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,加州大學伯剋利分校數學係設立瞭一項書麵考試,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剋服的一個主要障礙。《國外數學名著係列(影印版)35:伯剋利數學問題集(第三版)》的目的即為齣版這些考試材料,以期對本科生準備該項考試有所幫助。
全書收錄最近25年的1250餘道伯剋利數學考試試題,對所有計劃攻讀數學博士學位的學生,《國外數學名著係列(影印版)35:伯剋利數學問題集(第三版)》中的試題和解答都頗具價值;讀者研讀完《國外數學名著係列(影印版)35:伯剋利數學問題集(第三版)》,在諸如實分析、多變量微積分、微分方程、度量空間、復分析、代數學及綫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齣各套試題。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綫。
新版已包含直至2003鞦季學期的最近考試試題和解答,增添瞭以前版本未收錄的許多新的試題及題解。
內頁插圖
目錄
Preface
Ⅰ Real Analysis
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
……
Ⅱ Solutions
1 Real Analysis
2 Multivariable Calculus
3 Differential Equations
4 Metric Spaces
5 Complex Analysis
6 Algebra
7 Linear Algebra
Ⅲ Appendices
A How to Get the Exams
B Passing Scores
C The Syllabus
References
Index
前言/序言
國外數學名著係列(影印版)35:伯剋利數學問題集(第三版) [Berkeley Problems in Mathematics(Third Edition)] epub pdf mobi txt 電子書 下載 2024
國外數學名著係列(影印版)35:伯剋利數學問題集(第三版) [Berkeley Problems in Mathematics(Third Edition)] 下載 epub mobi pdf txt 電子書
國外數學名著係列(影印版)35:伯剋利數學問題集(第三版) [Berkeley Problems in Mathematics(Third Edition)] mobi pdf epub txt 電子書 下載 2024
國外數學名著係列(影印版)35:伯剋利數學問題集(第三版) [Berkeley Problems in Mathematics(Third Edition)] epub pdf mobi txt 電子書 下載 2024