The Case of the Missing Speedometer: The First Day of Calculus

This article describes the way I\u27ve been teaching the first day of Calc I, my single-variable Calculus class. By the end of the hour students have (A) dictated difference quotients for me to write on the board, (B) dictated one example of the limit of difference-quotients definition of derivative of a function at a point, and (C) calculated a few derivatives. The more rigorous definitions of function, of operations on functions, and of limits can wait until later. This approach has been very successful, and students have said they get it this time around

On Not Teaching Addition: A Homeschooling Parent Teaches and Researches Math

Interactions with the humans in one’s life can have bearings on the way one interacts with one’s work – and vice versa. In particular, the ways in which a math person who is also a parent interacts with their children can correlate with the ways that person interacts with students, colleagues, and with math itself. This article describes some of that correlation in one mathmom’s life. In particular, this mathmom worked toward balancing, both as a mom and as a teacher, her beliefs and feelings with societal mindsets and practices

Her x\u27s and y\u27s: Limericks about Women Mathematicians

This poetry folder is just what its title says, limericks about women mathematicians. A few of them I’ve known personally, most not. There are, of course, many many many other women mathematicians; even though I write limericks prolifically, I could never finish writing about them all

The Graduate Student Blues

This is a memoir about my rather unconventional path to a mathematics Ph.D. There were difficulties, due partly to university politics, partly to my youth and immaturity, and partly to the thesis material itself – it was, in the words of some of my fellow students, “not what’s being done now”. I had written the thesis entirely on my own, without help from my Master’s thesis advisor or any other professor at my school. This is not the usual procedure of course. Nobody in my department could understand the thesis or was willing to vouch for it. There followed three years of suffering, self-doubt, anger, vulnerability – and determination. The memoir also explores the connections among love for math, career in math, academia itself, and investment in other passions of life

The Night I Almost Didn\u27t Grow Up

This is a short memoir about the role that math played in a certain part of my young life

Permission to Add: Math-teaching Limericks

Throughout my years and decades of being a teacher, I have written limericks about every course I’ve taught, and sometimes courses I haven’t taught but reviewed textbooks in. Here I share several of these limericks

Poynting's theorem for planes waves at an interface: a scattering matrix approach

We apply the Poynting theorem to the scattering of monochromatic electromagnetic planes waves with normal incidence to the interface of two different media. We write this energy conservation theorem to introduce a natural definition of the scattering matrix S. For the dielectric-dielectric interface the balance equation lead us to the energy flux conservation which express one of the properties of S: it is a unitary matrix. For the dielectric-conductor interface the scattering matrix is no longer unitary due to the presence of losses at the conductor. However, the dissipative term appearing in the Poynting theorem can be interpreted as a single absorbing mode at the conductor such that a whole S, satisfying flux conservation and containing this absorbing mode, can be defined. This is a simplest version of a model introduced in the current literature to describe losses in more complex systems.Comment: 5 pages, 3 figures, submitted to Am. J. Phy