During late June and early July of 1987 a three week program (dubbed "microprogram") in Commutative Algebra was held at the Mathematical Sciences Research Institute at Berkeley. The intent of the microprogram was to survey recent major results and current trends in the theory of commutative rings, especially commutative Noetherian rings. There was enthusiastic international participation. The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from the speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field. The editors would like to express their appreciation to the director of MSRI, Professor Irving Kaplansky, who first suggested the possibility of such a conference and made the task of organization painless. We would also like to thank the IVISRI staff who were unfailingly efficient, pleasant, and helpful during the meeting, and the manager of MSRI, Arlene Baxter, for her help with this volume. Finally we would like to express our appreciation to David Mostardi who did much of the typing and put the electronic pieces together.

This volume contains the proceedings of a Symposium held in honor of Emmy Noether's lOOth birthday which was sponsored by the Association for Women in Mathematics, and held at Bryn Mawr College on March 17, 18 and 19, 1982. It was fitting that the Symposium be held at Bryn Mawr, where Noether held her last position. Indeed, the lectures were held in Goodhart Hall, where the famous Memorial Address was delivered by Hermann Weyl on April 29, 1935. The Association for Women in Mathematics is honored to have sponsored this event, which was judged by many of those attending to have been not only scien- tifically successful but a specially moving occasion. There were nine scientific lectures by Nathan Jacobson, Richard Swan, Judith Sally, David Mumford, Michele Vergne, Olga Taussky-Todd, Karen Uhlenbeck, Walter Feit, and Armand Borel. There was also a panel discussion on "Emmy Noether in Erlangen, Gottingen, and Bryn Mawr" in which Gottfried Noether, Olga Taussky-Todd, Grace Quinn, Ruth McKee, and Marguerite Lehr par- ticipated. The last four were at Bryn Mawr during Emmy Noether's time and presented their personal reminiscences of her. Gottfried Noether is a nephew of Emmy Noether and gave an account of her life and career in Germany.

This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K-8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes. Five seminars are dedicated to fractions and decimals because of their importance in the classroom curriculum. The standard topics are covered in detail, but are arranged in an order that is slightly different from the usual one. Multiplication is treated first, and with that in hand, common denominators and equivalent fractions are more readily understood and are available for use when discussing addition. The book is intended for the professional development of teachers. It is appropriate for teacher education programs as well as for enrichment programs such as Mathematical Circles for Teachers. There are numerous activities in each seminar that teachers can bring into their classrooms. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

This geometry book is written foremost for future and current middle school teachers, but is also designed for elementary and high school teachers. The book consists of ten seminars covering in a rigourous way the fundamental topics in school geometry, including all of the significant topics in high school geometry. The seminars are crafted to clarify and enhance understanding of the subject. Concepts in plane and solid geometry are carefully explained, and activities that teachers can use in their classrooms are emphasised. The book draws on the pictorial nature of geometry since that is what attracts students at every level to the subject. The book should give teachers a firm foundation on which to base their instruction in the elementary and middle grades. In addition, it should help teachers give their students a solid basis for the geometry that they will study in high school. The book is also intended to be a source for problems in geometry for enrichment programmes such as Math Circles and Young Scholars.