The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…

Although the mathematics community has long accepted the concept of limit as the foundation of modern Calculus, the concept of limit itself has been marginalized in undergraduate Calculus education. In this paper, I analyze the strategy of conceptual conflict to teach the concept of limit with the aid of an online tool--Desmos graphing calculator.…

We calculate the number of subgroups in a direct product of finite cyclic groups by applying the fundamental theorem of finite abelian groups and a well-known structure theorem due to Goursat. We also suggest ways in which the results can be generalized to a direct product of arbitrary finite groups.

This article gives an elementary proof of the famous identity [image omitted]. Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity [image omitted].

This paper is a case study of the teaching of an undergraduate abstract algebra course, in particular the way the instructor presented proofs. It describes a framework for proof writing based on Selden and Selden (2009) and the work of Alcock (2010) on modes of thought that support proof writing. The paper offers a case study of the teaching of a…

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

Weber (2009) suggested that counterexamples can be generated by a syntactic proof production, apparently contradicting our earlier assertion (Alcock & Inglis, 2008). Here we point out that this ostensible difference is the result of Weber working with theoretical definitions that differ slightly from ours. We defend our approach by arguing that…

The effects of training Hispanic college students in test-taking skills were examined. A mathematics achievement test was found to have slightly lower internal consistency and higher predictive validity for the group given training than for the control group. (MNS)

The extent to which students' ratings of teacher performance in mathematics courses are reliable, valid, and unbiased was investigated. Data on 746 courses by 52 faculty members over a 4-year period were used in a multiple regression analysis. It was found that students gave higher evaluations to faculty members when the students had previously…

In validating tests for course placement in college, the criterion variable is usually defined in terms of the grade earned in a particular standard course. This study considers the issue of interpreting incomplete (I) and withdrawal (W) grades either as unsuccessful outcomes or as missing data. The effects of either type of interpretation on…