All the mathematics you missed : but need to know for graduate school = 数学拾遗 : 研究生必备数学...
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分类号：O13
ISBN：9787302090854
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简介
Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge ,but few have such a backgroud .This book will help stedents see the broad outline of mathematics and to fill in the gaps in their knowlegde.
The author explains the basic points and a few key results of the most important undergradute topics in mathematics ,emphasizing the intutions 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 biliography 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 mathemaics.
目录
Preface
On the Structure of Mathematics
brief Summaries of Topics
0.1 Linear Algebra
0.2 Real Analysis
0.3 Differentiating Vector-Valued Functions
0.4 Point Set Topology
0.5 Classical Tsokes' theorems
0.6 Diferential forms and Stokes' Theorem
0.7 Curvature for Curves and Surfaces
0.8 Geometry
0.9 comples Analysis
0.10 Countability and the Axiom of Choice
0.11 Algebra
0.12 Lebesgue Integration
0.13 Fourier Analylsis
0.14 Differential Equations
0.15 Combinatorics and Probability Theory
0.16 Algorithms
1 Linear Algebra
2 * and * Real Analysis
3 Calculus for Vector-Valued Functions
4 Point Set Topology
5 Classical Stokes' Theorems
6 diffenrential 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
A Equivalence Relations
On the Structure of Mathematics
brief Summaries of Topics
0.1 Linear Algebra
0.2 Real Analysis
0.3 Differentiating Vector-Valued Functions
0.4 Point Set Topology
0.5 Classical Tsokes' theorems
0.6 Diferential forms and Stokes' Theorem
0.7 Curvature for Curves and Surfaces
0.8 Geometry
0.9 comples Analysis
0.10 Countability and the Axiom of Choice
0.11 Algebra
0.12 Lebesgue Integration
0.13 Fourier Analylsis
0.14 Differential Equations
0.15 Combinatorics and Probability Theory
0.16 Algorithms
1 Linear Algebra
2 * and * Real Analysis
3 Calculus for Vector-Valued Functions
4 Point Set Topology
5 Classical Stokes' Theorems
6 diffenrential 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
A Equivalence Relations
All the mathematics you missed : but need to know for graduate school = 数学拾遗 : 研究生必备数学...
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