Janet Beery

Formulating figurate numbers

The multiplication formula for figurate numbers (or binomial coefficients) we use today appeared in western Europe in verbal form in the late 1500s and in symbolic form in the early 1600s. In this paper, we first recount the early history of figurate numbers and especially of multiplicative means for computing them. We then focus on the development of multiplication formulas for figurate numbers in the late sixteenth and early seventeenth centuries by Cardano, Faulhaber, Briggs, and Harriot. Throughout the paper, we invite the reader to consider what it means to ‘have a formula for’ a mathematical relationship. Indeed, the story of figurate number formulas is interesting not only in its own right but because it provides rich fodder for a broader discussion of mathematical formulas. A preliminary version of this paper was presented during the July 2008 quadrennial meeting of the International Study Group on Relations Between History and Pedagogy of Mathematics, and appeared in the proceedings of that conference.

STARTING SMALL: GRADUAL INTRODUCTION OF COMPUTERS INTO CALCULUS COURSES*

ABSTRACT Using an incremental approach to introduce computers into calculus courses over several years, utilizing inexpensive, easy-to-use software, offers a low-cost alternative to more costly computer algebra systems and their support hardware. The use of small, easily modified programs also provides flexibility in designing classroom demonstrations or homework exercises. * Based on a presentation given at the Conference on the Teaching of Calculus held at Harvard University on 12–13 June 1992.

CALCULUS WITH EXPLORATORY LABORATORIES

ABSTRACT Laboratory sessions emphasizing exploration and application of calculus concepts are a regular and integral part of the authors calculus courses. Many laboratory sessions are computer-based, and all require a written report from each laboratory team. Benefits include increased student motivation and understanding, and a more lively calculus classroom. * Based on a presentation given at the Conference on the Teaching of Calculus held at Harvard University on 12–13 June 1992.

Women in Mathematics

March 2019 Notices of the aMericaN MatheMatical society 395 lection are written for a broad mathematical audience that includes students. This volume grew out of a contributed paper session at MAA MathFest 2015 that was sponsored by the Association for Women in Mathematics (AWM). In connection with the celebration of the one hundredth anniversary of the Mathematical Association of America, the session sought to “recognize the contributions, achievements, and progress of women mathematicians over the past 100 years” through “talks about mathematics done by women and historical or biographical presentations celebrating women in mathematics.” As the editors note in their preface, the resulting collection of articles is a mix of current scholarship and exposition on a wide variety of topics related to women in mathematics as opposed to a balanced study of the participation of women in mathematics during this time. Some of the articles summarize or extend work that has appeared previously, including Judy Green and Jeanne LaDuke’s detailed documentary history of all of the American women who earned PhDs in mathematics from American and European universities between 1886 and 1939 and Margaret Murray’s research on American women who earned PhDs in mathematics between the years 1940 and 1959. As a result, the volume also serves as a survey of a portion of the existing literature and compellingly invites the reader to delve deeper into that work. The first two parts of the book are dedicated to telling the stories of women mathematicians in articles that range in style from formal historical and cultural studies to personal reflections and collections of interviews. These articles include more than eighty biographical profiles of women mathematicians and statisticians as well as numerous more concise descriptions of the experiences and contributions of women in these fields. The profiles are a mix of short sketches grouped within larger discussions of the mathematical and social context of a particular time, place, or culture and more in-depth studies of the professional and personal lives of individual women. Most of the profiles Women in Mathematics: Celebrating the Centennial of the Mathematical Association of America Janet L. Beery, Sarah J. Greenwald, Jacqueline A. Jensen-Vallin, and Maura B. Mast, editors Springer International Publishing, 2017 ISBN: 978-3319666938

Pollution Police: How to Determine Spectroscopic Selection Rules.

Pollution Police is a laboratory or classroom project intended to show students how quantum mechanical selection rules can be developed. Students see how elementary linear algebra and group theory are used to describe molecular symmetry, how chemical character tables are constructed, and how spectroscopic selection rules are determined from the symmetry. In addition to the connection between symmetry and spectroscopy, students also learn about point groups, symmetry elements, symmetry operations, and degenerate vibrations, all in the context of identifying atmospheric pollutants from their infrared spectra.