中文名: 伯克利數學問題集
原名: Berkeley Problems in Mathematics
作者: (美)Paulo Ney de Souza Jorge-Nuno Silva
資源格式: DJVU
版本: 第三版
出版社: Springer
書號: 0387008926
發行時間: 2004年
地區: 美國
語言: 英文
簡介:

內容簡介:
1977年，為考查一年級的博士研究生是否已經成功掌握為攻讀數學博士學位所需的基本數學知識和技能，加州大學伯克利分校數學系設立了一項書面考試，作為獲得博士學位的首要要求之一。該項考試自其創設以來，已成為研究生獲得博士學位必須克服的一個主要障礙。本書的目的即為出版這些考試材料，以期對本科生准備該項考試有所幫助。
全書收錄最近25年的1250余道伯克利數學考試試題，對所有計劃攻讀數學博士學位的學生，本書中的試題和解答都頗具價值；讀者研讀完本書，在諸如實分析、多變量微積分、微分方程、度量空間、復分析、代數學及線性代數等學科的解題能力都將得到提高。
這些問題按學科及難易程度編排，每道試題均注明相應的考試年月，讀者可以依此方便地整理出各套試題。附錄介紹如何得到電子版試題，考試大綱以及各次考試的及格線。
新版已包含直至2003秋季學期的最近考試試題和解答，增添了以前版本未收錄的許多新的試題及題解。

目錄:
Preface
I Problems.
1 Real Analysis
1.1 Elementary Calculus
1.2 Limits and Continuity
1.3 Sequences, Series, and Products
1.4 Differential Calculus
1.5 Integral Calculus
1.6 Sequences of Functions
1.7 Fourier Series
1.8 Convex Functions
2 Multivariable Calculus
2.1 Limits and Continuity
2.2 Differential Calculus
2.3 Integral Calculus
3 Differential Equations
3.1 First Order Equations
3.2 Second Order Equations
3.3 Higher Order Equations
3.4 Systems of Differential Equations
4 Metric Spaces
4.1 Topology of Rn
4.2 General Theory
4.3 Fixed Point Theorem
5 Complex Analysis
5.1 Complex Numbers
5.2 Series and Sequences of Functions
5.3 Conformal Mappings
5.4 Functions on the Unit Disc
5.5 Growth Conditions
5.6 Analytic and Meromorphic Functions
5.7 Cauchy's Theorem
5.8 Zeros and Singularities
5.9 Harmonic Functions
5.10 Residue Theory
5.11 Integrals Along the Real Axis
6 Algebra
6.1 Examples of Groups and General Theory
6.2 Homomorphisms and Subgroups
6.3 Cyclic Groups
6.4 Normality, Quotients, and Homomorphisms
6.5 Sn, An, Dn, ...
6.6 Direct Products
6.7 Free Groups, Generators, and Relations
6.8 Finite Groups
6.9 Rings and Their Homomorphisms
6.10 Ideals
6.11 Polynomials
6.12 Fields and Their Extensions
6.13 Elementary Number Theory
7 Linear Algebra
7.1 Vector Spaces
7.2 Rank and Determinants
7.3 Systems of Equations
7.4 Linear Transformations
7.5 Eigenvalues and Eigenvectors
7.6 Canonical Forms
7.7 Similarity
7.8 Bilinear, Quadratic Forms, and Inner Product Spaces
7.9 General Theory of Matrices..
II Solutions
1 Real Analysis
1.1 Elementary Calculus
1.2 Limits and Continuity
1.3 Sequences, Series, and Products
1.4 Differential Calculus
1.5 Integral Calculus
1.6 Sequences of Functions
1.7 Fourier Series
1.8 Convex Functions
2 Multivariable Calculus
2.1 Limits and Continuity
2.2 Differential Calculus
2.3 Integral Calculus
3 Differential Equations
3.1 First Order Equations
3.2 Second Order Equations
3.3 Higher Order Equations
3.4 Systems of Differential Equations
4 Metric Spaces
4.1 Topology of Rn
4.2 General Theory
4.3 Fixed Point Theorem
5 Complex Analysis
5.1 Complex Numbers
5.2 Series and Sequences of Functions
5.3 Conformal Mappings
5.4 Functions on the Unit Disc
5.5 Growth Conditions
5.6 Analytic and Meromorphic Functions
5.7 Cauchy's Theorem
5.8 Zeros and Singularities
5.9 Harmonic Functions
5.10 Residue Theory
5.11 Integrals Along the Real Axis
6 Algebra
6.1 Examples of Groups and General Theory
6.2 Homomorphisms and Subgroups
6.3 Cyclic Groups
6.4 Normality, Quotients, and Homomorphisms
6.5 Sn, An, Dn, ...
6.6 Direct Products
6.7 Free Groups, Generators, and Relations
6.8 Finite Groups
6.9 Rings and Their Homomorphisms
6.10 Ideals
6.11 Polynomials
6.12 Fields and Their Extensions
6.13 Elementary Number Theory
7 Linear Algebra
7.1 Vector Spaces
7.2 Rank and Determinants
7.3 Systems of Equations
7.4 Linear Transformations
7.5 Eigenvalues and Eigenvectors
7.6 Canonical Forms
7.7 Similarity
7.8 Bilinear, Quadratic Forms, and Inner Product Spaces
7.9 General Theory of Matrices
III Appendices
A How to Get the Exams
A.1 On-line
A.2 Off-line, the Last Resort
B Passing Scores
C The Syllabus
References
Index