Beginning graduate students in mathematics and other quantitative
subjects are expected to have a daunting breadth of mathematical
knowledge, but few have such a background. This book will help
students see the broad outline of mathematics and to fill in the gaps in
their knowledge.
The author explains the basic points and a few key results of the most
important undergraduate topics in mathematics, emphasizing the
intuitions behind the subject. The topics include linear algebra, vector
calculus, differential geometry, real analysis, point-set topology,
differential equations, probability theory, complex analysis, abstract
algebra, and more. An annotated bibliography offers a guide to further
reading and more rigorous foundations.
This book will be an essential resource for advanced undergraduate
and beginning graduate students in mathematics, the physical sciences,
engineering, computer science, statistics, and economics, and for anyone
else who needs to quickly learn some serious mathematics.
Thomas A. Garrity is Professor of Mathematics at Williams College in
Williamstown, Massachusetts. He was an undergraduate at the
University of Texas, Austin, and a graduate student at Brown University,
receiving his Ph.D. in 1986. From 1986 to 1989, he was G.c. Evans
Instructor at Rice University. In 1989, he moved to Williams College,
where he has been ever since except in 1992-3, when he spent the year at
the University of Washington, and 2000-1, when he spent the year at the
University of Michigan, Ann Arbor.
