All the Mathematics You Missed

Description

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.


Contents :

1: Linear Algebra
2: E and J Real Analysis
3: Point Set Topology
4 :Point Set Topology
5 :Classical Stokes' Theorems
6 : Differential Forms and Stokes' Thm.
7 :Curvature for Curves and Surfaces
8 :Geometry
9 :Complex Analysis
10 :Countability and the Axiom of Choice
11: Algebra
12 :Lebesgue Integration
13: Fourier Analysis
14 :Differential Equations
15 :Combinatorics and Probability
16: Algorithms




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