All the mathematics you missed
Subtitle: but need to know for graduate school
By: Thomas A. Garrity.
Publisher: Cambridge University Press
Published: 2002
Place of publication: Cambridge
Language: eng
Number of pages: 347
Subjects: Mathematics
Notes: Bibliogr.

1 6
Table of contents: title: Preface
pagenum: xiii; title: On the Structure of Mathematics
pagenum: xix; title: Brief Summaries of Topics
pagenum: xxiii; label: 0.1
title: Linear Algebra
pagenum: xxiii; label: 0.2
title: Real Analysis
pagenum: xxiii; label: 0.3
title: Differentiating Vector-Valued Functions
pagenum: xxiii; label: 0.4
title: Point Set Topology
pagenum: xxiv; label: 0.5
title: Classical Stokes' Theorems
pagenum: xxiv; label: 0.6
title: Differential Forms and Stokes' Theorem
pagenum: xxiv; label: 0.7
title: Curvature for Curves and Surfaces
pagenum: xxiv; label: 0.8
title: Geometry
pagenum: xxv; label: 0.9
title: Complex Analysis
pagenum: xxv; label: 0.10
title: Countability and the Axiom of Choice
pagenum: xxvi; label: 0.11
title: Algebra
pagenum: xxvi; label: 0.12
title: Lebesgue Integration
pagenum: xxvi; label: 0.13
title: Fourier Analysis
pagenum: xxvi; label: 0.14
title: Differential Equations
pagenum: xxvii; label: 0.15
title: Combinatorics and Probability Theory
pagenum: xxvii; label: 0.16
title: Algorithms
pagenum: xxvii; label: 1
title: Linear Algebra
pagenum: 1; label: 1.1
title: Introduction
pagenum: 1; label: 1.2
title: The Basic Vector Space \(\mathbf{R}^n\)
pagenum: 2; label: 1.3
title: Vector Spaces and Linear Transformations
pagenum: 4; label: 1.4
title: Bases and Dimension
pagenum: 6; label: 1.5
title: The Determinant
pagenum: 9; label: 1.6
title: The Key Theorem of Linear Algebra
pagenum: 12; label: 1.7
title: Similar Matrices
pagenum: 14; label: 1.8
title: Eigenvalues and Eigenvectors
pagenum: 15; label: 1.9
title: Dual Vector Spaces
pagenum: 20; label: 1.10
title: Books
pagenum: 21; label: 1.11
title: Exercises
pagenum: 21; label: 2
title: \(\epsilon\) and \(\delta\) Real Analysis
pagenum: 23; label: 2.1
title: Limits
pagenum: 23; label: 2.2
title: Continuity
pagenum: 25; label: 2.3
title: Differentiation
pagenum: 26; label: 2.4
title: Integration
pagenum: 28; label: 2.5
title: The Fundamental Theorem of Calculus
pagenum: 31; label: 2.6
title: Pointwise Convergence of Functions
pagenum: 35; label: 2.7
title: Uniform Convergence
pagenum: 36; label: 2.8
title: The Weierstrass M-Test
pagenum: 38; label: 2.9
title: Weierstrass' Example
pagenum: 40; label: 2.10
title: Books
pagenum: 43; label: 2.11
title: Exercises
pagenum: 44; label: 3
title: Calculus for Vector-Valued Functions
pagenum: 47; label: 3.1
title: Vector-Valued Functions
pagenum: 47; label: 3.2
title: Limits and Continuity
pagenum: 49; label: 3.3
title: Differentiation and Jacobians
pagenum: 50; label: 3.4
title: The Inverse Function Theorem
pagenum: 53; label: 3.5
title: Implicit Function Theorem
pagenum: 56; label: 3.6
title: Books
pagenum: 60; label: 3.7
title: Exercises
pagenum: 60; label: 4
title: Point Set Topology
pagenum: 63; label: 4.1
title: Basic Definitions
pagenum: 63; label: 4.2
title: The Standard Topology on \(\mathbf{R}^n\)
pagenum: 66; label: 4.3
title: Metric Spaces
pagenum: 72; label: 4.4
title: Bases for Topologies
pagenum: 73; label: 4.5
title: Zariski Topology of Commutative Rings
pagenum: 75; label: 4.6
title: Books
pagenum: 77; label: 4.7
title: Exercises
pagenum: 78; label: 5
title: Classical Stokes' Theorems
pagenum: 81; label: 5.1
title: Preliminaries about Vector Calculus
pagenum: 82; label: 5.1.1
title: Vector Fields
pagenum: 82; label: 5.1.2
title: Manifolds and Boundaries
pagenum: 84; label: 5.1.3
title: Path Integrals
pagenum: 87; label: 5.1.4
title: Surface Integrals
pagenum: 91; label: 5.1.5
title: The Gradient
pagenum: 93; label: 5.1.6
title: The Divergence
pagenum: 93; label: 5.1.7
title: The Curl
pagenum: 94; label: 5.1.8
title: Orientability
pagenum: 94; label: 5.2
title: The Divergence Theorem and Stokes' Theorem
pagenum: 95; label: 5.3
title: Physical Interpretation of Divergence Theorem
pagenum: 97; label: 5.4
title: A Physical Interpretation of Stokes' Theorem
pagenum: 98; label: 5.5
title: Proof of the Divergence Theorem
pagenum: 99; label: 5.6
title: Sketch of a Proof for Stokes' Theorem
pagenum: 104; label: 5.7
title: Books
pagenum: 108; label: 5.8
title: Exercises
pagenum: 108; label: 6
title: Differential Forms and Stokes' Theorem
pagenum: 111; label: 6.1
title: Volumes of Parallelepipeds
pagenum: 112; label: 6.2
title: Differential Forms and the Exterior Derivative
pagenum: 115; label: 6.2.1
title: Elementary k-forms
pagenum: 115; label: 6.2.2
title: The Vector Space of k-forms
pagenum: 118; label: 6.2.3
title: Rules for Manipulating k-forms
pagenum: 119; label: 6.2.4
title: Differential k-forms and the Exterior Derivative
pagenum: 122; label: 6.3
title: Differential Forms and Vector Fields
pagenum: 124; label: 6.4
title: Manifolds
pagenum: 126; label: 6.5
title: Tangent Spaces and Orientations
pagenum: 132; label: 6.5.1
title: Tangent Spaces for Implicit and Parametric Manifolds
pagenum: 132; label: 6.5.2
title: Tangent Spaces for Abstract Manifolds
pagenum: 133; label: 6.5.3
title: Orientation of a Vector Space
pagenum: 135; label: 6.5.4
title: Orientation of a Manifold and its Boundary
pagenum: 136; label: 6.6
title: Integration on Manifolds
pagenum: 137; label: 6.7
title: Stokes' Theorem
pagenum: 139; label: 6.8
title: Books
pagenum: 142; label: 6.9
title: Exercises
pagenum: 143; label: 7
title: Curvature for Curves and Surfaces
pagenum: 145; label: 7.1
title: Plane Curves
pagenum: 145; label: 7.2
title: Space Curves
pagenum: 148; label: 7.3
title: Surfaces
pagenum: 152; label: 7.4
title: The Gauss-Bonnet Theorem
pagenum: 157; label: 7.5
title: Books
pagenum: 158; label: 7.6
title: Exercises
pagenum: 158; label: 8
title: Geometry
pagenum: 161; label: 8.1
title: Euclidean Geometry
pagenum: 162; label: 8.2
title: Hyperbolic Geometry
pagenum: 163; label: 8.3
title: Elliptic Geometry
pagenum: 166; label: 8.4
title: Curvature
pagenum: 167; label: 8.5
title: Books
pagenum: 168; label: 8.6
title: Exercises
pagenum: 169; label: 9
title: Complex Analysis
pagenum: 171; label: 9.1
title: Analyticity as a Limit
pagenum: 172; label: 9.2
title: Cauchy-Riemann Equations
pagenum: 174; label: 9.3
title: Integral Representations of Functions
pagenum: 179; label: 9.4
title: Analytic Functions as Power Series
pagenum: 187; label: 9.5
title: Conformal Maps
pagenum: 191; label: 9.6
title: The Riemann Mapping Theorem
pagenum: 194; label: 9.7
title: Several Complex Variables: Hartogs' Theorem
pagenum: 196; label: 9.8
title: Books
pagenum: 197; label: 9.9
title: Exercises
pagenum: 198; label: 10
title: Countability and the Axiom of Choice
pagenum: 201; label: 10.1
title: Countability
pagenum: 201; label: 10.2
title: Naive Set Theory and Paradoxes
pagenum: 205; label: 10.3
title: The Axiom of Choice
pagenum: 207; label: 10.4
title: Non-measurable Sets
pagenum: 208; label: 10.5
title: Gödel and Independence Proofs
pagenum: 210; label: 10.6
title: Books
pagenum: 211; label: 10.7
title: Exercises
pagenum: 211; label: 11
title: Algebra
pagenum: 213; label: 11.1
title: Groups
pagenum: 213; label: 11.2
title: Representation Theory
pagenum: 219; label: 11.3
title: Rings
pagenum: 221; label: 11.4
title: Fields and Galois Theory
pagenum: 223; label: 11.5
title: Books
pagenum: 228; label: 11.6
title: Exercises
pagenum: 229; label: 12
title: Lebesgue Integration
pagenum: 231; label: 12.1
title: Lebesgue Measure
pagenum: 231; label: 12.2
title: The Cantor Set
pagenum: 234; label: 12.3
title: Lebesgue Integration
pagenum: 236; label: 12.4
title: Convergence Theorems
pagenum: 239; label: 12.5
title: Books
pagenum: 241; label: 12.6
title: Exercises
pagenum: 241; label: 13
title: Fourier Analysis
pagenum: 243; label: 13.1
title: Waves, Periodic Functions and Trigonometry
pagenum: 243; label: 13.2
title: Fourier Series
pagenum: 244; label: 13.3
title: Convergence Issues
pagenum: 250; label: 13.4
title: Fourier Integrals and Transforms
pagenum: 252; label: 13.5
title: Solving Differential Equations
pagenum: 256; label: 13.6
title: Books
pagenum: 258; label: 13.7
title: Exercises
pagenum: 258; label: 14
title: Differential Equations
pagenum: 261; label: 14.1
title: Basics
pagenum: 261; label: 14.2
title: Ordinary Differential Equations
pagenum: 262; label: 14.3
title: The Laplacian
pagenum: 266; label: 14.3.1
title: Mean Value Principle
pagenum: 266; label: 14.3.2
title: Separation of Variables
pagenum: 267; label: 14.3.3
title: Applications to Complex Analysis
pagenum: 270; label: 14.4
title: The Heat Equation
pagenum: 270; label: 14.5
title: The Wave Equation
pagenum: 273; label: 14.5.1
title: Derivation
pagenum: 273; label: 14.5.2
title: Change of Variables
pagenum: 277; label: 14.6
title: Integrability Conditions
pagenum: 279; label: 14.7
title: Lewy's Example
pagenum: 281; label: 14.8
title: Books
pagenum: 282; label: 14.9
title: Exercises
pagenum: 282; label: 15
title: Combinatorics and Probability
pagenum: 285; label: 15.1
title: Counting
pagenum: 285; label: 15.2
title: Basic Probability Theory
pagenum: 287; label: 15.3
title: Independence
pagenum: 290; label: 15.4
title: Expected Values and Variance
pagenum: 291; label: 15.5
title: Central Limit Theorem
pagenum: 294; label: 15.6
title: Stirling's Approximation for \(n!\)
pagenum: 300; label: 15.7
title: Books
pagenum: 305; label: 15.8
title: Exercises
pagenum: 305; label: 16
title: Algorithms
pagenum: 307; label: 16.1
title: Algorithms and Complexity
pagenum: 308; label: 16.2
title: Graphs: Euler and Hamiltonian Circuits
pagenum: 308; label: 16.3
title: Sorting and Trees
pagenum: 313; label: 16.4
title: P=NP?
pagenum: 316; label: 16.5
title: Numerical Analysis: Newton's Method
pagenum: 317; label: 16.6
title: Books
pagenum: 324; label: 16.7
title: Exercises
pagenum: 324; label: A
title: Equivalence Relations
pagenum: 327