All the Mathematics You Missed: But Need to Know for Graduate School

Few beginning graduate students in mathematics and other quantitative subjects possess the daunting breadth of mathematical knowledge expected of them when they begin their studies. This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

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 in 2000-1, when he spent the year at the University of Michigan, Ann Arbor