數(shù)學拾遺

內容概要

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.

書籍目錄

Preface On the Structure of Mathematicsbrief 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 Surfaces8 Geometry 9 Complex Analysis 10 countability and the Axiom of choice 11 Algebra 12 Lebesgue Integration 13 fourier Analysis14 differential Equations 15 Combinatorics and Probability 16 Algorithms A Equivalence Relations

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