All the mathematics you missed : but need to know for graduate school
 Author/Creator
 Garrity, Thomas A., 1959
 Language
 English.
 Imprint
 Cambridge, UK ; New York, NY : Cambridge University Press, 2002.
 Physical description
 xxvii, 347 p. : ill ; 24 cm.
Access
Available online

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QA37.3 .G37 2002

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QA37.3 .G37 2002
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. [329]337) and index.
 Contents

 On the Structure of Mathematics
 Linear Algebra
 Real Analysis
 Differentiating VectorValued Functions
 Point Set Topology
 Classical Stokes' Theorems
 Differential Forms and Stokes' Theorem
 Curvature for Curves and Surfaces
 Geometry
 Complex Analysis
 Countability and the Axiom of Choice
 Algebra
 Lebesgue Integration
 Fourier Analysis
 Differential Equations
 Combinatorics and Probability Theory
 Algorithms
 Linear Algebra
 The Basic Vector Space R[superscript n]
 Vector Spaces and Linear Transformations
 Bases and Dimension
 The Determinant
 The Key Theorem of Linear Algebra
 Similar Matrices
 Eigenvalues and Eigenvectors
 Dual Vector Spaces
 [epsilon] and [delta] Real Analysis
 Limits
 Continuity
 Differentiation
 Integration
 The Fundamental Theorem of Calculus
 Pointwise Convergence of Functions
 Uniform Convergence
 The Weierstrass MTest
 Weierstrass' Example
 Calculus for VectorValued Functions
 VectorValued Functions
 Limits and Continuity
 Differentiation and Jacobians
 The Inverse Function Theorem
 Implicit Function Theorem
 Point Set Topology
 The Standard Topology on R[superscript n]
 Metric Spaces
 Bases for Topologies
 Zariski Topology of Commutative Rings
 Classical Stokes' Theorems
 Preliminaries about Vector Calculus
 Vector Fields
 Manifolds and Boundaries
 Path Integrals
 Surface Integrals
 The Gradient
 The Divergence
 The Curl
 Orientability.
 Publisher's Summary
 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, first published in 2002, will help students to 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 all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential geometry, real analysis, pointset topology, probability, complex analysis, abstract algebra, and more. An annotated bibliography then offers a guide to further reading and to 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 who need to quickly learn some serious mathematics.
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Publisher description
Table of contents
Subjects
Bibliographic information
 Publication date
 2002
 Responsibility
 Thomas A. Garrity.
 ISBN
 0521792851
 9780521792851
 0521797071
 9780521797078