Foreword: MASS and
REU at Penn State
This book is part of a collection published jointly by the Amer-
ican Mathematical Society and the MASS (Mathematics Advanced
Study Semesters) program as a part of the Student Mathematical
Library series. The books in the collection are based on lecture
notes for advanced undergraduate topics courses taught at the MASS
and/or Penn State summer REU (Research Experiences for Under-
graduates). Each book presents a self-contained exposition of a non-
standard mathematical topic, often related to current research areas,
accessible to undergraduate students familiar with an equivalent of
two years of standard college mathematics and suitable as a text for
an upper division undergraduate course.
Started in 1996, MASS is a semester-long program for advanced
undergraduate students from across the USA. The program’s curricu-
lum amounts to sixteen credit hours. It includes three core courses
from the general areas of algebra/number theory, geometry/topology
and analysis/dynamical systems, custom designed every year; an in-
terdisciplinary seminar; and a special colloquium. In addition, ev-
ery participant completes three research projects, one for each core
course. The participants are fully immersed into mathematics, and
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