In this paper we present a short tutorial on creating mini-videos using two platforms--PCs and tablets such as iPads--and software packages that work with these devices. Specifically, we describe the step-by-step process of creating and editing videos using a Wacom Intuos pen-tablet plus Camtasia software on a PC platform and using the software…

California's AB 705 required community colleges to implement changes that would maximize students' likelihood of starting and completing transfer-level (or degree-appropriate) coursework in English and math/quantitative reasoning within one year. Under the law, colleges must use high school information (e.g., GPA, coursework, and/or grades in…

In this paper, we compare and contrast our experiences in using standards-based grading in different courses and across two separate institutions to explore the related tradeoffs and subtleties in designing and implementing such grading systems, guided by innovation diffusion theory. We summarize our individual courses, use Linda Nilson's criteria…

The "Unsolved Problems in Number Theory" book by Richard Guy provides nice problems suitable for a typical math major. We give examples of problems that have worked well in our senior seminar course and some nice results that senior math majors can obtain.

In this paper I discuss the motivation behind using an introduction to Fourier series as a method to unify the topics of integration techniques and series calculations in a Calculus II course.

Large foundational courses delivered in lecture halls are disadvantaged in eliciting participation from all students and maintaining engagement throughout the class session. We introduced a question-driven method facilitated by an audience response system, namely TopHat™, that allows the instructor to engage students in solving Calculus problems…

The mathematics behind Inge Lehmann's discovery that the inner core of the Earth is solid is explained using data collected around the Earth on seismic waves and their travel time through the Earth.

Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…

Given a function defined on a subset of the plane whose partial derivatives never change sign, the signs of the partial derivatives form a two-dimensional pattern. We explore what patterns are possible for various planar domains.

A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.

This article introduces the notion of the quartile-quartile line as an alternative to the regression line and the median-median line to produce a linear model based on a set of data. It is based on using the first and third quartiles of a set of (x, y) data. Dynamic spreadsheets are used as exploratory tools to compare the different approaches and…

This contribution focuses on a scheme developed to characterize the level of difficulty of an examination in the course "Linear Algebra for Engineers" and on the transfer of the underlying idea to a similar scheme for examinations in the course "Analysis I for Engineers". Using these schemes, it is possible to define standards…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

This work discusses the creation and use of infographics in an undergraduate mathematics course. Infographics are a visualization of information that combines data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from…

In April 2015 New Mexico faculty, Dana Center staff, and New Mexico Higher Education (NMHED) co-presented the need for better math pathways statewide. Faculty from 6 institutions (New Mexico State University, New Mexico Highlands University, Dine College, Eastern New Mexico University, El Paso Community College, and San Juan College) participated…