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Publisher:

Mathematical Association of America

Publication Date:

1997

Number of Pages:

146

Format:

Paperback

Series:

MAA Notes 46

Price:

29.95

ISBN:

978-0-88385-156-2

Category:

Anthology

[Reviewed by , on ]

Virginia Knight

02/11/1999

This book is certainly not for women only! It will be useful to anyone interested in creating an exciting and successful environment for undergraduate research. In this collection of articles there are descriptions of successful summer mathematics programs for undergraduates that have encouraged students, and in particular women, to pursue and complete graduate study in mathematics.

The book grew out of a 1994 conference in Berkeley, "Women in Mathematics: Scaling the Heights and Beyond." It is divided into three sections that can be read separately or in any order and each of which is worth the price of the book. The sections are:

**On Women and Mathematics****Course Designs****Model Programs**

Let's take them in reverse order. **Model Programs** gives overviews of seven successful summer programs for undergraduates. The Spelman-Bryn Mawr Mathematics Program, the Mills College Summer Mathematics Institute (SMI), the Summer Program for Women in Mathematics (SPWM) at George Washington University, and Carlton and St. Olaf College's Summer Mathematics Program are for women only. The University of Michigan REU (Research Experience for Undergraduates) Program in Mathematics, the Mount Holyoke Summer Research Institute, and the Director's Summer Program at the National Security Agency (NSA) are for both men and women.

Included in the descriptions is almost everything you would want to know about running a summer undergraduate research program. Most articles start with the program goals and end with the program's impact on its participants. They address all manner of questions such as: What was the target student audience? How were the participants chosen? Who were the faculty, assistants and other mentors? How was the program organized? What were the daily and weekly schedules for students? What were the values and problems of having a diverse mix of students? What social activities, field trips, guest lectures were included? What resources were needed? What were issues about funding? What was the impact on the faculty and graduate student assistants?

The core of the programs will be of much interest to the mathematicians who read the book: What mathematics was addressed and how was it presented? What were the most workable teaching and learning techniques used? How were students led into research? How flexible does a program need to be? What adjustments were implemented during the program?

The article on the Mount Holyoke Summer Research Institute also includes brief descriptions of projects in five areas: Effective Methods in Analytic Geometry, Singular Viscous Fingering, Local Zeta Functions, Critical Points of Real Polynomials, and Topics in Comparative Number Theory. It lists references to both published and unpublished papers resulting from these projects.

The results of these exemplary programs are quite impressive. For some programs we are given data on the number of students continuing to graduate studies, the number that have completed degrees, and the number employed in the mathematical sciences. Quotations from student evaluations are inspirational and let us all know that these programs do make a difference.

The only disappointment in this section is the brevity of the offering from the NSA. While it is understandable that there are security restrictions regarding the nature of the mathematics involved, the only information given is a few broad goals and how a student may apply to the NSA program. I am sure that the NSA has also had its successes, its failures, and its issues especially regarding women undergraduates in its program. It would seem that it would be possible to share some of these without breaching national security.

The **Course Designs** section of the book consists of seven detailed descriptions of field tested courses used in undergraduate research programs. Most include a description of the institute or the environment in which the course was used, the mathematical background needed by the students, an outline of the material presented and studied, lists of exercises, descriptions of interactions of students with the material and others, and references. Most of the course designs are in sufficient detail to be emulated by a faculty member in the field.

Here is a list of the courses that are described:

Probability and Stochastic Processes | Ani Adhikari and Deborah Nolan |

Hyperplane Arrangements | Helene Barcelo |

Algebra Seminar Taught by a Number Theorist | Antonia Bluher |

A Seminar on Linear Optimization | Lynne M. Butler |

What are Numbers? | Svetlana Katok |

Algebraic Coding Theory | Vera Pless |

Quadratic Reciprocity and Continued Fractions | Lynne Walling |

All courses in this section of the book have been offered at the Mills Summer Mathematics Institute. Some have also been used with coed groups.

There is value here for anyone conducting undergraduate research or designing a research program for undergraduates, whether or not the mathematics is on these topics and whether or not the participants are all women. There are wonderful examples of how to build student confidence by group work, how to design easier exercises leading up to open and/or challenging problems, and how students can benefit from writing and oral presentations. The authors are very honest about what worked and what didn't work. Reading this may not prevent all the pitfalls, but it may let the reader avoid some and know that others are to be expected.

To end at the beginning, in the section **On Women in Mathematics**, the first three articles, by Lenore Blum, Deborah Tepper Haimo, and Carol Wood, should be of interest to all faculty who teach undergraduate mathematics majors. Blum gives an 20 year perspective of the efforts to obtain equity for women in mathematics. She also explains the current need for programs for talented women, such as those described later in the book. Haimo makes the case that "changing the culture" in mathematics communities will promote excellence in mathematics "based on a broader and more representative population." Wood lists accomplishments of the AWM and gives an important proposal for the future that addresses the critical point where women enter graduate study.

This section concludes with results compiled from a quantitative survey of math majors at the University of California at Berkeley and applications for the Mills Summer Mathematics Institute. The students "express thoughts on their major, their academic performance and their future plans in mathematics. The gender differences are striking."

All three sections of this book are must reading for anyone interested in starting or improving undergraduate research programs as well as anyone committed to equity in the mathematics community for women and other underrepresented groups.

Virginia Knight is professor of mathematics and head of the Department of Mathematics and Computer Science at Meredith College.

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