently to invite the most mathematically talented students to become mathematics majors. The purpose of this paper is to use the same data source to predict persistence in declared majors for all incoming students.

In order to categorize the students, the authors use cluster analysis, one of the tools of data mining, to see if students in particular majors share similar strengths based on the available data. The authors follow up this analysis by running a multivariate analysis of variance (MANOVA) to confirm that the means of the clusters are significantly different.

The cluster analysis resulted in five distinct clusters, which were confirmed by the results of the MANOVA. The authors also found how many students in each cluster persisted in their chosen major.

These results will help to improve counseling and proper placement of incoming freshmen. They will also be helpful in long-range planning of upper-level courses. Retention of students in their majors is an important concern for colleges and universities as it relates to planning issues, such as scheduling classes, particularly for upper classmen. This could also affect departmental requirements, such as the size of the faculty.

The Minister of Civil Aviation, Lord Pakenham, has appointed Mr J. Roland Adams, K.C., to hold a Public Court of Inquiry into the accident which occurred at Mill Hill, London, N.W.7, on Tuesday, October 17, 1950, to the British European Airways Dakota aircraft G‐AG1W.

This paper investigates the dependence structure and market risk of the currency exchange rate portfolio from the Malaysian ringgit perspective.

The marginal return of the five major exchange rates series, i.e. United States dollar (USD), Japanese yen (JPY), Singapore dollar (SGD), Thai baht (THB) and Chinese Yuan Renminbi (CNY) are modelled by the Bayesian generalized autoregressive conditional heteroskedasticity (GARCH) (1,1) model with Student's t innovations. In addition, five different copulas, such as Gumbel, Clayton, Frank, Gaussian and Student's t, are applied for modelling the joint distribution for examining the dependence structure of the five currencies. Moreover, the portfolio risk is measured by Value at Risk (VaR) that considers the extreme events through the extreme value theory (EVT).

The finding shows that Gumbel and Student's t are the best-fitted Archimedean and elliptical copulas, for the five currencies. The dependence structure is asymmetric and heavy tailed.

The findings of this paper have important implications for diversification decision and hedging problems for investors who involving in foreign currencies. The authors found that the portfolio is diversified with the consideration of extreme events. Therefore, investors who are holding an individual currency with VaR higher than the portfolio may consider adding other currencies used in this paper for hedging.

This is the first paper estimating VaR of a currency exchange rate portfolio using a combination of Bayesian GARCH model, EVT and copula theory. Moreover, the VaR of the currency exchange rate portfolio can be used as a benchmark of the currency exchange market risk.