In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current…

This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…

Mathematical induction is one of the major proof techniques taught to mathematics students in the first years of their undergraduate degrees. In addition to its importance to mathematics, induction is also required for computer science and related disciplines. However, even if the concepts of a proof by induction are taught and understood, many…

A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…

An issue for many mathematics departments is the success rate of precalculus students. In an effort to increase the success rate, this quantitative study investigated how class size and teaching approach influenced student achievement and students' attitudes towards learning mathematics. Students' achievement and their attitudes toward learning…

In this article we consider an example suitable for investigation in many mid and upper level undergraduate mathematics courses. Fourier series provide an excellent example of the differences between uniform and non-uniform convergence. We use Dirichlet's test to investigate the convergence of the Fourier series for a simple periodic saw tooth…

In this article we describe a project that we used in our undergraduate linear algebra courses to help our students successfully master fundamental concepts and definitions and generate interest in the course. We describe our philosophy and discuss the projects overall success.

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

This article details the application of an economic theory to the fiscal operation of a small engineering consulting firm. Nobel Prize-winning economist Wassily Leontief developed his general input-output economic theory in the mid-twentieth century to describe the flow of goods and services in the U.S. economy. We use one mathematical model that…

The decreasing number of U.S. citizens with advanced degrees in the mathematical sciences is a growing concern. Also of concern is the small number of advanced degrees in the sciences going to African Americans, Latinos, and women. Several Research Experience for Undergraduates (REU) programs have been developed to address these issues. In this…

For over a decade it has been a common observation that a "fog" passes over the course in linear algebra once abstract vector spaces are presented. See [2, 3]. We show how this fog may be cleared by having the students translate "abstract" vector-space problems to isomorphic "concrete" settings, solve the "concrete" problem either by hand or with…

External performance assessments for teachers of mathematics have traditionally been accomplished through reviews of student comments as well as through formal evaluations by superiors. Additionally, evaluating lecture-based teaching (as opposed to more active learning environments) focuses primarily on classroom performance, curriculum planning,…

This paper describes a modification of a popular TV game show, "American Idol[R]," conducted in an undergraduate calculus course. The focal point of this game show is to get students to interact in competitive self-assessment. Student competition is an effective device to engage students in the learning process. Placing students in the role of…

This article offers our ideas on why it is important to teach our students how to speak about mathematics and some practical resources for incorporating speaking activities, helping students prepare, evaluating student presentations, and getting your department to talk about student presentations. The ideas in this article were compiled when the…

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)